Intuitionistic non-normal modal logics: A general framework

Autor: Charles Grellois, Nicola Olivetti, Tiziano Dalmonte
Přispěvatelé: 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), Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU), 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), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Dalmonte, Tiziano
Jazyk: angličtina
Rok vydání: 2020
Předmět:
FOS: Computer and information sciences
Computer Science - Logic in Computer Science
[INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO]
Computer science
[INFO] Computer Science [cs]
Modal operator
0603 philosophy
ethics and religion
01 natural sciences
Constructive
Computer Science::Logic in Computer Science
FOS: Mathematics
[INFO]Computer Science [cs]
0101 mathematics
03B45
010102 general mathematics
Sequent calculus
Semantic framework
[INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO]
06 humanities and the arts
Mathematics - Logic
Logic in Computer Science (cs.LO)
Decidability
Algebra
Philosophy
Modal
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES
TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS
060302 philosophy
Dynamic logic (modal logic)
Non normality
Logic (math.LO)
Zdroj: Journal of Philosophical Logic
Journal of Philosophical Logic, Springer Verlag, 2020
Journal of Philosophical Logic, 2020
ISSN: 0022-3611
1573-0433
Popis: We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider the more important case of bimodal logics, which contain both modal operators. In this case we define several interactions between Necessity and Possibility of increasing strength, although weaker than duality. For all logics we provide both a Hilbert axiomatisation and a cut-free sequent calculus, on its basis we also prove their decidability. We then give a semantic characterisation of our logics in terms of neighbourhood models. Our semantic framework captures modularly not only our systems but also already known intuitionistic non-normal modal logics such as Constructive K (CK) and the propositional fragment of Wijesekera's Constructive Concurrent Dynamic Logic.
Preprint
Databáze: OpenAIRE
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