Logic

邏輯系統

  • Propositional logic

    deals with specific objects and concrete statements& that are either true or false, such as John is married to Sue.

  • Predicate logic(first-order logic, FOL)

    allows statements to contain variables, such as if X is married to Y then Y is married to X.

  • Temporal logic

  • Fuzzy logic

Propositional Logic

邏輯狀態

  • valid(有效性)

    如果一個句子是有效的，則在每一個解釋之下皆為真。例如: TRUE, ¬FALSE, (P∨¬P)。

  • satisfiable(可滿足的)

    如果一個句子是可滿足的，則存在某個解釋使其為真。例如: TRUE, P, ¬P。

  • unsatisfiable(不可滿足的)

    如果一個句子是可滿足的，則在每一個解釋之下皆為假。例如: ¬TRUE, FALSE, ¬(P∨¬P)。

Some Definitions

  • KB ╞ S(read KB entails S)

    means that S must be true whenever all the statements in KB are true

  • KB ├ S(read KB derives S or S can be proved from KB)

    means that S can be produced by applying the rules of inference to KB

Inference(Proof System)

  • Soundness(可靠性)

    i is sound if whenever KB├i α, it is also true that KB╞ α

  • Completeness(完備性)

    i is complete if whenever KB╞ α, it is also true that KB├i α

First-Order Logic (FOL)

Unification

Most General Unifier

Reference