کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778165 | 1633433 | 2017 | 52 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A micrological study of negation
ترجمه فارسی عنوان
یک مطالعه میکروولوژی از نفی
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
چکیده انگلیسی
Tensorial logic is a primitive logic of tensor and negation which refines linear logic by relaxing the hypothesis that linear negation is involutive. Thanks to this mild modification, tensorial logic provides a type-theoretic account of game semantics where innocent strategies are portrayed as temporal refinements of traditional proof-nets in linear logic. In this paper, we study the algebraic and combinatorial structure of negation in a non-commutative variant of tensorial logic. The analysis is based on a 2-categorical account of dialogue categories, which unifies tensorial logic with linear logic, and discloses a primitive symmetry between proofs and anti-proofs. The micrological analysis of tensorial negation reveals that it can be decomposed into a series of more elementary components: an adjunction Lâ£R between the left and right negation functors L and R; a pair of linear distributivity laws κ and κ which refines the linear distributivity law between â and â
in linear logic, and generates the Opponent and Proponent views of innocent strategies between dialogue games; a pair of axiom and cut combinators adapted from linear logic; an involutive change of frame (â)â reversing the point of view of Prover and of Denier on the logical dispute, and reversing the polarity of moves in the dialogue game associated to the tensorial formula.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 2, February 2017, Pages 321-372
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 2, February 2017, Pages 321-372
نویسندگان
Paul-André Melliès,