Related papers: Towards Functorial Language-Games
The syntactic categories of categorial grammar formalisms are structured units made of smaller, indivisible primitives, bound together by the underlying grammar's category formation rules. In the trending approach of constructive…
Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…
The interaction between syntax (formal language) and its semantics (meanings of language) is one which has been well studied in categorical logic. The results of this particular study are employed to understand how the brain is able to…
In order to communicate, humans flatten a complex representation of ideas and their attributes into a single word or a sentence. We investigate the impact of representation learning in artificial agents by developing graph referential…
As the key to sentiment analysis, sentiment composition considers the classification of a constituent via classifications of its contained sub-constituents and rules operated on them. Such compositionality has been widely studied previously…
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…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
Using quilted Floer cohomology and relative quilt invariants, we define a composition functor for categories of Lagrangian correspondences in monotone and exact symplectic Floer theory. We show that this functor agrees with geometric…
As interaction between autonomous agents, communication can be analyzed in game-theoretic terms. Meaning game is proposed to formalize the core of intended communication in which the sender sends a message and the receiver attempts to infer…
Naming game simulates the process of naming an object by a single word, in which a population of communicating agents can reach global consensus asymptotically through iteratively pair-wise conversations. We propose an extension of the…
Compositionality is at the heart of computer science and several other areas of applied category theory such as computational linguistics, categorical quantum mechanics, interpretable AI, dynamical systems, compositional game theory, and…
We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary.…
The mathematical representation of semantics is a key issue for Natural Language Processing (NLP). A lot of research has been devoted to finding ways of representing the semantics of individual words in vector spaces. Distributional…
The predictions of text classifiers are often driven by spurious correlations -- e.g., the term `Spielberg' correlates with positively reviewed movies, even though the term itself does not semantically convey a positive sentiment. In this…
This paper presents a construction which transforms categorical models of additive-free propositional linear logic, closely based on de Paiva's dialectica categories and Oliva's functional interpretations of classical linear logic. The…
Most categorical models of meaning use a functor from the syntactic category to the semantic category. When semantic information is available, the problem of grammar induction can therefore be defined as finding preimages of the semantic…
We present a doctrinal approach to category theory, obtained by abstracting from the indexed inclusions (via discrete fibrations and opfibrations) of the left and of the right actions of X in Cat in categories over X. Namely, a "weak…
Inductions and game semantics are two useful extensions to traditional logic programming. To be specific, inductions can capture a wider class of provable formulas in logic programming. Adopting game semantics can make logic programming…
We look at intensionality from the perspective of computation. In particular, we review how game semantics has been used to characterize the sequential functional processes, leading to powerful and flexible methods for constructing fully…
We present a factorized compositional distributional semantics model for the representation of transitive verb constructions. Our model first produces (subject, verb) and (verb, object) vector representations based on the similarity of the…