相关论文: Correspondence, Canonicity, and Model Theory for M…

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…

The unification problem in a propositional logic is to determine, given a formula F, whether there exists a substitution s such that s(F) is in that logic. In that case, s is a unifier of F. When a unifiable formula has minimal complete…

We relate the cohomology of the Orlik-Solomon algebra of a discriminantal arrangement to the local system cohomology of the complement. The Orlik-Solomon algebra of such an arrangement (viewed as a complex) is shown to be a linear…

We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we…

Localic relations are relations internal to the category of locales, forming the point-free analogues of set-theoretic relations, and providing the general backdrop of localic order theory. This work studies 'open cone' localic relations,…

This paper belongs to the field of probabilistic modal logic, focusing on a comparative analysis of two distinct semantics: one rooted in Kripke semantics and the other in neighbourhood semantics. The primary distinction lies in the…

We study what we call topological cylindric algebras and tense cylindric algebras defined for every ordinal $\alpha$. The former are cylindric algebras of dimension $\alpha$ expanded with $\sf S4$ modalities indexed by $\alpha$. The…

The paper presents a solution to the long-standing question about the decidability of the two-variable fragment of the superintuitionistic predicate logic $\mathbf{QLC}$ defined by the class of linear Kripke frames, which is also the…

Canonical relativized cylindric set algebras are used to sharpen the relative representation theorem for weakly associative relation algebras, that every complete atomic weakly associative relation algebra is isomorphic with the…

Modal logic with propositional quantifiers (i.e. second-order propositional modal logic (SOPML)) has been considered since the early time of modal logic. Its expressive power and complexity are high, and its van-Benthem-Rosen theorem and…

We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory. Specifically, we show that the power of several propositional proof systems, such as Horn resolution, bounded-width…

For any 1-reduced simplicial set $K$ we define a canonical, coassociative coproduct on $\Om C(K)$, the cobar construction applied to the normalized, integral chains on $K$, such that any canonical quasi-isomorphism of chain algebras from…

Coalgebra, as the abstract study of state-based systems, comes naturally equipped with a notion of behavioural equivalence that identifies states exhibiting the same behaviour. In many cases, however, this equivalence is finer than the…

We introduce the operation of possibility qualification and show how. this modal-like operator can be used to represent "typical" or default knowledge in a theory of nonmonotonic reasoning. We investigate the representational power of this…

In this Master's thesis, we consider the problem of classifying, up to conjugation by linear symplectomorphisms, linear canonical relations (lagrangian correspondences) from a finite-dimensional symplectic vector space to itself. We give an…

Let K be an abstract elementary classes which has arbitrarily large models and satisfies the amalgamation and joint embedding properties. Theorem 1. Suppose K is \chi-tame. If K is categorical in some \lambda^+ >LS(K) then it is categorical…

We construct phase-space structure of a typical higher-order theory of gravity, in the background of anisotropic Bianchi-1 mini-superspace, following `Modified Horowitz Formalism' as well as applying `Dirac Algorithm' (after taking care of…

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…

J{\'o}nsson and Tarski's notion of the perfect extension of a Boolean algebra with operators has evolved into an extensive theory of canonical extensions of lattice-based algebras. After reviewing this evolution we make two contributions.…

This paper extends the fundamental results of frame theory to a non-commutative setting where the role of locales is taken over by \'etale localic categories. This involves ideas from quantale theory and from semigroup theory, specifically…