Tutorial Contents Tutorial Three: Propositional Calculus: Tableaux - The Sentence Tableaux Rules - Testing Arguments for Validity - Sequents - Syntactic Sequents - Semantic Sequents - Soundness and Completeness - Correctness of Sequents and Validity of Arguments
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There are two types of sequent: syntactic sequents and semantic sequents.
Syntactic sequents are defined (in our case) in terms of tableaux. Semantic sequents are defined in terms of truth. The idea behind calling sequents of the first sort "syntactic" is that the tableau rules depend for their application solely on the syntax of the formulae involved; they do not depend on any meaning that the formulae may have. In particular they do not depend on the definition of the truth-functors in terms of truth and falsity. (Though, of course, they were actually chosen with these definitions in mind.) By contrast the definition of semantic sequents does depend on the meaning of the truth-functors.





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