Non-normal modal logics: bi-neighbourhood semantics and its labelled calculi
| Autor: | Dalmonte, Tiziano, Olivetti, Nicola, Negri, Sara |
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| Přispěvatelé: | Laboratoire des Sciences de l'Information et des Systèmes (LSIS), Centre National de la Recherche Scientifique (CNRS)-Arts et Métiers Paristech ENSAM Aix-en-Provence-Université de Toulon (UTLN)-Aix Marseille Université (AMU), Logique, Interaction, Raisonnement et Inférence, Complexité, Algèbre (LIRICA), Laboratoire d'Informatique et Systèmes (LIS), Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU), Aix Marseille Université (AMU), University of Helsinki, Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Arts et Métiers Paristech ENSAM Aix-en-Provence-Centre National de la Recherche Scientifique (CNRS), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Helsingin yliopisto = Helsingfors universitet = University of Helsinki |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
[MATH.MATH-LO]Mathematics [math]/Logic [math.LO]
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Non-normal modal logic TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS Computer Science::Logic in Computer Science Labelled sequent calculi Computer Science::Programming Languages [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO] ComputingMethodologies_GENERAL Neighbourhood semantics |
| Zdroj: | Advances in Modal Logic 2018 Advances in Modal Logic 2018, Aug 2018, Berne, Switzerland |
| Popis: | International audience; The classical cube of non-normal modal logics is considered, and an alternative neighbourhood semantics is given in which worlds are equipped with sets of pairs of neighbourhoods. The intuition is that the two neighbourhoods of a pair provide independent positive and negative evidence (or support) for a formula. This bi-neighbourhood semantics is significant in particular for logics without the monotonicity property. It is shown that this semantics characterises the cube of non-normal modal logics and that there is a mutual correspondence between models in the standard and in the bi-neighbourhood semantics. On the basis of this alternative semantics, labelled sequent calculi are developed for all the logics of the classical cube. The calculi thus obtained are fully modular and have good structural properties, first of all, syntactic cut elimination. Moreover, they provide a decision procedure and an easy countermodel extraction, both in the bi-neighbourhood and in the standard semantics. |
| Databáze: | OpenAIRE |
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