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Debug the knowledge base

We can test the knowledge base with small faults and see improper behavior.

• For example, Failure to assert 1 0 may lead to wrong answers for any input save for particular ones like 000 and 110. Debugging through observing each gate’s output helps pinpoint such faults.

To build a First-Order Logic (FOL) knowledge base, needs careful domain analysis, vocabulary choice, and axiom encoding to ensure that the logical results are correct.

Inference in First-Order Logic

Inference in First-Order Logic (FOL) involves deriving new facts or statements from existing ones. This process is crucial for reasoning, knowledge representation, and automating logical deductions. Before we delve into some inference rules, let’s first cover some fundamental concepts of FOL.

Substitution

Substitution is a fundamental operation in first-order logic that involves replacing a variable with a specific constant or phrase within an expression. This process is essential for effectively applying inference rules.

• When we write F[b/y], we are substituting the variable y with the constant b in the formula F.
• Using quantifiers for substitution needs to be done carefully to maintain logical consistency.
• First-Order Logic enables reasoning about specific objects and entire categories within a given domain.

Equality

In first-order logic (FOL), equality is an important aspect that allows us to express that two terms refer to the same object. The equality operator (=) is used to confirm that two expressions point to the same entity.

• The expression ¬(a = b) indicates that a and b are not identical objects.

For example, the statement Manager(Alex) = Sophia means that Sophia is the manager of Alex. Combining negation with equality helps to show that two concepts are distinct.

FOL Inference Rules for Quantifier

The inference rules for FOL are an extension of Propositional Logic by adding quantifiers and predicates. The rules below are the key ones:

Universal Generalization

Universal generalization is a valid inference rule that asserts if premise P(c) holds true for any arbitrary element c within the universe of discourse, we can conclude that x P(x) is also true.

If premise P(c) holds true for any arbitrary element c in the discourse universe we can arrive at the conclusion that x P(x).

It can be represented as − P(c), x P(x)

• Universal Generalization (UG )is valid only if c represents a general case applicable to all elements in the domain.

Example

Let us say the given statement is like this Loves(John, IceCream), Loves(Mary, IceCream), Loves(Sam, IceCream) the FOL representation using inference rule is as below −

• x Loves(x, IceCream) (if John, Mary, and Sam represent all entities).

Universal Instantiation

Universal Instantiation (UI) is an inference rule for First-Order Logic that derives a particular instance from a universally quantified statement. If it is true for all items of a domain, then it has to be the case for any specific element in the domain as well.

According to the UI rule, we can infer any sentence P(c) by replacing every object in the discourse universe with a ground term c (a constant within domain x) from x P(x).

It can be represented as − x P(x), P(c)

• According to the UI rule, any sentence P(c) is derivable, replacing a ground word c-for any object belonging to the universe of discourse-as a ground substitution for any x P(x).
• UI enables thinking of individual circumstances from universal facts.
• This is widely applied in theorem proving and automated reasoning.
• UI is the negation of Universal Generalization (UG).

Example

Let us say the given statement be “Everyone who teaches at a university has an advanced degree.” x(Teaches(x,University)→ HasAdvancedDegree(x)) [ x P(x)].

• By applying Universal Instantiation (UI) inference rule we can infer that for a specific professor, say Dr. Amrit − Teaches(Dr.Amrit,University)→ HasAdvancedDegree(Dr.Amrit).

Existential Instantiation

Existential Instantiation (EI) is a First-Order Logic inference rule that allows for the replacement of an existentially quantified variable with a new, arbitrary constant in order to represent an unknown but existing entity.

This rule indicates that from the formula x P(x), one can deduce P(c) by introducing a new constant symbol c.

It can be represented as − x P(x), P(c)

• EI is also known as Existential Elimination.
• It can only be used once to replace an existential sentence with a particular instance.
• The new knowledge base (KB) is not logically equal to the old KB; yet, if the old KB was satisfactory, the new one is still satisfactory.
• According to EI, we can infer P(c) from xP(x) by introducing a new constant c.
• The inserted constant c must be new and not previously used in the KB.

Example

Let us say the given statement is “Someone has published a research paper.” x (HasPublishedResearch(x)) [ x P(x) ].

• By applying the Existential Instantiation (EI) inference rule, we can infer that for a specific researcher, say Dr. Arjun − HasPublishedResearch(Dr.Arjun).

Existential Introduction

Existential Introduction (EI), often referred to as Existential Generalization (EG), is a valid inference rule in First-Order Logic. It allows us to introduce an existential quantifier when we can confirm that a proposition holds true for at least one instance.

It can be represented as − P(c), x P(x)

• It lets us move from a specific instance to a more general existential statement.
• If P(c) is true for a certain c, we can infer that there exists some x for which P(x) is true.
• The new existential statement is logically valid but different from the statement in question.

Example

Let us say the given statement is “Mr. Raj works at Tutorials Point.” WorksAt(Mr.Raj, TutorialsPoint) [ P(c) ].

• By applying the Existential Introduction (EI) inference rule, we can generalize that “There exists someone who works at Tutorials Point.” − x (WorksAt(x, TutorialsPoint)).

Generalized Modus Ponens (GMP) Rule

Generalized Modus Ponens is an extension of the traditional Modus Ponens rule of First-Order Logic. It allows multiple premises, variables, and substitutions. This facilitates logical reasoning by substituting variables in the premises and making replacements to reach conclusions.

Generalized Modus Ponens can be described as “P implies Q and P is asserted to be true, therefore Q must be true.

It can be represented as − P1→Q1,P2→Q2,,Pn→Qn,P1P2Pn, Q1Q2Qn

• Combines three steps of natural deduction (Universal Elimination, And Introduction, Modus Ponens) into one.
• Provides direction and simplification to the proof process for standard inferences.

Example

Let us say the given rule is “If a person works at Tutorials Point and has expertise in AI, then they are an AI Instructor.” x (WorksAt(x, TutorialsPoint) HasExpertise(x, AI) → AIInstructor(x))

• Given facts: WorksAt(Ravi, TutorialsPoint)
• HasExpertise(Ravi, AI): By applying the Generalized Modus Ponens (GMP) inference rule, we can conclude: AIInstructor(Ravi).

Propositional logic deals with declarative statements that are either true or false. However, it has a significant disadvantage it cannot state relationships between objects or convey general statements quickly.

For example, consider the following sentence. “The sky is hot” propositional logic only decides that a statement is true or false, but it cannot explain the relationship between the sun and heat. Similarly, if we want to declare that “All students in a class like mathematics,” propositional logic would require a different statement for each student, which is impractical for huge collections of things.

This is where First-Order Logic comes in. FOL expands propositional logic by including quantifiers and variables, allowing us to construct such assertions more efficiently.

First-Order Logic in Artificial intelligence

First-Order Logic, more popularly known as Predicate Logic, or First-Order Predicate Logic for short, is an extension of Propositional Logic. Unlike propositional logic which only tells that a statement is either true or false, First-Order Logic allows us to define relationship between objects, general rules, and quantified statements.

