Related papers: Modal logic with the difference modality of topolo…

The Halpern-Shoham logic is a modal logic of time intervals. Some effort has been put in last ten years to classify fragments of this beautiful logic with respect to decidability of its satisfiability problem. We contribute to this effort…

We present deductive systems for various modal logics that can be obtained from the constructive variant of the normal modal logic CK by adding combinations of the axioms d, t, b, 4, and 5. This includes the constructive variants of the…

I introduce modal group theory, in which we study the category of all groups, considering embeddability as providing a notion of modal possibility. Using HNN extensions and Britton's lemma, I demonstrate that the modal language of groups is…

Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality…

The paper investigates an evidence-based semantics for epistemic logics. It is shown that the properties of knowledge obtained from a potentially infinite body of evidence are described by modal logic S5. At the same time, the properties of…

This paper aims at providing a comprehensive solution to the archaic open problem: how to define semantics of three-valued modal logic with vivid intuitive picture, convincing philosophical justification as well as versatile practical…

Finite topological spaces became much more essential in topology, with the development of computer science. The task of this paper is to study and investigate some properties of such spaces with the existence of an ordered relation between…

We investigate the expressivity and computational complexity of two modal logics on finite forests equipped with operators to reason on submodels. The logic ML(|) extends the basic modal logic ML with the composition operator | from static…

Even in spaces of formal power series is required a topology in order to legitimate some operations, in particular to compute infinite summations. Many topologies can be exploited for different purposes. Combinatorists and algebraists may…

Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…

Executing complex manipulation in cluttered environments requires satisfying coupled geometric and temporal constraints. Although Spatio-Temporal Logic (SpaTiaL) offers a principled specification framework, its use in gradient-based…

In arXiv:1604.08705 we introduced the propositional modal logic $\textbf{TSC}$ (which stands for Turing Schmerl Calculus) which adequately describes the provable interrelations between different kinds of Turing progressions. In…

The boxdot conjecture asserts that every normal modal logic that faithfully interprets T by the well-known boxdot translation is in fact included in T. We confirm that the conjecture is true. More generally, we present a simple semantic…

Doctrines are categorical structures very apt to study logics of different nature within a unified environment: the 2-category Dtn of doctrines. Modal interior operators are characterised as particular adjoints in the 2-category Dtn. We…

A modal logic based on quantum logic is formalized in its simplest possible form. Specifically, a relational semantics and a sequent calculus are provided, and the soundness and the completeness theorems connecting both notions are…

We propose modal Markov logic as an extension of propositional Markov logic to reason under the principle of maximum entropy for modal logics K45, KD45, and S5. Analogous to propositional Markov logic, the knowledge base consists of…

Hybrid logic extends modal logic with special propositions called nominals, each of which is true at only one state in a model. This enables us to describe some properties of binary relations, such as irreflexivity and anti-symmetry, which…

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 describe a family of decidable propositional dynamic logics, where atomic modalities satisfy some extra conditions (for example, given by axioms of the logics K5, S5, or K45 for different atomic modalities). It follows from recent…

The Vietoris space of a Stone space plays an important role in the coalgebraic approach to modal logic. When generalizing this to positive modal logic, there is a variety of relevant hyperspace constructions based on various topologies on a…