Constraint Tableaux for Two-Dimensional Fuzzy Logics

Autoři: Mgr. Marta Bílková, Ph.D.
Rok vydání: 2021
Typ publikace: Konferenční příspěvek (mezinárodní konf.)
Periodikum: TABLEAUX 2021: Automated Reasoning with Analytic Tableaux and Related Methods
Bibliografická citace: BÍLKOVÁ, Marta, FRITTELLA, S., KOZHEMIACHENKO, D. Constraint Tableaux for Two-Dimensional Fuzzy Logics. In: DAS, A., NEGRI, S., eds. TABLEAUX 2021: Automated Reasoning with Analytic Tableaux and Related Methods. Cham: Springer, 2021, S. 20-37. Lecture Notes on Computer Science, 12842. ISBN 978-3-030-86058-5. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-030-86059-2_2
DOI: 10.1007/978-3-030-86059-2_2
ID: 547122

Abstrakt

We introduce two-dimensional logics based on Łukasiewicz and Gödel logics to formalize reasoning with graded, incomplete and inconsistent information. The logics are interpreted on matrices, where the common underlying structure is the bi-lattice (twisted) product of the [0, 1] interval. The first (resp. second) coordinate encodes the positive (resp. negative) information one has about a statement. We propose constraint tableaux that provide a modular framework to address their completeness and complexity.