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What is a model in propositional logic?

  • A.An assignment of true or false to every proposition symbol
  • B.A sentence that is true under every possible assignment
  • C.A physical system the logic is intended to describe
  • D.A proof that a sentence follows from a set of premises

Answer: A

A model fixes a truth value for each symbol, and a sentence is true or false in each model, so all the semantic notions are defined by quantifying over models. Sentences true in every model are valid, proofs are syntactic objects, and the physical system is what the logic is about rather than part of it. Defining meaning by reference to a set of possible worlds is what makes entailment a precise relation rather than an intuition. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

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