相关论文: Cluster expansion and the boxdot conjecture

We consider modal logics of products of neighborhood frames and prove that for any pair $L$ and $L'$ of logics from set $\{S4, D4, D, T\}$ modal logic of products of $L$-neighborhood frames and $L'$-neighborhood frames is the fusion of $L$…

In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…

Extending Sellers' result, Das et al. recently proved some congruence results for generalized overcubic partitions using theta functions and posed some related conjectures. In this paper, we provide a combinatorial proof of a result in…

We propose to generalize the volume conjecture to knotted trivalent graphs and we prove the conjecture for all augmented knotted trivalent graphs. As a corollary we find that for any link L there is a link containing L for which the volume…

We prove the Box Conjecture for pairs of commuting nilpotent matrices, as formulated by Iarrobino et al [28]. This describes the Jordan type of the dense orbit in the nilpotent commutator of a given nilpotent matrix. Our main tool is the…

DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…

In this paper, we tell a story about incompleteness in modal logic. The story weaves together a paper of van Benthem, `Syntactic aspects of modal incompleteness theorems,' and a longstanding open question: whether every normal modal logic…

We study the language inclusion problem $L_1 \subseteq L_2$ where $L_1$ is regular or context-free. Our approach relies on abstract interpretation and checks whether an overapproximating abstraction of $L_1$, obtained by overapproximating…

The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an…

In previous work [Lewitzka, Log. J. IGPL 2017], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from G\"odel's interpretation…

In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…

The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely generated modules over a finite-dimensional $\sk$-algebra. They say, roughly speaking, that infinite representation type implies the existence of lots of…

In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as close as possible to the Bayesian and is unrestricted, that is one is able to use any operator without restriction. A notion of…

We show that Grothendieck's standard conjectures are implied by either of two other motivic conjectures: (a) by that of the existence of the motivic t-structure, and (b) by (a weak form of) Suslin's Lawson homology conjecture.

Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and…

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…

This paper addresses one of the fundamental open questions in the realm of existential rules: the conjecture on the finite controllability of bounded derivation depth rule sets (bdd $\Rightarrow$ fc). We take a step toward a positive…

Given a field $K$ and an ample (not necessarily Hausdorff) groupoid $G$, we define the concept of a line bundle over $G$ inspired by the well known concept from the theory of C*-algebras. If $E$ is such a line bundle, we construct the…

The Language of Thought (LOT) hypothesis posits that at least some important cognitive processes involve language-like representations. These representations must be processed by appropriate hardware. Since the organ of biological cognition…

G\"odel's Incompleteness Theorems suggest that no single formal system can capture the entirety of one's mathematical beliefs, while pointing at a hierarchy of systems of increasing logical strength that make progressively more explicit…