Propositional Logic Details

• Logical Constants: true, false

• Propositional Symbols: P, Q, … (atomic sentences)

• Wrapping parentheses: (….)

• Connectives

  

• Literal: the ****atomic sentence or negated atomic sentence.

Examples

• (P ^ Q) → R

  If it is 22nd January and 11 A.M., then the AI exam begins.

• Q → P

  If it is 22nd January, then it is exam day.

• Tautology (A valid Sentence) is a sentence that is true under all interpretations.

• Contradictions (Inconsistent Sentence) is a sentence that is false under all interpretations.

• P entails Q, written P |= Q, which means that whenever P is True, so is Q. In other words, all models of P are also models of Q.

Truth Tables for Five Logical Connectives

Modus Phonens

Inference Rule

Logical inference generates new sentences from a knowledge base (KB).

• Sound Inference Rule:
  • Every sentence X it produces logically follows from the KB.
  • Ensures no contradictions are created.