Lecture 5 Flashcards
What is the purpose of logic in AI?
Logic helps represent and manipulate information to solve problems, especially when dealing with imperfect information.
What is a knowledge base (KB)?
A collection of true statements written in set notation that represents the agent’s knowledge.
What are the three essential components of a formal logic system?
Syntax (structure of formulae), semantics (meaning of symbols), and calculus (rules for manipulating formulae).
What is propositional logic?
A declarative language that uses distinct symbols and operators to evaluate whether propositions are true or false.
What does the syntax of propositional logic describe?
The rules for constructing well-formed formulae using symbols and operators.
What is the semantics of propositional logic?
The meaning assigned to symbols and formulae, used to evaluate their truth or falsehood.
What is the purpose of operators in propositional logic?
Operators connect symbols to form complex statements and determine their truth values.
What are the five operators in propositional logic?
Negation (¬), conjunction (⋀), disjunction (∨), implication (→), and biconditional (⇔).
How does the negation operator (¬) work?
It changes the truth value of a proposition: T → F or F → T.
What is the conjunction operator (⋀) interpreted as, and when is it true?
Conjunction means ‘and’ and is true only when both propositions it connects are true.
What is the disjunction operator (∨) interpreted as, and when is it true?
Disjunction means ‘or’ and is true when at least one of the propositions it connects is true.
What does the implication operator (→) signify?
‘Implies’ indicates that the first proposition being true guarantees the second is true; false only if the first is true and the second is false.
What is the biconditional operator (⇔), and when is it true?
‘If and only if’; true when both propositions have the same truth value (both true or both false).
What is a truth table?
A table that lists all possible truth value combinations for a set of propositions and evaluates a statement based on those values.
How do you calculate the number of rows in a truth table?
The number of rows is 2^n, where n is the number of variables in the statement.
What is a model in the context of a knowledge base?
An interpretation of truth values for propositions that satisfies the knowledge base, making all its statements true.
What does it mean if a sentence is satisfiable?
There exists at least one model where the sentence is true.
What does it mean if a sentence is valid?
The sentence is always true, regardless of the truth values of its components.
What is logical entailment?
A sentence is entailed if it is true in all models of the knowledge base.
How can truth tables help identify models of a knowledge base?
By highlighting rows where the final column (the statement) evaluates to true, the truth values in these rows represent the models.