Key components of First-Order Logic

The fundamental components of First-Order Logic (FOL), which helps in the systematic representation of relationships, objects, and logical propositions, are as follows −

• Constants are different objects or constant values that exist inside given domain. For example − Krish, Bob, 5, Apple.
• Variables are symbols that can take several values inside a particular domain. Commonly used symbols for variables are x,y,z. If the domain consists of students, then x could represent any student in the class.
• Predicates are statements that describe properties of objects or their relationships. They accept at least one parameter, which may be a constant or a variable. For example − Father(John, Robert). Here father is predicate which tells the relation between John and Robert.
• Functions map elements to distinct values. They take arguments in the form of input elements and return a single value as output. For example − Age(Alice) = 25 → means “Alice’s age is 25.”
• Quantifiers tell whether a sentence is true for all objects in the domain or just one. For example − xLikes(x,Math) → “All students like Mathematics.” and xLikes(x,Math) → “There exists at least one student who likes Mathematics.”
• Logical connectives enable to logically combine numerous statements or propositions. They allow complicated statements to be constructed from simpler ones. For example − CompletesTraining(x)→EligibleForPromotion(x). If an employee x completes the required training, then they automatically become eligible for a promotion.

Logical Components in Formal Logic

The following table lists the constants, variables, functions, predicates, quantifiers, and logical connectives which are used to build formal logic −

Components	Examples
Constants	1, 5, Apple, Bob, India
Variables	x, y, z, a, b
Predicates	Father, Teacher, Brother
Functions	sqrt, LeftLegOf, AgeOf, add(x, y)
Quantifiers	∀ (for all), ∃ (there exists)
Connectives	∧ (and), ∨ (or), ¬ (not), → (implies), ↔ (if and only if)

Syntax and Semantics of First-Order Logic (FOL)

The syntax of FOL describes the form of valid assertions by employing constants, variables, predicates, functions, quantifiers, and logical connectives. Statements are composed of words (which represent objects) and atomic formulae (which convey facts).

The semantics of first-order logic (FOL) define the meaning of assertions by interpreting predicates and words throughout a domain. An interpretation gives real-world meaning to objects and relationships.

Example

The following example demonstrates how syntax and semantics are applied in First-Order Logic (FOL) to represent a real-world statement −

• Consider a statement “Every customer who makes a purchase receives an invoice”.
• The FOL representation of the statement using syntax and semantics is as follows x(Customer(x)Purchases(x,Product)→ReceivesInvoice(x))
• Thus, syntax defines the structure, and semantics give it meaning.

Quantifiers in First-Order Logic

Quantifiers in First-Order Logic define the number of objects in the domain that meet a specific condition. They allow us to communicate statements about all or some objects in a systematic manner.

Types of Quantifiers in FOL

First-Order Logic has two main types of quantifiers −

• Universal Quantifier ( ) “For All”
• Existential Quantifier ( ) “There Exists”

Universal Quantifier ( ): The universal quantifier (x) is used to state that a statement applies to all items in the domain. It is used to convey general truths or rules.

For example, let the statement be “All employees in a company must follow the rules.” By using FOL the representation would be x(Employee(x)→FollowsRules(x)) meaning “For every x, if x is an employee, then x follows the rules.”

Existential Quantifier ( ): The existential quantifier “x” indicates that at least one object in the domain meets the provided condition.It is used to indicate that something exists without listing all instances.

For example, let the statement be “There is at least one employee who received a promotion. The FOL representation would be “x(Employee(x)ReceivedPromotion(x)) meaning “There exists some x, such that x is an employee and x received a promotion.”

Sentences in First-Order Logic

In First-Order Logic (FOL), sentences are used to represent facts and relationships. These sentences can be classified into atomic sentences and complex sentences, as explained below −

Atomic Sentences

An atomic sentence is the most basic form of a statement in First-Order Logic. It consists of a predicate and arguments, which can be either constants or variables. An atomic statement asserts a fact about things without using logical connectives.

Structure of Atomic Sentences: Predicate(Argument 1,Argument 2,...,Argument n)

where −

• The predicate represents a property or relationship.
• The arguments represent objects (constants or variables).

Example

The following example demonstrate the use of atomic sentences in First-Order Logic to represent facts and relationships −

• Teacher(John, Mathematics) This atomic sentence states that John is a teacher of Mathematics.

Complex sentence

Two or more atomic statements connected by logical connectives like AND (), OR (), NOT (¬), Implies (→), and Bi-conditional () create a complex sentence. These sentences allow us to express more complex logical statements.

Example

The following examples demonstrate the use of complex sentences in First-Order Logic to represent facts and relationships −

• (y Teacher(y) Teaches(y, Math)) “There exists at least one teacher who teaches Mathematics.”
• (x Customer(x) → Buys(x, TutorialsPointCourses)) “For all customers, if x is a customer, then x buys courses from Tutorials Point.”
• (y Employee(y) WorksFor(y, TutorialsPoint)) “There exists at least one employee who works for Tutorials Point.”

Free and Bound Variables in First-Order Logic

Variables in FOL can be either free or bounded depending on the fact that a variable is controlled by any quantifier.

Free Variable

A free variable cannot be quantified using or . It can hold any value but has no fixed meaning unless assigned.

Example

Let us consider a statement “y is the price of a product.”

• The FOL representation for the above statement will be P(y) (where P(y) means y is the price of a product).
• Here, y is free because we don’t specify which products price we are referring to.

Bound Variable

A bound variable is within the scope of a quantifier and is dependent on it, so its value is limited by the quantifier.

Example

Let the sentence be “There exists a product whose price is less than $10.”

• The FOL representation of the above sentence is yP(y) (where P(y) means y is less than $10).
• Here, the existential quantifier () constrains the variable y, indicating that it is applicable to a specific product in the context.

Challenges and limitations of First Order Logic

When utilizing First-Order Logic (FOL) for knowledge representation and reasoning, several key challenges and limitations arise, as follows −

• Challenges in Handling Uncertainty: FOL requires facts to be definitively true or false, making it difficult to represent probabilistic or uncertain information.
• High Computational Demands: When dealing with extensive knowledge bases, logical inference in FOL can become slow and resource-intensive.
• Limited Expressive Power: Concepts from the real world that involve fuzzy or probabilistic logic, such as “most people” or “approximately,” are difficult for FOL to articulate.
• Rigid Rule-Based Framework: The necessity for facts and rules to be explicitly defined results in a structure that is inflexible and struggles to incorporate new information.
• Common-Sense thinking Difficulty: FOL finds it difficult to manage common sense thinking that incorporates assumptions, exceptions, or insufficient information.

Inference is the process of making logical inferences or drawing conclusions from given information, facts or assumptions. It is an essential aspect of thinking or allowing us to go from what we know to what we do not know by using logical principles or patterns.

In our daily lives, we use inference to make decisions or solve problems. For example, if we hear a car alarm sound from the parking lot, we infer that someone has probably broken into that person’s car or probably a false alarm went off. We don’t know what truly had happened, but based on the prior knowledge we have with car alarms we made an assumption.

