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General Topos Semantics for Higher-Order Modal Logic

3 pagesPublished: July 28, 2014

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:
BibTeX entry
@inproceedings{TACL2013:General_Topos_Semantics_for,
  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},
  pages     = {14--16},
  year      = {2014},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/dRg},
  doi       = {10.29007/nv5m}}
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