On the Semantics of Intensionality

G. A. Kavvos*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

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Abstract

In this paper we propose a categorical theory of intensionality. We first revisit the notion of intensionality, and discuss its relevance to logic and computer science. It turns out that 1-category theory is not the most appropriate vehicle for studying the interplay of extension and intension. We are thus led to consider the P-categories of Čubrić, Dybjer and Scott, which are categories only up to a partial equivalence relation (PER). In this setting, we introduce a new P-categorical construct, that of exposures. Exposures are very nearly functors, except that they do not preserve the PERs of the P-category. Inspired by the categorical semantics of modal logic, we begin to develop their theory. Our leading examples demonstrate that an exposure is an abstraction of well-behaved intensional devices, such as Gödel numberings. The outcome is a unifying framework in which classic results of Kleene, Gödel, Tarski and Rice find concise, clear formulations, and where each logical device or assumption involved in their proofs can be expressed in the same algebraic manner.
Original languageEnglish
Title of host publicationFoundations of Software Science and Computation Structures
Subtitle of host publication20th International Conference, FOSSACS 2017, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Uppsala, Sweden, April 22-29, 2017, Proceedings
EditorsJavier Esparza, Andrzej S. Murawski
PublisherSpringer Berlin Heidelberg
Pages550-566
Number of pages17
ISBN (Electronic)978-3-662-54458-7
ISBN (Print)978-3-662-54457-0
DOIs
Publication statusPublished - 16 Mar 2017
Event20th International Conference on Foundations of Software Science and Computation Structures (FoSSaCS 2017) - Uppsala, Sweden
Duration: 22 Apr 201729 Apr 2017
Conference number: 2017
https://etaps.org/2017/fossacs

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Nature
Volume10203
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference20th International Conference on Foundations of Software Science and Computation Structures (FoSSaCS 2017)
Abbreviated titleFoSSaCS
CountrySweden
CityUppsala
Period22/04/1729/04/17
Internet address

Structured keywords

  • Programming Languages

Keywords

  • semantics
  • fixed point
  • intensionality
  • recursion
  • self-reference
  • category theory
  • logic
  • modal logic

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