General Topos Semantics for Higher-Order Modal Logic

3 pages•Published: July 28, 2014

Steve Awodey, Kohei Kishida and Hans-Christoph Kotzsch

Abstract

Topos-theoretic semantics for modal logic usually uses structures induced by a surjective geometric morphism between toposes. This talk develops an algebraic generalization of this framework. We take internal adjoints between certain internal frames within a topos, which provides semantics for (intuitionistic) higher-oder modal logic.

Keyphrases: categorical logic, higher order modal logic, topos theoretic semantics

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 14-16.

Links:	https://easychair.org/publications/paper/dRg
	https://doi.org/10.29007/nv5m

BibTeX entry

@inproceedings{TACL2013:General_Topos_Semantics_Higher,
  author    = {Steve Awodey and Kohei Kishida and Hans-Christoph Kotzsch},
  title     = {General Topos Semantics for Higher-Order Modal Logic},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/dRg},
  doi       = {10.29007/nv5m},
  pages     = {14-16},
  year      = {2014}}

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