On modal logic of deductive closure

On modal logic of deductive closure

A new modal logic D is introduced. It describes properties of provability by interpreting modality as a deductive closure operator on sets of formulas. Logic D is proven to be decidable and complete with respect to this semantics.

On a Four-Valued Modal Logic with Deductive Implication

In this paper we propose to enrich the four-valued modal logic associated to Monteiro’s Tetravalent modal algebras (TMAs) with a deductive implication, that is, such that the Deduction Meta–theorem holds in the resulting logic. All this lead us to establish some new connections between TMAs, symmetric (or involutive) Boolean algebras, and modal algebras for extensions of S5, as well as their lo...

On Modal Deductive Databases

We present a query language called MDatalog, which is an extension of Datalog for multimodal deductive databases. We define modal relational algebras and give the seminaive evaluation algorithm and the magic-set transformation for MDatalog queries. Results of this paper are proved for the multimodal logics of belief KDI4s5, KDI45, KD4s5s, KD45(m), which are extensions of the monomodal logic KD4...

Multimodal Logic Programming and Its Applications to Modal Deductive Databases

Spatial logic of tangled closure operators and modal mu-calculus

There has been renewed interest in recent years in McKinsey and Tarski’s interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the modal mu-calculus and to a logic of tangled closure operators that was developed by Fernández-Duque after these two languages had been shown by Dawar and Ot...