Unit-4 Knowledge representation Flashcards
Q: What is First-Order Logic (FOL)?
A: First-Order Logic (FOL), also known as predicate logic, is a formal system that allows for the representation and reasoning of knowledge and relationships in a structured way, extending propositional logic.
Q: How does FOL improve upon propositional logic?
A: FOL allows for more complex expressions by introducing predicates, which represent properties of objects and relationships between them, enabling reasoning about individual elements in a domain.
Q: What are predicates in FOL?
A: Predicates are functions that take one or more arguments and return a truth value (true or false), expressing properties or relationships (e.g., likes(x, y)).
Q: Define constants and variables in FOL.
A: Constants represent specific entities in the domain (e.g., “lion”), while variables act as placeholders for unspecified objects (e.g., in likes(x, y), x and y are variables).
Q: What are the main components of FOL syntax?
A: The main components include constants, variables, predicates, functions, quantifiers (universal and existential), and logical connectives.
Q: Explain the role of quantifiers in FOL.
A: Quantifiers specify the scope of variables:
Universal Quantifier (∀) indicates a statement holds for all instances (e.g., ∀x Likes(x, IceCream)). Existential Quantifier (∃) indicates at least one instance exists for which the statement is true (e.g., ∃x Likes(x, Pizza)).
Q: What are logical connectives in FOL?
A: Logical connectives are operators used to combine statements:
AND (∧), OR (∨), NOT (¬), Implication (→), and Biconditional (↔).
Q: What does the negation symbol (¬) represent in FOL?
A: Negation (¬) represents logical NOT, which negates the truth value of a proposition (e.g., ¬p means “It is not raining”).
Q: Describe the process of inference in First-Order Logic.
A: Inference in FOL involves deriving new knowledge from a set of logical statements using rules of deduction, such as Modus Ponens and Modus Tollens.
Q: What is Modus Ponens?
A: Modus Ponens is an inference rule stating that if P → Q (if P then Q) and P are both true, then Q must also be true.
Q: What is Modus Tollens?
A: Modus Tollens is an inference rule stating that if P → Q and ¬Q (not Q) are true, then ¬P must also be true.
Q: What is resolution in FOL?
A: Resolution is an inference rule used in automated theorem proving, which refutes the negation of a statement to derive conclusions.
Q: Explain unification in FOL.
A: Unification is the process of finding substitutions for variables in logical expressions to make two expressions identical, crucial for theorem proving and logic programming.
Q: What conditions must be met for unification to occur?
A: For unification:
The predicate symbols must be the same. The number of arguments in both expressions must match. No similar variables should be present in the same expression.
Q: Provide an example of unification in FOL.
A: Given expressions P(f(X), Y) and P(Z, g(a)), unification can yield substitutions Z = f(X) and Y = g(a) to make them identical.
