Algebraic Semantics for One-Variable Lattice-Valued Logics

0560680 - ÚI 2024 RIV GB eng C - Konferenční příspěvek (zahraniční konf.)
Cintula, Petr - Metcalfe, G. - Tokuda, N.
Algebraic Semantics for One-Variable Lattice-Valued Logics.
Advances in Modal Logic. Volume 14. London: College Publications, 2022 - (Fernández-Duque, D.; Palmigiano, A.; Pinchinat, S.), s. 237-257. ISBN 978-1-84890-413-2.
[AIML 2022: Advances in Modal Logic. Rennes (FR), 22.08.2022-25.08.2022]
Grant CEP: GA ČR(CZ) GA22-01137S
Institucionální podpora: RVO:67985807
Klíčová slova: Modal Logic * Substructural Logics * Lattice-Valued Logics * One-Variable Fragment * Superamalgamation * Sequent Calculus * Interpolation
Obor OECD: Pure mathematics
http://www.collegepublications.co.uk/aiml/?00011

The one-variable fragment of any first-order logic may be considered as a modal logic, where the universal and existential quantifiers are replaced by a box and diamond modality, respectively. In several cases, axiomatizations of algebraic semantics for these logics have been obtained: most notably, for the modal counterparts S5 and MIPC of the one-variable fragments of first-order classical logic and intuitionistic logic, respectively. Outside the setting of first-order intermediate logics, however, a general approach is lacking. This paper provides the basis for such an approach in the setting of first-order lattice-valued logics, where formulas are interpreted in algebraic structures with a lattice reduct. In particular, axiomatizations are obtained for modal counterparts of one-variable fragments of a broad family of these logics by generalizing a functional representation theorem of Bezhanishvili and Harding for monadic Heyting algebras. An alternative proof-theoretic proof is also provided for one-variable fragments of first-order substructural logics that have a cut-free sequent calculus and admit a certain bounded interpolation property
Trvalý link: https://hdl.handle.net/11104/0333542