## Bresolin, Davide and Muñoz-Velasco, Emilio and Sciavicco, Guido - On Sub-Propositional Fragments of Modal Logic

lmcs:2550 - Logical Methods in Computer Science, June 22, 2018, Volume 14, Issue 2
On Sub-Propositional Fragments of Modal Logic

Authors: Bresolin, Davide and Muñoz-Velasco, Emilio and Sciavicco, Guido

In this paper, we consider the well-known modal logics $\mathbf{K}$, $\mathbf{T}$, $\mathbf{K4}$, and $\mathbf{S4}$, and we study some of their sub-propositional fragments, namely the classical Horn fragment, the Krom fragment, the so-called core fragment, defined as the intersection of the Horn and the Krom fragments, plus their sub-fragments obtained by limiting the use of boxes and diamonds in clauses. We focus, first, on the relative expressive power of such languages: we introduce a suitable measure of expressive power, and we obtain a complex hierarchy that encompasses all fragments of the considered logics. Then, after observing the low expressive power, in particular, of the Horn fragments without diamonds, we study the computational complexity of their satisfiability problem, proving that, in general, it becomes polynomial.

Source : oai:arXiv.org:1611.08800
DOI : 10.23638/LMCS-14(2:16)2018
Volume: Volume 14, Issue 2
Published on: June 22, 2018
Submitted on: July 18, 2017
Keywords: Computer Science - Logic in Computer Science,03D15