TY - JOUR
T1 - Unified inverse correspondence for LE-logics
AU - Palmigiano, Alessandra
AU - Panettiere, Mattia
N1 - Publisher Copyright:
© 2025
PY - 2026/1
Y1 - 2026/1
N2 - We generalize Kracht's theory of internal describability from classical modal logic to the family of all logics canonically associated with varieties of normal lattice expansions (LE algebras). We work in the purely algebraic setting of perfect LEs; the formulas playing the role of Kracht's formulas in this generalized setting pertain to a first order language whose atoms are special inequalities between terms of perfect algebras. Via duality, formulas in this language can be equivalently translated into first order conditions in the frame correspondence languages of several types of relational semantics for LE-logics.
AB - We generalize Kracht's theory of internal describability from classical modal logic to the family of all logics canonically associated with varieties of normal lattice expansions (LE algebras). We work in the purely algebraic setting of perfect LEs; the formulas playing the role of Kracht's formulas in this generalized setting pertain to a first order language whose atoms are special inequalities between terms of perfect algebras. Via duality, formulas in this language can be equivalently translated into first order conditions in the frame correspondence languages of several types of relational semantics for LE-logics.
KW - Inverse correspondence
KW - Kracht's theory
KW - LE-logics
KW - Non-classical logics
KW - Unified correspondence
UR - https://www.scopus.com/pages/publications/105011263365
UR - https://www.scopus.com/inward/citedby.url?scp=105011263365&partnerID=8YFLogxK
U2 - 10.1016/j.apal.2025.103635
DO - 10.1016/j.apal.2025.103635
M3 - Article
AN - SCOPUS:105011263365
SN - 0168-0072
VL - 177
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 1
M1 - 103635
ER -