Related papers: Esakia's theorem for the amended monadic intuition…
In a 1985 commentary to his collected works, Kolmogorov remarked that his 1932 paper "was written in hope that with time, the logic of solution of problems [i.e., intuitionistic logic] will become a permanent part of a [standard] course of…
We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal…
In this note we discuss a variant of linear logic with idempotent exponential modalities. We propose a sequent calculus system and discuss its semantics. We also give a concrete relational model for this calculus.
We study an intuitionistic version of common knowledge logic (CK), called ICK, which was introduced by J\"ager and Marti. ICK extends intuitionistic propositional logic (IPL) by multiple box modalities interpreted as knowledge operators for…
We investigate intuitionistic modal logics with locally interpreted $\square$ and $\lozenge$. The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
For each natural number $n$ we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than $n$ and no strictly ascending chains. The case $n=0$ is the G\"odel-L\"ob…
We investigate the logical structure of intuitionistic Kripke-Platek set theory IKP, and show that the first-order logic of IKP is intuitionistic first-order logic IQC.
We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…
Partial Combinatory Algebras (PCAs) provide a foundational model of the untyped $\lambda$-calculus and serve as the basis for many notions of computability, such as realizability theory. However, PCAs support a very limited notion of…
Consider a linear ordering equipped with a finite sequence of monadic predicates. If the ordering contains an interval of order type \omega or -\omega, and the monadic second-order theory of the combined structure is decidable, there exists…
We study the structure of the Eisenstein component of Hida's ordinary p-adic Hecke algebra attached to modular forms, in connection with the companion forms in the space of modular forms (mod p). We show that such an algebra is a Gorenstein…
We investigate the set-theoretic strength of several maximality principles that play an important role in the study of modal and intuitionistic logics. We focus on the well-known Fine and Esakia maximality principles, present two…
Intuitionistic conditional logic, studied by Weiss, Ciardelli and Liu, and Olkhovikov, aims at providing a constructive analysis of conditional reasoning. In this framework, the would and the might conditional operators are no longer…
In this paper, a proof-theoretic method to prove uniform Lyndon interpolation for non-normal modal and conditional logics is introduced and applied to show that the logics $\mathsf{E}$, $\mathsf{M}$, $\mathsf{EN}$, $\mathsf{MN}$,…
With the aim of studying social properties of belief merging and having a better understanding of impossibility, we extend in three ways the framework of logic-based merging introduced by Konieczny and Pino P\'erez. First, at the level of…
This paper builds on the recent ASPIC+ formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC+ to accommodate a broader range of…
Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality $!_r$ captures how many times a…
We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…