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- W4247695961 abstract "Publisher SummaryThis chapter proposes a general approach to semantics. Because of Gödel's completeness theorem (GCT), the standard semantics works properly, and thus alternative types of semantics as sheaves, forcing, polyadic algebras are of less importance in the classical case. Two forms of Gödel's theorem exist. In the nonclassical area it is essential to distinguish between logics and theories. A theory is an extension of basic calculus by additional axioms postulating specific properties of objects being studied. A typical example is Heyting arithmetic, which formalizes the intuitionistic viewpoint on natural numbers. Logic is a theory whose theorems may be considered as ‘logical laws' common for a certain class of theories and not depending on specific ‘application domains'. Logic laws can be treated as schemata for producing theorems, and define a logic just as substitution-closed theory. The chapter explains how a semantics is generated and introduces standard classical semantics, algebraic semantics, neighborhood (or topological) semantics, the semantics of Kripke quasi-sheaves, and the Kripke bundles." @default.
- W4247695961 created "2022-05-12" @default.
- W4247695961 date "2009-01-01" @default.
- W4247695961 modified "2023-09-27" @default.
- W4247695961 title "Introduction: What is semantics?" @default.
- W4247695961 doi "https://doi.org/10.1016/s0049-237x(09)70730-x" @default.
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