Related papers: A Category Theoretic View of Contextual Types: fro…

The categorical compositional distributional (DisCoCat) model of meaning developed by Coecke et al. (2010) has been successful in modeling various aspects of meaning. However, it fails to model the fact that language can change. We give an…

Latent or continuous chain-of-thought methods replace explicit textual rationales with a number of internal latent steps, but these intermediate computations are difficult to evaluate beyond correlation-based probes. In this paper, we view…

We present a type theory dealing with non-linear, "ordinary" dependent types (which we will call cartesian) and linear types, where both constructs may depend on terms of the former. In the interplay between these, we find new type formers…

Initial Semantics aims at characterizing the syntax associated to a signature as the initial object of some category. We present an initial semantics result for typed higher-order syntax together with its formalization in the Coq proof…

Despite the empirical success of foundation models, we do not have a systematic characterization of the representations that these models learn. In this paper, we establish the contexture theory. It shows that a large class of…

This is the first of a pair of papers where we construct and investigate a closed monoidal structure on the category of generalized algebraic theories (in the sense of Cartmell). In the present text, as a starting point, we define the…

Reading a document and extracting an answer to a question about its content has attracted substantial attention recently. While most work has focused on the interaction between the question and the document, in this work we evaluate the…

Capabilities to categorize a clause based on the type of situation entity (e.g., events, states and generic statements) the clause introduces to the discourse can benefit many NLP applications. Observing that the situation entity type of a…

Recent works show that discourse analysis benefits from modeling intra- and inter-sentential levels separately, where proper representations for text units of different granularities are desired to capture both the meaning of text units and…

We study concrete sheaf models for a call-by-value higher-order language with recursion. Our family of sheaf models is a generalization of many examples from the literature, such as models for probabilistic and differentiable programming,…

The framework of causal models provides a principled approach to causal reasoning, applied today across many scientific domains. Here we present this framework in the language of string diagrams, interpreted formally using category theory.…

Given a small simplicial category $\C$ whose underlying ordinary category is equipped with a Grothendieck topology $\tau$, we construct a model structure on the category of simplicially enriched presheaves on $\C$ where the weak…

Chain-of-Thought (CoT) prompting helps models think step by step. But naive CoT breaks down in visually grounded social tasks, where models must perceive, understand, and judge all at once; bridging perception with norm-grounded reasoning.…

This chapter contains an exposition of the sheaf-theoretic framework for contextuality emphasising resource-theoretic aspects, as well as some original results on this topic. In particular, we consider functions that transform empirical…

We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is naturally interpreted in a class of structured…

In this work we shall introduce a new model structure on the category of pro-simplicial sheaves, which is very convenient for the study of \'etale homotopy. Using this model structure we define a pro-space associated to a topos, as a result…

A common framework is provided that comprises classical ordinal item response models as the cumulative, sequential and adjacent categories models as well as nominal response models and item response tree models. The taxonomy is based on the…

Intensional computation derives concrete outputs from abstract function definitions; extensional computation defines functions through explicit input-output pairs. In formal semantics: intensional computation interprets expressions as…

The program of internal type theory seeks to develop the categorical model theory of dependent type theory using the language of dependent type theory itself. In the present work we study internal homotopical type theory by relaxing the…

Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…