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• W1615459473 abstract "This chapter reviews some aspects of categorical logic. Logic is divided into three parts—namely, proof theory, recursion theory, and model theory. To all these, category theory can make some contributions, although more in analyzing basic concepts and determining direction for further development than in addressing specific problems or pursuing technical details. On the other hand, techniques developed by logicians have proved very fruitful when lifted to the categorical level. Proofs can be described in various ways, one of them being in terms of deductive systems. A deductive system deals with deductions, also called “entailments,” f : A → B, where A and B are formulas. The deduction symbol is assumed to be reflexive and transitive. The chapter also introduces the variable arrows and formulas. A typical metatheorem in elementary logic is the deduction theorem, which may be stated in the present context as asserting the following: if A is assumed, or rather T → A, and if, from this assumption, it is proved that B, or rather T → B, then there must exist a deduction A → B not depending on this assumption." @default.
• W1615459473 created "2016-06-24" @default.
• W1615459473 creator A5021511629 @default.
• W1615459473 date "1995-01-01" @default.
• W1615459473 modified "2023-09-23" @default.
• W1615459473 title "Some aspects of categorical logic" @default.
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• W1615459473 doi "https://doi.org/10.1016/s0049-237x(06)80039-x" @default.
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