Related papers: Modal reduction principles across relational seman…
Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly…
Narrowing extends term rewriting with the ability to search for solutions to equational problems. While first-order rewriting and narrowing are well studied, significant challenges arise in the presence of binders, freshness conditions and…
Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent computations where code usage plays a central role. The theory of program equivalence for modal and coeffectful languages, however, is…
In Outline of a Theory of Truth, Kripke introduces some of the central concepts of the logical study of truth and paradox. He informally defines some of these -- such as groundedness and paradoxicality -- using modal locutions. We introduce…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
This paper deals with many-valued modal logics, based only on the necessity operator, over a residuated lattice. We focus on three basic classes, according to the accessibility relation, of Kripke frames: the full class of frames evaluated…
We present a clausal resolution-based method for normal multimodal logics of confluence, whose Kripke semantics are based on frames characterised by appropriate instances of the Church-Rosser property. Here we restrict attention to eight…
Achieving high-performance in multi-object tracking algorithms heavily relies on modeling spatio-temporal relationships during the data association stage. Mainstream approaches encompass rule-based and deep learning-based methods for…
We introduce categorical modularity, a novel low-resource intrinsic metric to evaluate word embedding quality. Categorical modularity is a graph modularity metric based on the $k$-nearest neighbor graph constructed with embedding vectors of…
We define and axiomatize three new logics based on the connexive logic $\mathsf{C}$, the modal logic $\mathsf{CnK}$ and the conditional logics $\mathsf{CnCK}$ and $\mathsf{CnCK}_R$. These logics display strong connexivity properties and are…
One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…
In multi-user semantic communication, language mismatche poses a significant challenge when independently trained agents interact. We present a novel semantic equalization algorithm that enables communication between agents with different…
Multi-role dialogue summarization requires modeling complex interactions among multiple speakers while preserving role-specific information and factual consistency. However, most existing methods optimize for automatic metrics such as ROUGE…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
Let $K$ be an algebraically closed field of arbitrary characteristic, $X$ an irreducible variety and $Y$ an irreducible projective variety over $K$, both are not necessarily smooth. Let $f:X\rightarrow X$ and $g:Y\rightarrow Y$ be dominant…
The identification of semantic relations between terms within texts is a fundamental task in Natural Language Processing which can support applications requiring a lightweight semantic interpretation model. Currently, semantic relation…
First-Order Logic (FOL), also called first-order predicate calculus, is a formal language that provides a framework to comprehensively represent a world and its present state, including all of its entities, attributes, and complex…
In the present paper, we study the correspondence and canonicity theory of modal subordination algebras and their dual Stone space with two relations, generalizing correspondence results for subordination algebras in…
We extend the theory of unified correspondence to a very broad class of logics with algebraic semantics given by varieties of normal lattice expansions (LEs), also known as `lattices with operators'. Specifically, we introduce a very…
We initiate the study of correspondences for Smale spaces. Correspondences are shown to provide a notion of a generalized morphism between Smale spaces and are a special case of finite equivalences. Furthermore, for shifts of finite type, a…