TY - GEN
T1 - Correspondence Theory on Vector Spaces
AU - Palmigiano, Alessandra
AU - Panettiere, Mattia
AU - Switrayni, Ni Wayan
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - This paper extends correspondence theory to the framework of K-algebras, i.e. vector spaces endowed with a bilinear operation, seen as ‘Kripke frames’. For every K-algebra, the lattice of its subspaces can be endowed with the structure of a complete (non necessarily monoidal) residuated lattice. Hence, a sequent of the logic of residuated lattices can be interpreted as a property of its lattice of subspaces. Thus, correspondence theory can be developed between the propositional language of this logic and the first order language of K-algebras, analogously to the well known correspondence theory between classical normal modal logic and the first-order language of Kripke frames. In this paper, we develop such a theory for the class of analytic inductive inequalities.
AB - This paper extends correspondence theory to the framework of K-algebras, i.e. vector spaces endowed with a bilinear operation, seen as ‘Kripke frames’. For every K-algebra, the lattice of its subspaces can be endowed with the structure of a complete (non necessarily monoidal) residuated lattice. Hence, a sequent of the logic of residuated lattices can be interpreted as a property of its lattice of subspaces. Thus, correspondence theory can be developed between the propositional language of this logic and the first order language of K-algebras, analogously to the well known correspondence theory between classical normal modal logic and the first-order language of Kripke frames. In this paper, we develop such a theory for the class of analytic inductive inequalities.
KW - Correspondence theory
KW - Non classical logics
KW - Residuated lattices
KW - Vector spaces
UR - http://www.scopus.com/inward/record.url?scp=85196740670&partnerID=8YFLogxK
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U2 - 10.1007/978-3-031-62687-6_10
DO - 10.1007/978-3-031-62687-6_10
M3 - Conference contribution
AN - SCOPUS:85196740670
SN - 9783031626869
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 140
EP - 156
BT - Logic, Language, Information, and Computation
A2 - Metcalfe, George
A2 - Studer, Thomas
A2 - de Queiroz, Ruy
PB - Springer Science and Business Media Deutschland GmbH
T2 - 30th International Workshop on Logic, Language, Information and Computation, WoLLIC 2024
Y2 - 10 June 2024 through 13 June 2024
ER -