Related papers: A Theory of Conversion Relations for Prefixed Unit…

Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…

Surprisal theory links human processing effort to the predictability of an upcoming linguistic unit, but empirical work often leaves the notion of a unit underspecified. In practice, experimental stimuli are segmented into linguistically…

We introduce the concept of a prenormed model of a particular kind of finitary single-sorted first-order theories, interpreted over a category with finite products. These are referred to as prealgebraic theories, for the fact that their…

We investigate the mathematical structure of unit systems and the relations between them. Looking over the entire set of unit systems, we can find a mathematical structure that is called preorder (or quasi-order). For some pair of unit…

This paper is a brief overview of the concepts involved in measuring the degree of contextuality and detecting contextuality in systems of binary measurements of a finite number of objects. We discuss and clarify the main concepts and…

This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…

This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic…

In this paper we develope a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to…

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…

Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…

We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…

The article explores function terms within uniform theories. It examines the uniformity of these theories through an algebraic lens. The paper compares the uniformity of terms and predicates within axiom schemas. It demonstrates the…

We present a domain-specific type theory for constructions and proofs in category theory. The type theory axiomatizes notions of category, functor, profunctor and a generalized form of natural transformations. The type theory imposes an…

We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…

We use type-theoretic techniques to present an algebraic theory of $\infty$-categories with strict units. Starting with a known type-theoretic presentation of fully weak $\infty$-categories, in which terms denote valid operations, we extend…

Reordering is a challenge to machine translation (MT) systems. In MT, the widely used approach is to apply word based language model (LM) which considers the constituent units of a sentence as words. In speech recognition (SR), some phrase…

Argument mining tasks require an informed range of low to high complexity linguistic phenomena and commonsense knowledge. Previous work has shown that pre-trained language models are highly effective at encoding syntactic and semantic…

We apply category theory to extract multimodal document structure which leads us to develop information theoretic measures, content summarization and extension, and self-supervised improvement of large pretrained models. We first develop a…

Determining the attachments of prepositions and subordinate conjunctions is a key problem in parsing natural language. This paper presents a trainable approach to making these attachments through transformation sequences and error-driven…

Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term…