What is Inference

Inference is the process in artificial intelligence through which intelligent systems derive new knowledge or make decisions based on the information that exists. It enables artificial intelligence agents to reason, solve problems, and learn. For instance, in a spam detection system, inference means analyzing an email and deciding, whether it is spam or not, according to the patterns of learning.

Key Concepts of Inference in AI

Inference in AI allows the machine to infer meaningful conclusions, predict and optimize decision-making by using the available data and applying logical rules. Following are few key components of inference system −

• Reasoning: AI agents uses inference to draw logical conclusions from facts and rules, allowing them to answer questions and solve problems.
• Learning: Inference is applied in machine learning where models learn patterns from data and then apply inference to predict new data.
• Decision-Making: AI systems use inference to compare multiple decisions and determine the best action based on their knowledge and goals.

Rules of Inference in AI

The rules of inference are the logical principles or guidelines that allows us to draw proper valid conclusions from given assumptions. They show how statements can be combined logically to produce new, logically consistent conclusions. Some common rules include Modus Ponens, Modus Tollens, Hypothetical Syllogism, and Disjunctive Syllogism. These rules make sure that the conclusions have validity based on premises.

Inference Rules and Terminologies

The concept of implication is central to the study of inference rules. An implication (P → Q) states that if the P is true then Q must be true. There are many derived forms related to the concept of implication.

• Converse: Flipping the variables of implication i.e, P → Q is Q → P. It changes the inference in such a way that if Q is a true statement then P must be true.
• Contrapositive: The negation of the converse is ¬Q → ¬P. This terminology tells that if Q is not true, then P cannot be true. The contrapositive is logically equivalent to implication if one is true, the other must also be true.
• Inverse: The negation of original implication is ¬P → ¬Q. It says that if P is false, then Q cannot be true. The inverse and converse are logically equivalent.

The following truth table represents the logical equivalency between these forms, particularly between the contrapositive and the implication as well as between the inverse and the converse.

P	Q	P → Q	Q → P	¬ Q → ¬ P	¬ P → ¬ Q
T	T	T	T	T	T
T	F	F	T	F	T
F	T	T	F	T	F
F	F	T	T	T	T

Types of Inference Rules

The following inference rules illustrate several logical procedures for obtaining conclusions, demonstrating how provided premises lead to valid conclusion in reasoning systems.

Modus Ponens

The Modus Ponens is one of the best and important rule in inference, which states that if P, P → Q is true the Q must be true.

Notation of Modus Ponens = $$\frac{P→Q , P}{\Q}$$

Example

The following example illustrates the application of Modus Ponens in logical inference −

• Premise 1: If students complete a Tutorials Point course then they will receive a certificate. (If P then Q)
• Premise 2: A student has completed a course from Tutorials Point. (P is true.)
• Conclusion: Student will receive a certificate. (Q is true.)

Modus Tollens

Modus Tollens rule states that, If P implies Q (P → Q) and Q is false, then P must also be false. It can be represented as −

Notation of Modus Tollens = $$\frac{P → Q , ¬ Q}{\ ¬P}$$

Example

The following example illustrates the application of Modus Tollens in logical inference −

• Premise 1: If the dog is hungry, then it will bark. (If P then Q)
• Premise 2: The dog isn’t barking. (Q is false.)
• Conclusion: The dog isn’t hungry. (P is False)

Hypothetical Syllogism

The hypothetical syllogism rule states that, if P implies Q (P → Q) and Q implies R (Q → R), then P implies R (P → R). It can be represented as −

Notation of Hypothetical Syllogism =$$\frac{P → Q, Q → R} {\ P → R}$$

Example

The following example illustrates the application of Hypothetical Syllogism in logical inference −

• Premise 1: If company launches a new marketing campaign then brand awareness increases. (If P then Q)
• Premise 2: As brand awareness increases, there is an increased expectation of sale. (If Q then R)
• Conclusion: Therefore, if the company introduces a new marketing campaign, sales will increase. (If P then R)

Disjunctive Syllogism

Disjunctive is one of the common rule which states that, if we have P or Q (PQ), and we know that P is false, then Q must be true. It can be represented as −

Notation of Disjunctive Syllogism = $$\frac{¬P, P Q}{\ Q}$$

Example

The following example illustrates the application of Disjunctive Syllogism in logical inference −

• Premise 1: Either the light is on, or the bulb is broken. (P or Q)
• Premise 2: The light is not on. (P is false)
• Conclusion: Therefore, the bulb is broken. (Q is true)

Addition

Addition rule states that, if P is true, then we can conclude P or Q (PQ), regardless of Q. It can be represented as −

Notation of addition = $$\frac{p}{\ P → Q}

Example

The following example illustrates the application of Addition in logical inference −

• Premise: We provide digital marketing training. (P is true)
• Conclusion: Therefore, we provide digital marketing training or social media marketing training. (P or Q)

Simplification

Simplification rule state that, if P and Q (PQ) are both true, then we can conclude that P is true and Q is true. It can be represented as −

Notation of simplification = $$\frac{P Q}{\ P}

Example

The following example illustrates the application of Simplification in logical inference −

• Premise: This AI tutorial explains about propositional logic and First-order-logic (P and Q)
• Conclusion 1: Therefore, this AI tutorial explains propositional logic. (P is true)
• Conclusion 2: Therefore, this AI tutorial explains First-order-logic. (Q is true)

Resolution

Resolution rule state that, if we have PQ and ¬PR, then we can conclude QR. It can be represented as −

Notation of Resolution = $$\frac{PQ, ¬PR}{\Q R}

Example

The following example illustrates the application of Resolution in logical inference −

• Premise 1: Either the meeting is today, or it is tomorrow. (P or Q)
• Premise 2: Either the meeting is not today, or it will be online. (Not P or R)
• Conclusion: Therefore, either the meeting is tomorrow, or it will be online. (Q or R)

The most commonly used rules of inference or summarized in below table −

Rules of Inference	Tautology	Name
P, P → Q, Q	(P(P → Q)) → Q	Modus Ponens
¬Q, P → Q, ¬P	(¬Q (P → Q)) → ¬P	Modus Tollens
P → Q, Q → R, P → R	((P → Q) (Q → R)) → (P → R)	Hypothetical Syllogism
¬P, P Q, Q	(¬P (P Q)) → Q	Disjunctive Syllogism
P, (P Q)	P → (P Q)	Addition
P Q, P	(P Q) → P	Simplification
P Q, ¬P R, Q R	((P Q) (¬P R)) → (Q R)	Resolution

Applications of Inference Rules

Inference rules are used in a various industries, from healthcare to entertainment, allowing AI to analyze difficult problems or situations and offer insightful results. The following are some important uses of inference rules in various fields −

• Medical Diagnosis Systems In medical AI applications, inference is used to evaluate patient information, including symptoms and test results, and provide a diagnosis. The system uses medical knowledge and rules to infer the causes of the disease and precautions, which helps a doctor to decide on an exact diagnosis.
• Virtual Assistants:(Siri, Alexa) Virtual assistants use inference to understand and act on human commands. They apply natural language processing to infer what a person is asking for or what a question means, which helps them provide suitable answers or take appropriate actions.
• Recommender Systems: (Netflix, Amazon) Inference plays a role in suggesting items, movies, and information to users. AI looks at past user activity to guess their likes and dislikes. This allows it to predict movies they might enjoy, which makes for a better user experience.
• Autonomous Vehicles: Self-driving cars rely on inference to make choices as they go. Their sensors help them gather info about what’s around them (like people walking other cars, and road signs). This lets them drive through traffic.

