A modal logic for Pawlak's approximation spaces with rough cardinality n - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Article Dans Une Revue Fundamenta Informaticae Année : 2008

A modal logic for Pawlak's approximation spaces with rough cardinality n

Résumé

The natural modal logic corresponding to Pawlak's approximation spaces is S5, based on the box modality [R]A (and the diamond modality 〈R〉A=¬[R]¬A), where R is the corresponding indiscernibility relation of the approximation space S=(W,R). However the expressive power of S5 is too weak and, for instance, we cannot express that the space S has exactly n equivalence classes (we say that S is roughly-finite and n is the rough cardinality of S). For this reason we extend the modal logic S5 with a new box modality [S]A, where S is the complement of R i.e. the discernibility relation of W. We propose a complete axiomatization, in this new language, of the logic ROUGH^n corresponding to the class of approximation spaces with rough cardinality n. We prove that the satisfiability problem for ROUGH^n is NP-complete.
Fichier non déposé

Dates et versions

hal-04000446 , version 1 (22-02-2023)

Identifiants

  • HAL Id : hal-04000446 , version 1

Citer

Philippe Balbiani, Petar Iliev, Dimiter Vakarelov. A modal logic for Pawlak's approximation spaces with rough cardinality n. Fundamenta Informaticae, 2008, 83 (4), pp.451--464. ⟨hal-04000446⟩
12 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More