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Atomic/Complex Sentence in Artificial Intelligence

Term = function (term1,....termn) or constant or variables
  •  A logical expression that refers to an object
           - LeftLegOf (Richard)
  • There are 2 kinds of terms:
           - Constant symbols: Table, Computer
           - Function symbols: LeftLeg(Pete), Sqrt(3), Plus(2,3) etc

Atomic Sentence  =    predicate (term1,.....,termn)
       or term1 = term2
An atomic sentence is formed from a predicate symbol followed by list of terms.

Examples:
          LargeThan(2,3) is false.
          Brother_of(Mary,Pete) is false.
          Married(Father(Richard),Mother(John)) could be true or false.

Note: Functions do not state facts and form no sentence:
  - Brother(Pete) refers to John (his brother) and is neither true nor false

Brother_of(Pete,Brother(Pete)) is True.
  Binary relation            Function

Complex Sentences

We make complex sentence with connectives (just like in propositional logic).
 
  More Examples
  • Brother(Richard, John) ∧ Brother(John, Richard)
  • King(Richard) ∨ King (john)
  • King(John)=> ᆨKing(Richard)
  • LessThan(plus(1,2),4)∧GreaterThan(1,2)
(Semantics are the same as in Propositional logic)

Variables
  • Person(John) is true or false because we give it a single argument 'John'
  • We can be much more flexible if we allow variables which can take on values in a domain. e.g., all person x, all integers i, etc.
              - E.g., can state rules like Person(x) => HasHead(x)
                        or Integer(i) => Integer(plus(i,1)

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