Propositional logic is a branch of logic that deals with propositions, which are statements that can be either true or false. It makes complex expressions by using logical connectives like AND, OR, NOT, and IMPLIES, and then applies rules to determine their truth values.

Propositional Logic in Artificial Intelligence

Artificial intelligence (AI) uses propositional logic as one of the major methods of knowledge representation using logical propositions. Propositions are statements that are either true or false but not both. More complex expressions are created by combining statements with logical operators like AND, OR, NOT, and IMPLIES. This enables an AI system to make better decisions using logical reasoning.

Artificial intelligence applies propositional logic in rule-based reasoning, automated theorem proving, and expert system decision-making. In machine learning, inference rules like Modus Ponens and Resolution allow machines to draw conclusions on the basis of the facts provided.

Propositions, in artificial intelligence, are sentences that are considered to state facts, situations, or claims about the world to enable the logical reasoning of the machines. The propositional logic expression consists of symbols (for these truths) and logical operators, often represented with parenthesis.

Example

Following are few examples of propositions (declarative statements) −

• The sun rises in the east.
• A triangle has four sides. (False)
• Water boils at 100C under normal atmospheric pressure.
• 2 + 2 = 5. (False)
• A self-driving car can operate without human intervention.

Facts about Propositional logic

Propositional logic is a formal system applied in mathematics, computer science, and artificial intelligence for reasoning about logical statements.

• It pays no attention to the context and content, it just determines whether propositions are true or false based on their structure.
• In propositional logic, operations are ordered according to precedence: Negation (¬) leads to conjunction (), then disjunction (), implication (→), and biconditional ().
• Truth tables are applied to determine whether a logical expression is valid, satisfiable, or equivalent.
• Propositional logic is limited because it can’t express a relationship between the objects and quantifiers like “for all” or “there exists,” where these are handled by First Order Logic.
• A proposition must be a declarative statement that holds a truth value of true or false, like the sky is blue. Statements like “Where is Krish?” is not a proposition because it is not declarative statement.

Key Components of Propositional Logic

Propositional logic involves basic building blocks such as propositions, logical connectives, and truth tables to form logical expressions which simplifies knowledge representation that help AI to reason and make decisions based on facts.

Propositions (Statements)

Propositional logic deals with two kinds of propositions, atomic and compound propositions which form the base for logical expressions.

• Atomic proposition: An atomic proposition is an basic statement which cannot be split into smaller units. It has a single proposition sign.For example, statement like “The car is parked in the garage”.
• Compound Proposition: A compound proposition is formed by combining two or more atomic propositions using logical connectives like AND, OR, NOT, Implies.For example, “She likes coffee OR she likes tea”.

Logical Connectives

Logical connectives, also known as logical operators, are symbols that connect or alter propositions in propositional logic. They help to form complex propositions and determine the relationships between the components. Below are the main types −

Conjunction

The combination of two propositions is only true if both of the propositions are true.

Example

The sun is shining AND it is a warm day.

• P = The sun is shining.
• Q = It is a warm day. → P Q.

The combination of above two statements become P Q. The statement, (“The sun is shining AND it is a warm day”) is TRUE only if both the statements is true, if either P or Q is FALSE the entire statement is FALSE.

Disjunction (OR, )

The disjunction of two propositions is true if at least one of the propositions is true.

Example

“It is raining OR it is snowing.” True if either condition is true, or both.

• P = It is raining.
• Q = It is snowing. → P Q.

Negation (NOT, ¬)

The negation of a proposition reverses its truth value, if the proposition is true, the negation is false, and vice versa.

For example, “The car is NOT parked in the driveway.”(True if the car is not parked in the driveway.)

Implication (IF-THEN, →)

An implication says that if the first proposition is true, then the second has to be true as well. It is only false when the first statement is right and the second statement is wrong. It is sometimes called if-then rules.

For example, “If it rains, then the ground gets wet.” (False only if it rains and the ground does not get wet.)

Biconditional (IF AND ONLY IF, )

A biconditional statement is true whenever the two propositions have the same truth value-both true or both false.

For example, “She is happy IF AND ONLY IF she passed the exam.” (True only if she passed the exam and is happy, or neither of them is true.)

Table for Propositional Logic Connectives

The following table presents the fundamental connectives used in Propositional Logic, along with their symbols, meanings, and examples −

Connective Symbols	Words	Terms	Example
	AND	Conjunction	A B
	OR	Disjunction	A B
→	Implies	Implication	A → B
	If and only if	Biconditional	A B
	either A or B but not both	Exclusive Or	A B
¬ or ~	NOT	Negation	¬A or ~B

Truth Table

A truth table is a systematic representation of all possible truth values of propositions and their logical combinations in propositional logic, particularly in artificial intelligence.

It helps to determine the validity of logical statements by showing how the truth value of a compound proposition changes with respect to the truth values of its individual components.

Conjunction

The AND operation of P Q is true if both the propositional variable P and Q are true.

The truth table is as follows −

P	Q	P Q
True	True	True
True	False	False
False	True	False
False	False	False

Disjunction

The OR operation of two Propositional variable P Q is true if atleast any of the propositional variable p or q is true.

The truth table is as follows −

P	Q	P Q
True	True	True
True	False	True
False	True	True
False	False	False

Implication

An implication P → Qrepresents if P then Q. It is false if P is true and Q is false. The rest cases are true.

The truth table is as follows −

P	Q	P → Q
True	True	True
True	False	False
False	True	True
False	False	True

Bi-conditional

P Q is Bi-conditional if both P and Q have both truth value i.e, both are false or both are true.

The truth table is as follows −

P	Q	P Q
True	True	True
True	False	False
False	True	False
False	False	True

Exclusive OR

P Q is said to be exclusive OR if exactly one of the propositions is true but not both.

The truth table is as follows −

P	Q	P Q
True	True	False
True	False	True
False	True	True
False	False	False

Negation

The logical operation which reverses the truth value of a proposition. For example if P is true the negation of P is false, and vice versa.

The truth table is as follows −

P	¬P
True	False
False	True

Tautologies, Contradictions, and Contingencies

Tautologies: A tautology is a proposition that is true regardless of the truth values assigned to its component propositions. In other words, no matter what we assign to the components of this statement, the final result will always be true.

Contradiction: A contradiction is a proposition that is always wrong, no matter which truth values are assigned to its components. It represents a statement that simply cannot be true.

Contingency: A contingency is a proposition that may not be necessarily true or false. The truth value of the entire statement is determined by the truth value of the propositions. That is, it may be true in some situations but false in others.

