Related papers: Modal logic of planar polygons
Taking inspiration from the monadicity of complete atomic Boolean algebras, we prove that profinite modal algebras are monadic over Set. While analyzing the monadic functor, we recover the universal model construction - a construction…
We show that if we enrich first order logic by allowing quantification over isomorphisms between definable ordered fields the resulting logic, L(Q_{Of}), is fully compact. In this logic, we can give standard compactness proofs of various…
We provide a characterization of those relation algebras which are isomorphic to the algebras of compatible relations of some $\Z_2$-set. We further prove that this class is finitely axiomatizable in first-order logic in the language of…
We study the topological $\mu$-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over $T_0$ and $T_D$ spaces. We also investigate…
We study the completeness problem for propositionally quantified modal logics on quantifiable general frames, where the admissible sets are the propositions the quantifiers can range over and expressible sets of worlds are admissible, and…
It is known that many modal and superintuitionistic logics are PSPACE-hard in languages with a small number of variables; however, questions about the complexity of similar fragments of many logics obtained by adding various axioms to…
We study the logic FO(~), the extension of first-order logic with team semantics by unrestricted Boolean negation. It was recently shown axiomatizable, but otherwise has not yet received much attention in questions of computational…
In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form $\forall x_0 \exists x_1 \dots \exists x_n \bigwedge x_i R_\lambda x_j$. We prove that many properties of these logics, such…
We consider quantified pretransitive Horn modal logic. It is known that such logics are complete with respect to predicate Kripke frames with expanding domains. In this paper we prove that they are also complete with respect to…
We introduce a modal logic, called Cone Logic, whose formulas describe properties of points in the plane and spatial relationships between them. Points are labelled by proposition letters and spatial relations are induced by the four…
We develop a method for showing that various modal logics that are valid in their countably generated canonical Kripke frames must also be valid in their uncountably generated ones. This is applied to many systems, including the logics of…
I investigate modal group theory for arbitrary homomorphisms. Possibility is interpreted by the existence of a group homomorphism out of the given group, so the semantics is governed by the possibility of collapse: elements may be…
A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames have already been established. By "traditional" classes of frames, we mean those…
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…
Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces satisfying all the axioms of GLP are…
Hybrid logic is a modal logic with additional operators specifying nominals and is highly expressive. For example, there is no formula corresponding to the irreflexivity of Kripke frames in basic modal logic, but there is in hybrid logic.…
This paper is an exposition of the completion of a modular group with respect to its inclusion into SL_2(Q) and the connection with the theory of modular forms and variations of mixed Hodge structure over modular curves. Among the goals of…
Polyhedral semantics is a recently introduced branch of spatial modal logic, in which modal formulas are interpreted as piecewise linear subsets of an Euclidean space. Polyhedral semantics for the basic modal language has already been well…
We prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…