Products of modal logics and tensor products of modal algebras

Dov Gabbay, Ilya Shapirovsky, Valentin Shehtman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

One of natural combinations of Kripke complete modal logics is the product, an operation that has been extensively investigated over the last 15 years. In this paper we consider its analogue for arbitrary modal logics: to this end, we use productlike constructions on general frames and modal algebras. This operation was first introduced by Y. Hasimoto in 2000; however, his paper remained unnoticed until recently. In the present paper we quote some important Hasimoto's results, and reconstruct the product operation in an algebraic setting: the Boolean part of the resulting modal algebra is exactly the tensor product of original algebras (regarded as Boolean rings). Also, we propose a filtration technique for Kripke models based on tensor products and obtain some decidability results.

Original languageEnglish
Pages (from-to)570-583
Number of pages14
JournalJournal of Applied Logic
Volume12
Issue number4
DOIs
StatePublished - Dec 2014

Bibliographical note

Publisher Copyright:
© 2014 Elsevier B.V. All rights reserved.

Keywords

  • Filtration
  • Finite model property
  • Logical invariance
  • Modal algebra
  • Product of modal logics
  • Tabular logic
  • Tensor product

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