Precedence of connectives

In propositional logic, the order of operations (precedence) is as follows −

Precedence	Operators
First preference	Parenthesis
Second preference	Negation
Third preference	Conjunction(AND)
Fourth preference	Disjunction(OR)
Fifth preference	Implication
Sixth preference	Biconditional

Note: Operators with the same precedence are evaluated from left to right.

Example: Shopping Decision

Statement: “If the item is on sale AND I have a coupon, I will buy it OR I will wait for a better deal.”

Propositions: A proposition is a declarative statement that might be true or false, but not both.

• P = The item is on sale.
• Q = I have a coupon.
• R = I will buy it.
• S = I will wait for a better deal.

Propositional Logic Expression: A propositional logic expression is the set of propositions joined together by logical connectives to form a meaningful statement. We write the logical expression using symbols and connectives.

(P Q) → (R S)

Step-by-Step Evaluation −

Here we follow the logical reasoning step by step.

• Conjunction: Evaluate (P Q) and see whether the two conditions that have to be satisfied, sale and coupon, are met.
• Disjunction: Consider (R S ) to determine whether the decision is to buy or wait.
• Implication: If P and Q are true, then the conclusion must be R or S, so the AI system will make the right decision.

This is how we implement the precedence rules in propositional logic, first evaluating the parentheses, then conjunction, followed by disjunction, and finally implication (IF-THEN) to reach a logical decision.

Logical equivalence

Logical equivalence in propositional logic means that two statements, or propositions, always have the same truth value regardless of the truth values assigned to the individual components.

• Symbols: “” or “” represents logical equivalence. P Q means “P is logically equivalent to Q”.
• It simplifies complex logical phrases, which makes the AI system understand and interpret more effectively.
• Logical equivalence lets AI draw new conclusions from preceding knowledge. If two propositions are true and the AI knows one is true, then it can conclude that the other proposition is also true.
• In some AI systems like expert systems, uses logical equivalence to reduce the complexity of search or reasoning by replacing complex phrases with simpler, equivalent phrases.

Properties of Operators

Commutation: The order of variables in AND () and OR () does not affect the result. ( swapping positions doesnt change meaning.). Following are examples of commutation.

• P Q Q P
• P Q Q P

Association: The way propositions are grouped in AND () and OR () does not matter. ((Parentheses can be rearranged without changing meaning.). Following are examples of association.

• (P Q) R P (Q R)
• (P Q) R P (Q R)

Distribution: AND () can be distributed over OR (), and OR () can be distributed over AND (). ((Like multiplying over addition in algebra.). Following are examples of distribution.

• P (Q R) (P Q) (P R)
• P (Q R) (P Q) (P R)

De Morgan’s Law: Describes how negation interacts with both conjunction and disjunction. Following are examples of De Morgan’s Law.

• ¬(P Q) ¬P ¬Q
• ¬(P Q) ¬P ¬Q

Double Negation: A negation of a negation is the same proposition. Following are examples of double negation.

• ¬(¬P)P

Implication (→): Implication can be rewritten using NOT (¬) and OR (). Following are examples of Implication.

• P → Q ¬P Q

Idempotence: An operation is idempotent if repeating it a number of times yields the same result as doing it once. Following are examples of Idempotence.

• P P P
• P P P

Syntax of Propositional Logic

The syntax of propositional logic specifies rules and symbols required to construct valid logical propositions. It consists of propositions, logical connectives, and parentheses that assist in representing knowledge in a structured way.

• Propositions (Atomic Statements): These are simple statements that may be either true or false. They are usually represented by capital letters like P, Q, R, etc.
• Logical Connectives (Operators): The symbols that can be used to connect or transform propositions in a way that combines or alters their truth values such as , , ¬, →,
• Parentheses: are used to group propositions and order operations properly e.g, (P Q) → R
• Compound Propositions: It is a logical statement which is obtained by combining several atomic propositions through logical connectives like , , ¬, →, and . For example, (P Q) (¬R).

Applications of Propositional Logic in AI

Following are the applications of propositional logic −

• Automated Reasoning: Automated reasoning uses propositional logic which enables machine to deduce new knowledge from existing facts. This helps in problem-solving and decision making.For example, let the known facts be “The room is dark” and “The lights turn on”. If AI detects darkness, it automatically turn on lights. This way it can use or infer the existing knowledge.
• Knowledge Representation: AI uses propositional logic to represent facts and relationships using propositions (statements that are either true or false) and logical connectivities such as , , ¬ and →. This logical representation helps AI to make decisions and answer queries quicker by simplifying complex representation into a structured form.For example, let the statements be “The customer buys a smartphone.” and “The system recommends a phone case”. The logical representation for this would be P → Q meaning if the customer buys a smartphone, the AI system will recommend to buy a phone case.
• Decision Making: AI uses propositional logic to make decisions based on conditions.For example, “If the car is low on fuel (P), and the fuel station is nearby (Q), then the car will stop for refueling” (P Q → Refuel).
• Planning and problem-solving: These are fundamental activities of AI, where machines process a situation, establish objectives, and decide a sequence of steps to achieve a desired outcome. Propositional logic helps the AI describe goals, constraints, and conditions in a structured way, so that systems can logically determine what actions to take next.For example, “If a meeting room is available (P) and all the participants are free (Q), the AI schedules the meeting” (P Q) → R.
• Expert System: Expert Systems uses propositional logic to represent facts and apply rule-based reasoning to draw conclusions.For example, “The applicant has a stable job (P) , The applicant has a good credit score (Q), The loan is approved” (P Q) → R here we use logical representation to draw conclusions.
• Game Playing: In games like chess, AI uses propositional logic to make decisions.For example, “”If the queen is near the king (P) and we can block it (Q), then we will move the piece” (P Q → Move Piece).
• Natural Language Processing: Propositional logic enables AI to evaluate language patterns, extract meaning, and make logical conclusions in chatbots, virtual assistants, machine translation, and automated text processing.For example, for the sentence “If it rains (P), take an umbrella (Q)”, the AI learns that if it is raining, it should take an umbrella.

Limitations of Propositional Logic

Following are the limitations of propositional logic

• Propositional logic handles declarative statements as true or false however it can’t show objects and how they relate to each other. For example, “The sun is hot” propositional logic only tells whether this statement is true or false, but it cannot tell the relationship between sun and other objects like cloud.
• It can’t express ideas like “All humans are mortal” or “Some students passed the exam” because it doesn’t have universal () or existential () quantifiers.
• We can’t represent complex statements with variables such as “If a person is a student then they have an ID card.”
• As the number of facts increases propositional logic, requires too many individual propositions, making it inefficient for large AI systems.
• It struggles with incomplete or uncertain data, which many real-world AI applications need.
• Since propositional logic has these drawbacks, we use First-Order Logic (FOL) to overcome them. FOL adds objects, relationships, and quantifiers, increasing its usefulness for AI reasoning.

Techniques of Knowledge Representation

They are mainly four types of knowledge representation which are as follows −

• Logical Representation
• Semantic Network Representation
• Frame representation
• Production Rules

Logical Representation

Logical representation is a method of representing knowledge using symbols and rules to describe facts and relationships respectively. It follows a structured approach that includes syntax (the rules that define valid expressions) and semantics (meaning behind the expressions), resulting in clear AI reasoning.

