KNOWLEDGE REPRESENTATIO N Predicate and propositional Knowledge Predicate

KNOWLEDGE REPRESENTATIO N Predicate and propositional Knowledge

Predicate Logic ■ A propositional is a collection of declarative statements that has either a truth value "true” or a truth value "false". ■ A predicate is an expression of one or more variables defined on some specific domain. A predicate with variables can be made a proposition by either assigning a value to the variable or by quantifying the variable. For Example the following statement is not giving the full meaning. – All boys like cricket i. e. like (boys, cricket) ■ – ∀x: boys(x) like (x, cricket) Some boys like cricke i. e. like (boys, cricket) ■ ∃x: boys(x) like (x, cricket)

First Order Logic (FOL) ■ It is also known as first-order predicate calculus and predicate logic. ■ First-order logic uses quantified variables ■ allows the use of sentences that contain variables ■ Terms are simply names for objects ■ Terms could be – Variables – Constant – Logical function ■ Logical functions are not procedural as in programming languages. They do not need to be defined, and do not really return a value.

FOL Cont. . . ■ Symbolized reasoning in which statement is broken down into subject and predicate. ■ The predicate modifies or defines the properties of the subject ■ In first-order logic, a predicate can only refer to a single subject ■ Written as – Predicate (term 1; : : : ; term. N) – P is predicate and x is a subject (variable)

Model of First Order Logic ■ Sentences are true or false with respect to models, Which consist of – a domain – an interpretation ■ Domain – A non-empty finite Or infinite set of Arbitrary elements ■ Interpretation – Assigns to Each – constant symbol: a domain element – predicate symbol: a relation on the domain – function symbol: a function on the domain

Semantics in First-order Logic ■ An atomic sentence is true In a certain model (that consists of a domain and an interpretation) – If and only if the domain elements that are the interpretations of term 1 ; : : : ; termn are in the relation that is the interpretation of predicate ■ It is raining and the wind is blowing (R & W)

Propositional vs. Predicate Logic ■ In propositional logic, each possible atomic fact requires a separate unique propositional symbol ■ If there are n people and m locations, representing the fact that some person moved from one location to another requires nm 2 separate symbols. ■ Allows more flexible and compact representation of knowledge

Syntax of FOPL ■ Sentence→ – Atomic Sentence – Sentence Connective Sentence – Quantifier Variable Sentence – ¬ Sentence ■ Atomic. Sentence → Predicate(Term, . . . ) ■ Term → Function( Term, . . . ) – Constant – Variable

Symbols ■ Connective → ∨ | ∧ | ⇒ | ⇔ ■ Quanitfier → ∃ | ∀ ■ Constant → A | John| Car 1 ■ Variable → x|y|z|. . . ■ Predicate→ Brother|Owns| ■ Function → father-of|plus|