On the Decidability of Intuitionistic Tense Logic without Disjunction

Fei Liang; Zhe Lin

IJCAI 2020poster0 citations

On the Decidability of Intuitionistic Tense Logic without Disjunction

Abstract

Implicative semi-lattices (also known as Brouwerian semi-lattices) are a generalization of Heyting algebras, and have been already well studied both from a logical and an algebraic perspective. In this paper, we consider the variety ISt of the expansions of implicative semi-lattices with tense modal operators, which are algebraic models of the disjunction-free fragment of intuitionistic tense logic. Using methods from algebraic proof theory, we show that the logic of tense implicative semi-lattices has the finite model property. Combining with the finite axiomatizability of the logic, it follows that the logic is decidable.

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BibTeX

@inproceedings{ijcai2020p249,
  title     = {On the Decidability of Intuitionistic Tense Logic without Disjunction},
  author    = {Liang, Fei and Lin, Zhe},
  booktitle = {Proceedings of the Twenty-Ninth International Joint Conference on
               Artificial Intelligence, {IJCAI-20}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {Christian Bessiere},
  pages     = {1798--1804},
  year      = {2020},
  month     = {7},
  note      = {Main track},
  doi       = {10.24963/ijcai.2020/249},
  url       = {https://doi.org/10.24963/ijcai.2020/249},
}