Syntax is the organization of logical propositions, comparable to grammar in language. It guarantees that the statements are well-formatted so that AI systems can process them efficiently.

For example, when the syntax has errors (for instance, P Q →), an AI system can’t grasp or deduce meaning from it because the structure breaks logic. Logical syntax makes statements clear and allows the system to interpret them.

Semantics deals with how we understand logical statements determining if they’re true or false based on specific interpretations.

For example, let us consider two statements where P represents “It’s raining” and Q represents “The road is wet.” The syntax P → Q means “If it’s raining, the road is wet.” Semantics plays a key part in helping AI systems reach meaningful conclusions instead of just applying rules without understanding.

Types of Logical Representations

They are two types of logical representation which are mentioned below −

• Propositional logic (PL) has basic statements (propositions) that logical operators like AND, OR, and NOT connect.
• First-Order Logic (FOL) expands on PL by adding objects, relationships, and quantifiers such as (for all) and (exists).

Advantages of Logical Representation

The following are the key advantages of using logical representation in AI −

• Logical representation enables a clear and precise statement of knowledge, which removes uncertainty and ambiguity.
• It allows AI systems to infer and reason based on established facts and logical rules.
• This method is mathematically accurate and acceptable for AI implementation in the forms of expert systems and automated deduction.
• Logical representation is widely utilized in AI to perform theorem proof, knowledge-based systems, as well as natural language processing.

Disadvantages of Logical Representation

Despite its benefits, logical representation has certain limitations, as outlined below −

• Logical deduction can be computationally slow and complex, especially in First-Order Logic, where it requires more computer power.
• This approach does not handle uncertainty well, and it is hard to characterize real-world scenarios where knowledge is probabilistic or imperfect.
• It is strict and inflexible, demanding exact definitions of all facts and rules, and is hard to handle flexible or evolving information.
• As the knowledge base grows, the system becomes harder to control, leading to inefficiencies in reasoning and increased complexity.

Semantic Network Representation

Semantic network is a form of knowledge structuring according to a network of concepts and the relationships among them. Think of it as a map, where one idea is connected to other ideas to signify how they’re related, for example, “dog” and “animal.”

Semantic networks in AI enable programs to understand and draw conclusions by examining these connections. For example, if a program understands that “dogs are animals” and “animals need food,” it can deduce that “dogs need food” as well.

For example let us consider a university system in which there are various entities connected to each other. Let us represent these relations through nodes and arcs.

• John is a student.
• John pursues computer science.
• Computer science is a department.
• All departments belong to the university.
• John owns a laptop.
• John owns a Dell laptop.

This above network allows AI systems to draw new conclusions. For example, Since John is studying Computer Science, we can deduce that he is connected to the institution via his department. Since, John has a Dell laptop, its fair to assume he uses it for his academic work.

Advantages of Semantic Network Representation

The key advantages of semantic network representation are as follows −

• Using natural representations of real-world associations makes it easier to store data and retrieve information.
• It allows for inheritance, meaning AI can deduce characteristics (for instance, if all birds can fly, then an eagle is capable of flying).
• It’s easy to visualize and can be expanded by introducing new concepts and connections.
• Supports reasoning by following connections between related concepts.

Disadvantages of Semantic Network Representation

The following are the major disadvantages associated with semantic network representation −

• As more concepts and relationships are added, the network grows and becomes increasingly difficult to manage.
• There is no uniform method for representing relationships, leading to inconsistencies in how knowledge is illustrated.
• Finding relationships within a large network can require significant time and computational resources.
• Semantic networks have difficulty representing probabilistic or uncertain knowledge when compared to probabilistic models.

Frame Representation

Frame representation offers a method to organize details about objects, events, or concepts. This idea proposes that human memory uses “frames” or “templates” to represent general situations, objects, or events. Each frame has slots (features) and fillers (instances) that describe the traits of what it represents.

For example let us consider the definition of “car.” The frame for a car might have fields for color, model, make, and year. These fields could be filled with instances such as red, Model X, Tesla, and 2023.

Key Components of Frame Representation

The following are the main components of frame representation that help in the successful structuring and organization of knowledge.

• Frames are structures that hold data representing a specific entity, concept, or situation. They serve as templates for organizing relevant information.
• Slots are the properties and attributes of a frame. They describe the characteristics of the entity being represented. For example, in a “person” frame, the slots might include name, age, gender, and occupation.
• Fillers are the actual values assigned to these slots. In the case of the “person” frame, John Doe would fill the name slot.
• Frames can be merged to illustrate relationships between entities. For instance, a “car” frame might be linked with an “owner” frame to indicate ownership.
• Some slots may have default values that are assumed unless explicitly stated differently. For example, the default value for the color slot in a “car” frame could be black.

Advantages of Frame representation

Frame representation offers several benefits, which are listed below −

• It facilitates programming by organizing relevant information in a comprehensible and organized form.
• It is flexible and simple to extend, so new features and associations can be introduced with minimal effort.
• The visualization is straightforward, and people can easily comprehend how the information is stored and retrievable.
• This technique is suitable for many AI applications, including natural language processing and machine vision.

Disadvantages of Frame representation

Despite its usefulness, frame representation has some drawbacks, as mentioned below −

• Finding the relevant information over many frames can be challenging and time-consuming.
• Developing rules to accurately infer new knowledge from frames is difficult, especially for big systems.
• Representing highly complex or dynamic knowledge with frames can be difficult because it may necessitate multiple slots and connections.
• Frame-based systems are effective for structured knowledge, but they may not handle ambiguous or abstract concepts adequately.

Production Rules

Production rules are a knowledge representation technique that consists of a series of if-then rules that are used to make decisions and solve problems. These rules provide actions based on conditions and are widely utilized in expert systems and rule-based AI models.

A production rule is written as −

IF (Condition) THEN (Action)

For example, IF temperature > 40C THEN turn on the fan.

• Production rules are used in expert systems to solve problems using rule bases, inference engines, and reasoning methods such as forward and backward chaining.

Examples of Production Rules

The following are few examples of production rules illustrating how conditions meet certain actions in AI systems.

• If the patient has a temperature and a cough, then the diagnosis is flu.
• If the words like “win cash” or “free offer”, then mark the email as spam.
• If motion is detected at night, then switch on the lights.
• If the user says “hello”, then respond with “Hi! “How can I help you?”.

Advantages of Production Rules

The primary advantages of using production rules in AI are as follows −

• Production rules are simple to grasp since they contain IF-THEN expressions.
• Rules can be introduced and withdrawn without affecting the entire system. A smart home system, for example, can add new rules such as IF the temperature exceeds 30C, then turn on the air conditioner, without affecting existing rules.
• Used in AI-powered decision-making systems like medical diagnosis and automation.
• Both the rules (knowledge base) and the inference engine (processing) are maintained independently, making maintenance easier.

Disadvantages of Production Rules

The following are the key disadvantages of production rules in AI −

• As the number of regulations grows, managing them becomes more complex.
• Checking each rule one by one can slow down the system.
• Production rules do not learn from prior experiences unless integrated with machine learning.
• Traditional production rules perform best in clear-cut situations, but they struggle when faced with uncertain or probabilistic data.

