Perfect IFG-formulas

LE-逻辑的统一逆对应理论

Unified inverse correspondence for LE-logics

本文将Kracht内部可描述性理论推广至正规格扩张逻辑，在完美LE代数框架下建立一阶公式与关系语义框架条件之间的统一对偶翻译。

Lattice-ordered abelian groups and perfect MV-algebras: a topos-theoretic perspective

We establish, generalizing Di Nola and Lettieri's categorical equivalence, a Morita-equivalence between the theory of lattice-ordered abelian groups and that of perfect MV-algebras. Further, after observing that the two theories are not bi-interpretable in the classical sense, we identify, by considering appropriate topos-theoretic invariants on their common classifying topos, three levels of bi-intepretability holding for particular classes of formulas: irreducible formulas, geometric sentences and imaginaries. Lastly, by investigating the classifying topos of the theory of perfect MV-algebra…

Correspondence Theory for Modal Fairtlough-Mendler Semantics of Intuitionistic Modal Logic

We study the correspondence theory of intuitionistic modal logic in modal Fairtlough-Mendler semantics (modal FM semantics) \cite{FaMe97}, which is the intuitionistic modal version of possibility semantics \cite{Ho16}. We identify the fragment of inductive formulas \cite{GorankoV06} in this language and give the algorithm $\mathsf{ALBA}$ \cite{CoPa12} in this semantic setting. There are two major features in the paper: one is that in the expanded modal language, the nominal variables, which are interpreted as atoms in perfect Boolean algebras, complete join-prime elements in perfect distributi…