Knowledge Representation (KR) is the field of AI concerned with how knowledge can be formally represented and manipulated by machines.
In AI, Knowledge representation refers to the way in which information, facts, and rules about the world are formally structured so that a computer system can use them to solve complex tasks such as diagnosing a problem, understanding natural language, planning actions, or learning new information.
Knowledge representation in AI involves structuring information about the world in a way that a computer system can understand and use for reasoning and decision-making. Knowledge representation deals with how knowledge can be represented symbolically and manipulated in an automated way by reasoning programs. It’ about providing AI with the “knowledge” it needs to act intelligently.
Logical Reasoning
Logical reasoning is a fundamental aspect of knowledge representation in artificial intelligence (AI). It involves using formal logic to represent knowledge about the world and to infer new information from existing knowledge.
Logical reasoning involves drawing conclusions from premises using formal rules of logic. It uses formal logic (propositional or predicate logic) to derive new facts from existing knowledge.
Types of logic used:
Propositional Logic: Deals with simple statements (true/false).
Predicate Logic (First-order logic): Handles objects, properties, and relationships — more expressive.
Propositional Logic
Propositional logic, also known as propositional calculus or Boolean logic, is a branch of logic that deals with propositions, which are statements that can either be true or false. In the context of artificial intelligence (AI), propositional logic is used to represent knowledge and perform reasoning tasks.
Propositional Logic is a formal system in AI and computer science used to represent facts and reason about them. It’s the simplest form of logic and serves as a foundation for more complex knowledge representation systems like predicate logic.
Propositional logic represents knowledge using propositions — statements that are either true or false, but not both.
Examples of propositions:
- “It is raining”
- “The light is on”
- “AI is useful”
These can be symbolized as:
- P: It is raining
- Q: The light is on
- R: AI is useful
Logical Connectives
Propositional logic uses connectives to build complex expressions:
The main logical connectives include:
AND (∧): The conjunction of two propositions is true if both are true. For example, ( P ʌ Q ) is true if both ( P ) and ( Q ) are true.
OR (∨): The disjunction of two propositions is true if at least one is true. For example, ( P ˅ Q ) is true if either ( P ) or ( Q ) (or both) are true.
NOT (¬): The negation of a proposition is true if the proposition is false. For example, (¬ P ) is true if ( P ) is false.
IMPLIES (→): The implication ( P → Q ) is true unless ( P ) is true and ( Q ) is false.
BICONDITIONAL (↔): The biconditional ( P ↔ Q ) is true if both propositions are either true or false.
Predicate Logic (First order Logic)
Predicate Logic, also known as First-Order Logic (FOL), is a powerful and expressive way to represent knowledge in Artificial Intelligence. It is an extension of propositional logic that allows for more expressive representations of knowledge. It introduces the concepts of predicates, quantifiers, and variables, enabling the representation of relationships and properties of objects. In the context of artificial intelligence (AI), predicate logic is widely used for knowledge representation and reasoning.
Components of Predicate Logic:
Predicates: A predicate is a function that takes one or more arguments and returns a truth value. For example,
Human(x) → x is a human
Loves(john, mary) → John loves Mary
Terms: Terms can be constants (specific objects), variables (placeholders for objects), or functions (which return objects).
Quantifiers: Quantifiers allow for the expression of statements about “some” or “all” objects in a domain:
- Universal Quantifier (∀): Indicates that a statement is true for all elements in a domain.
- Existential Quantifier (∃): Indicates that there exists at least one element in the domain for which the statement is true.
Logical Connectives:
Similar to propositional logic, predicate logic uses logical connectives such as AND (∧), OR (∨), NOT (¬), IMPLIES (→), and BICONDITIONAL (↔) to form complex statements.
Normal Forms (CNF & DNF):
Normal forms are important concepts in propositional logic. They provide standardized ways to write logical formulas. These forms are useful in many AI applications, such as automated reasoning, expert systems, logic programming, and SAT solving.
The two most common normal forms are:
Conjunctive Normal Form (CNF)
A formula is in Conjunctive Normal Form if it is a conjunction (AND) of one or more disjunctions (OR) of literals.
Literals: A literal is a variable or its negation (e.g., A, ¬B).