Knowledge Representation (KR) plays an essential role in artificial intelligence that enables systems to organize and interpret information in a way similar to human thinking.

This allows AI systems to process data, make decisions, and tackle problems by keeping knowledge in a structure form. Just as humans use language or symbols to express thoughts, AI needs structures to represent the world around it.

What is Knowledge Representation in AI

Knowledge Representation in AI uses the methods and frameworks to encode and store knowledge making it accessible to reason and make decisions. It allows machines to process and use information to understand the world, solve problems, and learn from experiences.

• KR has an impact on simplifying and structuring large amounts of complex data, which makes it easier to analyze and apply AI.
• Good knowledge representation can boost machine learning by offering improved data structures that the system can employ to learn and recognize patterns.
• Knowledge representation frameworks can be used in different problem areas, like healthcare, robotics, or finance letting AI work in various contexts.
• By arranging knowledge well, KR helps make decisions faster and with more information.

What to represent in AI

Following are the kind of knowledge which needs to be represented in AI systems −

• Object Knowledge: Information about physical objects and their properties, for example, “A laptop has keyboard, mouse, screen”. or “A tree has branches, leaves, and roots. “This helps AI recognize and classify things in its environment.
• Event Knowledge: Knowledge about actions or events, for example, “A traffic light turns red” or “A user clicks a button.” This helps AI understand cause and effect.
• Performance Knowledge: Knowledge of how to do tasks, like “How to Bake a Cake” or “How to Troubleshoot a Machine.” It gives AI the efficiency to accomplish tasks.
• Meta Knowledge: Knowledge of what the system knows, such as understanding when to update the knowledge base or determining which information is most useful in a given context.
• Factual Knowledge: Verifiable statements or facts, such as “Water boils at 100C.” It serves as the basis of AI reasoning and decision-making.
• Knowledge base: A centralized source of maintaining facts, rules, and procedures, which enables the AI system to take decisions and address problems based on relevant knowledge.

Relation between Knowledge and Intelligence

Knowledge and intelligence are important concepts in Artificial Intelligence. Knowledge gives the facts and information needed for reasoning and to solve problems, while intelligence use that knowledge to fix problems, decide things, and adjust to new situations. An AI system that has more knowledge can seem more intelligent by making smart choices based on what it knows.

Knowledge without intelligence is nothing but having a raw information without the ability to use them while intelligence without knowledge means lacking the information to make smart decisions.

• Knowledge allows AI to assess different options and make decisions on past information and learned patterns.
• Example: Online stores use what customers have looked at before to suggest products.
• An intelligence makes an AI understand and implement knowledge in many different situations, therefore making it an accomplishment machine.

Types of Knowledge in AI

Following are the various types of Knowledge −

Declarative Knowledge

Declarative knowledge refers to facts, statements, or information that describe “what is known” about a domain. It can be described as static since the information can be represented as either assertions or truths.

For example, declarative knowledge has facts like “The sky is blue”, “Delhi is capital of India”, and “A triangle has three sides”. These statements are declarative knowledge because it is a fact that can be directly expressed and documented.

• Declarative knowledge contains various facts and knowledge regarding the world.
• It answers “what” queries rather than “how” to achieve anything.
• This type of knowledge is easy to convey through statements, databases, or documents.
• Examples include scientific truths, historical events, and general knowledge.
• AI uses declarative knowledge for reasoning, decision-making, and problem-solving.

AI Application: In a question-and-answer system, declarative knowledge is utilized to answer factual questions such as “What is the capital of France?”

Procedural Knowledge

Procedural knowledge refers to the knowledge, of how to perform a task. It involves procedures, methods, or processes that needed to achieve a task or solve a problem. It focuses on step-by-step procedures rather than just facts.

For example, solving a quadratic equation is an structured process that includes determining coefficients, applying the quadratic formula, and simplifying the result.

• Procedural knowledge gives step-by-step instructions for how to do a task.
• It explains “how” to do something rather than just stating the facts.
• This knowledge is acquired through practice and experience.
• Procedural knowledge more difficult to convey explicitly than declarative knowledge.
• It is widely used in artificial intelligence applications like automation, robotics, and expert systems.

AI Application −

• In robotics, procedural knowledge is applied when programming a robot to perform duties such as assembling auto-mobiles or navigating in a maze.
• A robot chef follows rules in a step-by-step manner to prepare a meal. “How To Make Tea: Boil water. Add tea leaves. Pour into a cup. Add sugar and milk to taste.”

Meta Knowledge

Meta-knowledge is a term that refers to “knowledge about knowledge.” It allows AI to understand what it knows, how reliable the information is, and when to apply it. This kind of knowledge allows AI systems to evaluate and enhance their reasoning and decision-making abilities.

For instance, if an AI chatbot knows that its answers are sourced from a reliable database, it will become more confident in its responses.

• Meta-knowledge is the capability of AI to evaluate the correctness and reliability of its own knowledge.
• It enables AI to determine whether it should use specific rules or facts.
• Crucial in learning, over time it sharpens the artificial intelligence decision to make.
• It is very useful for debugging AI models as it helps detecting gaps or inconsistencies.
• Meta-knowledge improves problem-solving by helping AI in choosing the best reasoning strategy.

AI application, a self-driving auto-mobile knows traffic laws and has meta-knowledge to recognize false sensor data caused by fog. It can then decide whether to slow down or switch to a backup system.

Heuristic knowledge

Heuristic knowledge is the rule-of-thumb or experience-based knowledge that helps in problem-solving and decision-making when complete information is not available. It helps in decision-making when specific rules or formulae are not available.

• Heuristic knowledge often relies on intuition, experience, or common sense.
• This knowledge is used in AI to make accurate and quick decisions, particularly in complex or unclear situations.
• Heuristic information reduces computation time by directing the search process toward likely solutions.
• It is widely used in applications such as game AI, medical diagnostics, and optimization problems where exact answers are hard to compute.

AI Application: In game-playing AI like chess or Go, heuristic knowledge helps the machine to evaluate board positions and make strategic decisions.

Structural Knowledge

Structural knowledge refers to the relationships and connections between different concepts or things in a domain. It helps AI understand how things are related.

• Structural knowledge describes how things are structured and connected.
• This knowledge is often represented as graphs, trees, or networks.
• Structural knowledge is widely used in many applications of artificial intelligence, for example, in semantic networks, ontologies, and knowledge graphs.
• This type of knowledge assists AI in inferring new relationships from the existing ones which improves future decision making process quick and accurate.
• Structural knowledge strengthens reasoning and decision-making by presenting information in an organized manner.

For example, an AI-driven medical diagnosis system understands, A fever is a symptom of flu. Flu is caused by a viral infection. Antiviral drugs can treat viral infections this way it connects different entities in a domain.

Humans are intelligent and do tasks which requires creativity by using the logic to solve problems, learn form their past experiences and change when the things are new. They solve the problems or handle the situations with the knowledge stored in their minds.

