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• W64194158 abstract "It is well-known that simple type theory is complete with respect to non-standard models. Completeness for standard models only holds when increasing the class of models, e.g., to cartesian closed categories. Similarly, dependent type theory is complete for locally cartesian closed categories. However, it is usually difficult to establish the coherence of interpretations of dependent type theory, i.e., to show that the interpretations of equal expressions are indeed equal. Several classes of models have been used to remedy this problem.We contribute to this investigation by giving a semantics that is both coherent and sufficiently general for completeness while remaining relatively easy to compute with. Our models interpret types of Martin-Lof's extensional dependent type theory as sets indexed over posets or, equivalently, as fibrations over posets. This semantics can be seen as a generalization to dependent type theory of the interpretation of intuitionistic first-order logic in Kripke models. This yields a simple coherent model theory with respect to which simple and dependent type theory are sound and complete." @default.
• W64194158 created "2016-06-24" @default.
• W64194158 creator A5048294977 @default.
• W64194158 creator A5091861223 @default.
• W64194158 date "2009-01-01" @default.
• W64194158 modified "2023-10-01" @default.
• W64194158 title "Kripke Semantics for Martin-Löf’s Extensional Type Theory" @default.
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• W64194158 doi "https://doi.org/10.1007/978-3-642-02273-9_19" @default.
• W64194158 hasPublicationYear "2009" @default.
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