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We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…

Language models (LMs) are used for a diverse range of tasks, from question answering to writing fantastical stories. In order to reliably accomplish these tasks, LMs must be able to discern the modal category of a sentence (i.e., whether it…

Initial semantics aims to capture inductive structures and their properties as initial objects in suitable categories. We focus on the initial semantics aiming to model the syntax and substitution structure of programming languages with…

Sequence-to-sequence translation methods based on generation with a side-conditioned language model have recently shown promising results in several tasks. In machine translation, models conditioned on source side words have been used to…

For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…

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.…

All languages have a noun category, but its realisation varies considerably. Depending on the language, semantic and/or morphosyntactic differences may be more or less pronounced. This paper explores these variations, using Riffian as a…

Motivated by questions from program transformations, eight notions of isomorphisms between term rewriting systems are defined, analysed, and classified. The notions include global isomorphisms, where the renaming of variables and function…

Dynamically Adaptive Systems modify their behav- ior and structure in response to changes in their surrounding environment and according to an adaptation logic. Critical sys- tems increasingly incorporate dynamic adaptation capabilities;…

We introduce the concept of an abstract evolution system, which provides a convenient framework for studying generic mathematical structures and their properties. Roughly speaking, an evolution system is a category endowed with a selected…

Drug discovery aims to find novel compounds with specified chemical property profiles. In terms of generative modeling, the goal is to learn to sample molecules in the intersection of multiple property constraints. This task becomes…

Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…

Categorization is a fundamental function of minds, with wide ranging implications for the rest of the cognitive system. In humans, categories are shared and communicated between minds, thus requiring explanations at the population level. In…

Large pre-trained language models have recently been expanded and applied to programming language tasks with great success, often through further pre-training of a strictly-natural language model--where training sequences typically contain…

Generative models are a class of AI models capable of creating new instances of data by learning and sampling from their statistical distributions. In recent years, these models have gained prominence in machine learning due to the…

The article defines and studies the genus of finite state deterministic automata (FSA) and regular languages. Indeed, a FSA can be seen as a graph for which the notion of genus arises. At the same time, a FSA has a semantics via its…

We study a new model theory for formal mathematical systems that we developed in a previous paper. We introduce isomorphic and homomorphic structures for formal languages, present some results and examples and conclude our paper with a…

Linear sequences of words are implicitly represented in our brains by hierarchical structures that organize the composition of words in sentences. Linguists formalize different frameworks to model this hierarchy; two of the most common…

My doctoral research focuses on understanding semantic knowledge in neural network models trained solely to predict natural language (referred to as language models, or LMs), by drawing on insights from the study of concepts and categories…

This chapter reviews the purpose and use of models from the field of complex systems and, in particular, the implications of trying to use models to understand or make decisions within complex situations, such as policy makers usually face.…