Algebraic Semantics for One-Variable Lattice-Valued Logics

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00560680" target="_blank" >RIV/67985807:_____/22:00560680 - isvavai.cz</a>
Result on the web
<a href="http://www.collegepublications.co.uk/aiml/?00011" target="_blank" >http://www.collegepublications.co.uk/aiml/?00011</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Algebraic Semantics for One-Variable Lattice-Valued Logics
Original language description
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
Czech name
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Czech description
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Project
<a href="/en/project/GA22-01137S" target="_blank" >GA22-01137S: Metamathematics of substructural modal logics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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