Luis Fariñas del Cerro Olivier Gasquet MINIMAL STRUCTURES FOR MODAL TABLEAUX : Some Examples

MINIMAL STRUCTURES FOR MODAL TABLEAUX: Some Examples

In this paper we present some examples of decision procedures based on tableau calculus for some monoand multimodal logics having a semantics involving properties that are not easily representable in tree-like structures (like e.g. density, confluence and persistence). We show how to handle them in our framework by generalizing usual tableaux (which are trees) to richer structures: rooted direc...

Tableaux Based Decision Procedures for Modal Logics of Confluence and Density

Modal Tableaux with Propagation Rules and Structural Rules

In this paper we generalize the existing tableau methods for modal logics. First of all, while usual modal tableaux are based on trees, our basic structures are rooted directed acyclic graphs (RDAG). This allows natural tableau rules for some modal logics that are diicult to capture in the usual way (such as those having an accessibility relation that is dense or connuent). Second, tableau rule...

Complete axiomatization of a relative modal logic with composition and intersection

We consider the question of the complete axiomatization of a relative modal logic with composition and intersection.

Logics of Contingency

We introduce the logic of positive and negative contingency. Together with modal operators of necessity and impossibility they allow to dispense of negation. We study classes of Kripke models where the number of points is restricted, and show that the modalities reduce in the corresponding logics.