Tensor products of modal logics

5 pages•Published: July 28, 2014

Abstract

We consider shifted products of modal algebras and logics first introduced by Y. Hasimoto in 2000. For logics this operation is similar to the well-known usual product but it is logically invariant. We prove the conjecture of D. Gabbay that shifted products act on Boolean algebras exactly as tensor products, so we call them tensor products of modal algebras. We also propose a filtration technique for models based on tensor products and obtain some decidability results.

Keyphrases: logical invariance, modal product, tensor products of modal logics

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 199-203.

Links:	https://easychair.org/publications/paper/nJH
	https://doi.org/10.29007/mtw5

BibTeX entry

@inproceedings{TACL2013:Tensor_products_modal_logics,
  author    = {Ilya Shapirovskiy and Valentin Shehtman},
  title     = {Tensor products of modal logics},
  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/nJH},
  doi       = {10.29007/mtw5},
  pages     = {199-203},
  year      = {2014}}

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