Structure of CNF:
CNF: (A1 ∨ A2 ∨…∨An) ∧ (B1 ∨ B2 ∨…∨ Bm) ∧…
Example: The formula
(A ∨ B) ∧ (¬C ∨ D)
is in CNF because it is a conjunction of two disjunctions.
Disjunctive Normal Form (DNF)
A formula is in Disjunctive Normal Form if it is a disjunction (OR) of one or more conjunctions (AND) of literals.
Structure of DNF:
DNF: (A1 ∧ A2 ∧…∧ An) ∨ (B1 ∧ B2 ∧…∧ Bm) ∨…
Example: The formula
(A ∧ ¬B) ∨ (C ∧ D)
is in DNF because it is a disjunction of two conjunctions.
Inference:
Inference in AI refers to the process of deriving new facts, conclusions, or knowledge from known facts or data using logical reasoning. It is a core part of intelligent behavior, allowing AI systems to make decisions, solve problems, and learn from known information. Inference is “thinking” or “reasoning” in AI.
In AI, inference refers to the process of deriving logical conclusions from a set of premises or known facts. It is a critical component of reasoning in artificial intelligence systems, enabling them to make decisions, solve problems, and draw conclusions based on available knowledge.
Types of Inference in Knowledge Representation:
Deductive Inference: This involves drawing specific conclusions from general rules or premises. If the premises are true, the conclusion must also be true. For example, if all humans are mortal (premise) and Socrates is a human (premise), then Socrates is mortal (conclusion).
Inductive Inference: This method involves making generalizations based on specific observations. For instance, if you observe that the sun has risen in the east every day of your life, you might conclude that the sun always rises in the east. Inductive reasoning does not guarantee the truth of the conclusion.
Abductive Inference: This is a form of reasoning that starts with an observation and seeks the simplest and most likely explanation. For example, if you find the grass wet, you might infer that it rained, although there could be other explanations (like someone watering the lawn).
Inference Chains:
In knowledge representation (KR), inference chains refer to sequences of logical steps or reasoning processes that derive new knowledge or conclusions from existing knowledge (facts and rules) in a structured way. Inference chains are a crucial component of knowledge representation in AI, enabling systems to derive new knowledge from existing information through logical reasoning. By understanding and applying inference rules, AI systems can make informed decisions, solve problems, and interact with the world in a meaningful way.
An inference chain consists of a series of statements (premises) and the logical rules applied to derive new statements (conclusions). Each step in the chain builds upon the previous one, leading to a final conclusion. An inference chain is a connected sequence of inference steps, each of which applies a rule to known information to derive new information. It’s a reasoning path from premises (known facts) to a conclusion.
Resolution:
Resolution in knowledge representation is a fundamental automated reasoning technique used primarily in logic-based systems, especially propositional and first-order logic. It’s a rule of inference that allows a system to deduce new clauses or detect contradictions in a set of known logical formulas. Resolution is most famously used in automated theorem proving and logic programming.
Forward Chaining and Backward Chaining:
In Artificial Intelligence (AI), Forward Chaining and Backward Chaining are two fundamental reasoning strategies used with rule-based systems (often implemented via production rules or logical inference systems).
Forward chaining is a data-driven approach that starts with known facts and applies rules to infer new information. In contrast, backward chaining is a goal-driven method that begins with a hypothesis and works backward to determine the necessary facts to support it.
Forward Chaining: A reasoning strategy that starts with known facts and applies rules to derive new facts or conclusions.
Forward chaining starts from the known facts and applies inference rules to extract more data until a goal is reached.
Process:
- Start with a set of facts.
- Apply rules whose conditions match the current facts.
- Add the conclusions of those rules to the fact base.
- Repeat until the goal is found or no more rules apply.
Backward Chaining: A reasoning strategy that starts with a goal or hypothesis and works backward to verify if the available facts support it.
Backward chaining starts from a goal and works backwards by looking for rules that could achieve that goal, trying to prove the conditions of those rules from known facts.
Process:
- Start with the goal.
- Find rules that conclude the goal.
- Set the conditions of those rules as sub-goals.
- Repeat until sub-goals match known facts or fail.