On the other hand, Artificial Intelligence stores this kind of intelligence in Knowledge-Based Agents (KBAs). These agents make decisions through reasoning by storing facts, rules, and relationships in a knowledge base. Unlike humans, they can analyze vast volumes of data quickly and accurately.

Knowledge Based Agents in Artificial Intelligence

In Artificial Intelligence, Knowledge-Based Agents(KBA) use stored information and reasoning techniques to make intelligent decisions and solve problems. They are designed to do complex tasks effectively by combining logic and organized information.

• Knowledge based agents depend on a knowledge base which stores facts, rules, and information about the world.
• They use an inference system for reasoning and draw conclusions from the knowledge base.
• KBAs can adapt to new situations by adding or updating their knowledge.
• KBAs are commonly used in problem-solving, decision-making, planning tasks and in domains like healthcare, education, and legal systems.
• KBAs improve the scalability and accuracy of decision-making by handling large amounts of structured data.

Example of Knowledge Based Agents

Health Care: Knowledge-based agents analyze patient’s data and medical history to suggest diagnoses or treatments which helps the doctor make wiser decisions. For instance, AI tools can identify patterns for the diagnosis of diseases like cancer and diabetes.

Business Intelligence: AI tools analyze large amounts of data to provide insights on market trends, customer behavior, and productivity. Companies use them to plan marketing campaigns and improve efficiency.

Architecture of Knowledge-Based Agents

First, the knowledge based agent receives the data from environment through sensors then it retrieves the relevant information, rules, facts form the knowledge base to understand the context. It then processes the relevant information through inference system using techniques like forward or backward chaining. Based on this reasoning, agent decides the best action.

Once the decision is made, the agent executes the action using actuators to affect the environment. If the agent is capable of learning, it updates the new information to the knowledge base for future tasks.

What is Knowledge base?

Knowledge base is the critical component of the Knowledge-Based Agent, which includes all the information, rules, and facts necessary for reasoning and decision.

It gives the agent all the information it needs to reason, make informed judgments, and act appropriately with reference to its environment.

• Facts are information about the world. For example, “The Earth orbits the Sun once every 365.25 days”.
• Rules are logical statements that relate facts. For example, “If the temperature drops below 0C, water will freeze into ice”.
• Updates: The knowledge base can be created or updated during the process in which an agent learns or introduces new knowledge so that over a period, its decision-making skill is increased.

For example, smart thermostat saves information as “Room temperature needs to be at 22C”, “If the temperature of room has exceeded to more than 25C then turn on air conditioner”.

Inference System

The inference engine proceeds to process knowledge in the knowledge base using logical reasoning to help the agent take intelligent decision and solve the problem. Imagine this as a tool to determine “what is next” from facts and regulations.

The inference system acts like the thinking part of the agent. It begins with a set of given facts and uses reasoning to obtain new facts or decide what to do.

This system also creates new knowledge from the existing information and includes them in the knowledge base to assist future decision making.

• In practical, an inference system is constructed around algorithms and logical representations such as propositional or first-order logic.
• Inference systems are used in many applications, such as expert systems, natural language processing, and automated reasoning. This allows machines to think logically and make judgments like humans.

This technique uses two basic approaches to introduce logic −

• Forward Chaining: This is based on the assumptions given. The inference engine checks the rules, applies them, and keep inferring the new facts until it reaches a conclusion or goal.
• Backward Chaining: Start from the goal and work backward. It determines which facts or conditions need to be satisfied to achieve that goal.

For example, the thermostat checks the current temperature, applies the criteria, and concludes, “The room is 27C, so I need to activate the cooling system.” This decision is made by inference system.

Sensors and Actuators

In knowledge-based agent sensors collect environmental information such as temperature, light, and movement, while actuators use that information to perform actions such as moving, turning, or cleaning. Robot vacuums use sensors to look for dirt and actuators to clean it or to avoid obstacles.

Operations Performed by KBA

Knowledge-based agents utilize three key procedures to take intelligent actions −

• TELL: The agent updates its knowledge base with new information from the environment. For example, if a robot sees a door open, it tells the knowledge base, “The door is open.”
• ASK: The agent asks the knowledge base what decision it should take. For example, it may ask, “Should I close the door or move forward?”.
• PERFORM: The agent will follow the guidance of the knowledge base, such as closing the door or moving forward. It performs the selected option.

These processes enable the agent to learn, make smart judgments, and efficiently adapt to its surroundings.

A Simple Knowledge Based Agent

Knowledge-Based Agent (KBA) processes perceptions, reasons using its knowledge base, and makes decisions. The following pseudocode represents a basic Knowledge-Based Agent −

function KB-AGENT(percept):  
persistent: KB, a knowledge base   
          t, a counter, initially 0, indicating time   
TELL(KB, MAKE-PERCEPT-SENTENCE(percept, t))   
Action = ASK(KB, MAKE-ACTION-QUERY(t))   
TELL(KB, MAKE-ACTION-SENTENCE(action, t))  
 t = t +1return action   

How a Knowledge-Based Agents works

A Knowledge-Based Agent continuously perceives its environment, utilizes stored knowledge for reasoning, and makes informed decisions. Below is the explanation of how it operates −

• MAKE-PERCEPT-SENTENCE: The agent updates its knowledge base with whatever it observes(environment) at time t by converting the percept into a logical sentence.
• MAKE-ACTION-QUERY: The agent looks in its knowledge base to determine which action it should execute given the current time step and latest knowledge.
• MAKE-ACTION-SENTENCE: After choosing an action the agent updates its knowledge base with a logical statement that describes the action which the agent intends to execute.
• The function returns the chosen action, which the agent will carry out in the environment.

Various levels of Knowledge Based Agent

A knowledge-based agent can be understood at multiple levels, each explaining a distinct aspect of how it perceives, processed, and acted. Following are the various level of Knowledge based agent −

Knowledge level

At this level, the focus is on what the agent knows. The agent make decisions from the facts, rules, and the logical relationship found in its knowledge base.

For example, In a sprinkler activating system the knowledge base has information like “the soil is dry” as well as “if the soil is dry then turn on sprinkler.” This describes what the system knows.

Logical Level

This level describes how the knowledge is represented and processed. The agent uses logic like that of propositional or first-order logic to infer, derive new information and to make decisions. Rule: “The soil is dry, therefore turn the sprinkler on. So the logical level will conclude “Turn the sprinkler on.”

Implementation level

This is the physical or software implementation of the agent. It uses programming languages, algorithms, and hardware to implement the knowledge and reasoning processes. The system is implemented with a soil moisture sensor, sprinkler actuator, and a program written in a simple language like Python that processes the sensor data and controls the sprinkler.

Future of Knowledge-Based Agents

Knowledge-Based Agents (KBAs) are changing with the evolution of artificial intelligence, using machine learning, natural language processing, and automated reasoning to reason with complex data, learn from new data, and make intelligent decisions. KBAs are used extensively in industries to automate and improve efficiency.

KBAs will use deep learning in the future to improve reasoning and manage uncertainty, and hence become indispensable in healthcare, finance, cybersecurity, and intelligent automation.