Related papers: A Sequent Calculus for Dynamic Topological Logic
Dynamic Topological Logic ($\mathcal{DTL}$) is a combination of $\mathcal{S}${\em 4}, under its topological interpretation, and the temporal logic $\mathcal{LTL}$ interpreted over the natural numbers. $\mathcal{DTL}$ is used to reason about…
We consider G\"odel temporal logic ($\sf GTL$), a variant of linear temporal logic based on G\"odel--Dummett propositional logic. In recent work, we have shown this logic to enjoy natural semantics both as a fuzzy logic and as a…
Dynamic topological logic ($\mathbf{DTL}$) is a trimodal logic designed for reasoning about dynamic topological systems. It was shown by Fern\'andez-Duque that the natural set of axioms for $\mathbf{DTL}$ is incomplete, but he provided a…
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…
Topological semantics for modal logic based on the Cantor derivative operator gives rise to derivative logics, also referred to as d-logics. Unlike logics based on the topological closure operator, d-logics have not previously been studied…
Topological semantics for modal logic based on the Cantor derivative operator gives rise to derivative logics, also referred to as $d$-logics. Unlike logics based on the topological closure operator, $d$-logics have not previously been…
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…
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for…
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…
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…
Dynamic topological logic (DTL) is a polymodal logic designed for reasoning about {\em dynamic topological systems. These are pairs (X,f), where X is a topological space and f:X->X is continuous. DTL uses a language L which combines the…
Temporal reasoning with conditionals is more complex than both classical temporal reasoning and reasoning with timeless conditionals, and can lead to some rather counter-intuitive conclusions. For instance, Aristotle's famous "Sea Battle…
In a previously published ENTCS paper (Santos et al. (2016)), we introduced a sequent calculus called $\mathbf{LMT^{\rightarrow}}$ for Minimal Implicational Propositional Logic ($\mathbf{LMT^{\rightarrow}}$). This calculus provides a proof…
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…
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…
We present the system G3S5, a Gentzen-style sequent calculus system for the modal propositional logic S5, which in a sense has the subformula property. We formulate the rules of G3 S5 in the system G3S5; which has the subformula property…
Extending and generalizing the approach of 2-sequents (Masini, 1992), we present sequent calculi for the classical modal logics in the K, D, T, S4 spectrum. The systems are presented in a uniform way-different logics are obtained by tuning…
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…
We develop a timeout based extension of propositional linear temporal logic (which we call TLTL) to specify timing properties of timeout based models of real time systems. TLTL formulas explicitly refer to a running global clock together…
We propose a cut-free cyclic system for Transitive Closure Logic (TCL) based on a form of hypersequents, suitable for automated reasoning via proof search. We show that previously proposed sequent systems are cut-free incomplete for basic…