Related papers: A Cut-free sequent calculus for modal logic S5
We introduce a sequent calculus for the propositional team logic with both the split disjunction and the inquisitive disjunction consisting of a Gentzen-style system (G3-like) for classical propositional logic together with two…
We present a rooted hypersequent calculus for modal propositional logic S5. We show that all rules of this calculus are invertible and that the rules of weakening, contraction, and cut are admissible. Soundness and completeness are…
A contraction-free and cut-free sequent calculus $\msf{G3SDM}$ for semi-De Morgan algebras, and a structural-rule-free and single-succedent sequent calculus $\msf{G3DM}$ for De Morgan algebras are developed. The cut rule is admissible in…
G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic…
We investigate a recent proposal for modal hypersequent calculi. The interpretation of relational hypersequents incorporates an accessibility relation along the hypersequent. These systems give the same interpretation of hypersequents as…
A cut-free G3-style sequent calculus GWFN2 for the subintuitionistic logic WFN2, along with its single-succedent variant GWFsN2, is introduced. The calculus GWFN2 is shown to extend naturally to a G3-style of the sequent calculus GF for…
This paper proposes a basic proof theoretic framework for major modal logics: {\sf S5} and some of its subsystems. The framework is based on a version of hypersequent calculus, and the basic modal systems we handle here are the system {\sf…
The finite model property of quasi-transitive modal logic $\mathsf{K}_2^3=\mathsf{K}\oplus \Box\Box p\rightarrow \Box\Box\Box p$ is established. This modal logic is conservatively extended to the tense logic $\mathsf{Kt}_2^3$. We present a…
Two Gentzen-style twist sequent calculi for the normal modal logic S4 are introduced and investigated. The proposed calculi, which do not employ the standard logical inference rules for the negation connective, are characterized by several…
This document serves as a companion to the paper of the same title, wherein we introduce a Gentzen-style sequent calculus for HXPathD. It provides full technical details and proofs from the main paper. As such, it is intended as a reference…
We introduce labelled sequent calculi for quantified modal logics with definite descriptions. We prove that these calculi have the good structural properties of G3-style calculi. In particular, all rules are height-preserving invertible,…
As part of a broader family of logics, [1, 3] introduced two key logical systems: $\mathsf{iK_{d}}$, which encapsulates the basic logical structure of dynamic topological systems, and $\mathsf{iK_{d*}}$, which provides a well-behaved yet…
We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…
We introduce a sequent calculus for the temporal-over-topological fragment $\textbf{DTL}_{0}^{\circ * \slash \Box}$ of dynamic topological logic $\textbf{DTL}$, prove soundness semantically, and prove completeness syntactically using the…
We introduce a new Gentzen-style framework of grafted hypersequents that combines the formalism of nested sequents with that of hypersequents. To illustrate the potential of the framework, we present novel calculi for the modal logics…
This paper introduces two sequent calculi for intuitionistic strong L\"ob logic ${\sf iSL}_\Box$: a terminating sequent calculus ${\sf G4iSL}_\Box$ based on the terminating sequent calculus ${\sf G4ip}$ for intuitionistic propositional…
In this paper we present a cut-free sequent calculus, called SeqS, for some standard conditional logics, namely CK, CK+ID, CK+MP and CK+MP+ID. The calculus uses labels and transition formulas and can be used to prove decidability and space…
This paper studies nested sequents for quantified modal logics. In particular, it considers extensions of the propositional modal logics definable by the axioms D, T, B, 4, and 5 with varying, increasing, decreasing, and constant domains.…
We show that first-order logic can be translated into a very simple and weak logic, and thus set theory can be formalized in this weak logic. This weak logical system is equivalent to the equational theory of Boolean algebras with three…
This paper introduces a refinement of the sequent calculus approach called cirquent calculus. While in Gentzen-style proof trees sibling (or cousin, etc.) sequents are disjoint sequences of formulas, in cirquent calculus they are permitted…