## An Overview on Quasi Hybrid Logic

(Diana Costa, Universidade de Aveiro)

Hybrid logic is a valuable tool for specifying relational structures: at the same time that it allows defining accessibility relations between states, it provides a way to name and mention what happens at each specific state.

As in standard knowledge bases, hybrid knowledge bases (i.e., sets of information specified by hybrid formulas) may contain inconsistencies coming from different sources, namely from the very mechanisms used to collect the relevant information. Being a fact, rather than a queer anomaly, inconsistency also needs to be addressed in the context of hybrid logic applications. I will introduce a paraconsistent version of hybrid logic which is able to accommodate inconsistencies at local points without implying global failure. A main feature of the resulting logic, crucial to our approach, is the fact that every hybrid formula has an equivalent formula in negation normal form. It will also be defined a measure to quantify the inconsistency of a hybrid knowledge base, useful as a possible basis for comparing knowledge bases.

The presentation will end with the introduction of proof-theoretical aspects, namely it will be presented a complete tableau system for Quasi-hybrid logic, by combining both tableaux for Quasi-classical and Hybrid logics.

Click for slides.

As in standard knowledge bases, hybrid knowledge bases (i.e., sets of information specified by hybrid formulas) may contain inconsistencies coming from different sources, namely from the very mechanisms used to collect the relevant information. Being a fact, rather than a queer anomaly, inconsistency also needs to be addressed in the context of hybrid logic applications. I will introduce a paraconsistent version of hybrid logic which is able to accommodate inconsistencies at local points without implying global failure. A main feature of the resulting logic, crucial to our approach, is the fact that every hybrid formula has an equivalent formula in negation normal form. It will also be defined a measure to quantify the inconsistency of a hybrid knowledge base, useful as a possible basis for comparing knowledge bases.

The presentation will end with the introduction of proof-theoretical aspects, namely it will be presented a complete tableau system for Quasi-hybrid logic, by combining both tableaux for Quasi-classical and Hybrid logics.

Click for slides.