相关论文: A categorical account of composition methods in lo…

We study the structure of the category of representations of $\mathbf{FA}$, the category of finite sets and all maps, mostly working over a field of characteristic zero. This category is not semi-simple and exhibits interesting features. We…

In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures,…

First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type…

We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of…

We classify the homogeneous finite-dimensional permutation structures, i.e., homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification…

In this paper we extend and prove in detail the Finite Rank Theorem for connection matrices of graph parameters definable in Monadic Second Order Logic with counting (CMSOL) from B. Godlin, T. Kotek and J.A. Makowsky (2008) and J.A.…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

A model checking computation checks whether a given logical sentence is true in a given finite structure. Provenance analysis abstracts from such a computation mathematical information on how the result depends on the atomic data that…

Compositionality is thought to be a key component of language, and various compositional benchmarks have been developed to empirically probe the compositional generalization of existing sequence processing models. These benchmarks often…

We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional type theory. The key concept we employ is that of a Lawvere…

Partial methods play an important role in formal methods and beyond. Recently such methods were developed for parity games, where polynomial-time partial solvers decide the winners of a subset of nodes. We investigate here how effective…

Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…

Recently, Baltag and van Benthem arXiv:2103.14946 [cs.LO] introduced a new decidable logic of functional dependence (LFD) with local dependence formulas and dependence quantifiers. The language is interpreted over dependence models, which…

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…

We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and…

While large language models (LLMs) appear to be increasingly capable of solving compositional tasks, it is an open question whether they do so using compositional mechanisms. In this work, we investigate how feedforward LLMs solve two-hop…

In this paper we investigate the complexity-theoretical aspects of cyclic and non-wellfounded proofs in the context of parsimonious logic, a variant of linear logic where the exponential modality ! is interpreted as a constructor for…

Reasoning over tabular data is a crucial capability for tasks like question answering and fact verification, as it requires models to comprehend both free-form questions and semi-structured tables. However, while methods like…

In comparison to graphs, combinatorial methods for the isomorphism problem of finite groups are less developed than algebraic ones. To be able to investigate the descriptive complexity of finite groups and the group isomorphism problem, we…

We propose a new framework for integrating quantifiers with other logical connectives in a higher-categorical setting. Our method systematically incorporates key coherence conditions-including those akin to the Beck-Chevalley property-and…