Paraconsistent Gödel Modal Logic

0560973 - ÚI 2023 RIV CH eng C - Conference Paper (international conference)
Bílková, Marta - Frittella, S. - Kozhemiachenko, D.
Paraconsistent Gödel Modal Logic.
Automated Reasoning: 11th International Joint Conference, IJCAR 2022 Proceedings. Cham: Springer, 2022 - (Blanchette, J.; Kovács, L.; Pattinson, D.), s. 429-448. Lecture Notes in Computer Science, 13385. ISBN 978-3-031-10768-9.
[IJCAR 2022: International Joint Conference on Automated Reasoning /11./. Haifa (IL), 08.08.2022-10.08.2022]
R&D Projects: GA ČR(CZ) GA22-01137S
EU Projects: European Commission(XE) 101007627 - MOSAIC
Institutional support: RVO:67985807
Keywords : Constraint tableaux * Gödel logic * Two-dimensional logics * Modal logics
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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
Permanent Link: https://hdl.handle.net/11104/0333737