A Tableau System for Quasi-Hybrid Logic
Hybrid logic is a valuable tool for specifying relational structures, at the same time that allows defining accessibility relations between states, it provides a way to nominate and make mention to what happens at each specific state. However, due to the many sources nowadays available, we may need to deal with contradictory information. This is the reason why we came with the idea of Quasi-hybrid logic, which is a paraconsistent version of hybrid logic capable of dealing with inconsistencies in the information, written as hybrid formulas.
In  we have already developed a semantics for this paraconsistent logic. In this paper we go a step forward, namely we study its proof-theoretical aspects. We present a complete tableau system for Quasi-hybrid logic, by combining both tableaux for Quasi-classical and Hybrid logics.
We are very grateful to J. Marcos for productive discussions, in several related topics, that were very important for achieving the reported results. We would also like to mention that the careful work of the anonymous reviewers have improved the quality of the present paper.
This work was supported in part by the Portuguese Foundation for Science and Technology (FCT) through CIDMA within project UID/MAT/04106/2013 and the project EU FP7 Marie Curie PIRSES-GA-2012-318986 GeTFun: Generalizing Truth-Functionality. Diana Costa also thanks the support of FCT via the Ph.D. scholarship PD/BD/105730/2014, and the Calouste Gulbenkian Foundation through the Research Stimulus Program 2015 (Programa de Estímulo à Investigação 2015).
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