Paraconsistent Gödel Modal Logic

Autoři: Mgr. Marta Bílková, Ph.D.
Rok vydání: 2022
Typ publikace: Konferenční příspěvek (mezinárodní konf.)
Periodikum: Automated Reasoning: 11th International Joint Conference, IJCAR 2022 Proceedings
Projekty: Metamatematika substrukturálních modálních logik
Bibliografická citace: BÍLKOVÁ, Marta, FRITTELLA, S., KOZHEMIACHENKO, D. Paraconsistent Gödel Modal Logic. In: BLANCHETTE, J., KOVÁCS, L., PATTINSON, D., eds. Automated Reasoning: 11th International Joint Conference, IJCAR 2022 Proceedings. Cham: Springer, 2022, S. 429-448. Lecture Notes in Computer Science, 13385. ISBN 978-3-031-10768-9
Dostupné z: doi:10.1007/978-3-031-10769-6_26
DOI: 10.1007/978-3-031-10769-6_26
ID: 560973

Abstrakt

We introduce a paraconsistent modal logic KG2, based on Gödel logic with coimplication (bi-Gödel logic) expanded with a De Morgan negation ¬. We use the logic to formalise reasoning with graded, incomplete and inconsistent information. Semantics of KG2 is two-dimensional: we interpret KG2 on crisp frames with two valuations v1 and v2, connected via ¬, that assign to each formula two values from the real-valued interval [0, 1]. The first (resp., second) valuation encodes the positive (resp., negative) information the state gives to a statement. We obtain that KG2 is strictly more expressive than the classical modal logic K by proving that finitely branching frames are definable and by establishing a faithful embedding of K into KG2. We also construct a constraint tableau calculus for KG2 over finitely branching frames, establish its decidability and provide a complexity evaluation