Logic

Logic:

•Logics are formal languages for representing information such that conclusions can be drawn

•S yntax defines the sentences in the language

•Semantics define the "meaning" of sentences;

 Entailment:

•Entailment means that one thing follows from another:

KB ╞ α

•Knowledge base KB entails sentence α if and only if α is true in all worlds where KB is true

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–E.g., the KB containing “the Giants won” and “the Reds won” entails “Either the Giants won or the Reds won”

–E.g., x+y = 4 entails  4 = x+y

–Entailment is a relationship between sentences (i.e., syntax) that is based on semantics