Introducing Polymodal Neighbourhood Logics

ON STRONG NEIGHBOURHOOD COMPLETENESS OF MODAL AND INTERMEDIATE PROPOSITIONAL LOGICS (Part II)

The property of strong neighbourhood completeness was introduced in the first part of this paper. By modifying the ultrabouqet construction, we prove this property for all Kripke-complete normal K4-logics and for a large class of Kripke-complete polymodal logics (called ‘acyclic). On the other hand, we present a simple counterexample of a polymodal logic with the f.m.p. which is not strongly ne...

The product of converse PDL and polymodal K

The product of two modal logics L1 and L2 is the modal logic determined by the class of frames of the form F G such that F and G validate L1 and L2, respectively. This paper proves the decidability of the product of converse PDL and polymodal K. Decidability results for products of modal logics of knowledge as well as temporal logics and polymodal K are discussed. All those products form rather...

PSPACE-decidability of Japaridze's polymodal logic

In this paper we prove that Japaridze’s Polymodal Logic is PSPACE-decidable. To show this, we describe a decision procedure for satisfiability on hereditarily ordered frames that can be applied to obtain upper complexity bounds for various modal logics.

Simulation of Modal Logics with Polymodal Logics

Normal Monomodal Logics Can Simulate All Others

This paper shows that non{normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be re ected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of n...