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Topological product of modal logics with the McKinsey axiom

Andrey Kudinov

Abstract

In this paper we consider the topological products of modal logics of S4.1 and S4. We prove that it is equal to the fusion of logics S4.1 and S4 plus one additional axiom. We also show that this product is decidable. This is an example of a topological product of logics that is greater than the fusion but less than the expanding product of the corresponding logics.

Topological product of modal logics with the McKinsey axiom

Abstract

In this paper we consider the topological products of modal logics of S4.1 and S4. We prove that it is equal to the fusion of logics S4.1 and S4 plus one additional axiom. We also show that this product is decidable. This is an example of a topological product of logics that is greater than the fusion but less than the expanding product of the corresponding logics.
Paper Structure (5 sections, 21 theorems, 31 equations, 1 figure)

This paper contains 5 sections, 21 theorems, 31 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Definitions and known results
  3. McKinsey axiom
  4. Completeness and decidability theorems
  5. Conclusions

Key Result

Theorem 2.1

If $F \twoheadrightarrow G$ then $Log(F) \subseteq Log(G).$

Figures (1)

  • Figure 1:

Theorems & Definitions (39)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • Theorem 2.1: p-morphism
  • Definition 2.8
  • Theorem 2.2: topological p-mophism
  • ...and 29 more