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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…
There are currently two main paradigms for evaluating large language models (LLMs), reference-based evaluation and preference-based evaluation. The first, carried over from the evaluation of machine learning models in general, relies on…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
This paper continues the investigation of the logic of competing theories, be they scientific, social, political etc. We introduce a many-valued, multi-type modal language which we endow with relational semantics based on enriched reflexive…
Past efforts to classify impartial three-player combinatorial games (the theories of Li and Straffin) have made various restrictive assumptions about the rationality of one's opponents and the formation and behavior of coalitions. One may…
Converging evidence suggests that human systems of semantic categories achieve near-optimal compression via the Information Bottleneck (IB) complexity-accuracy tradeoff. Large language models (LLMs) are not trained for this objective, which…
By varying prompts to a large language model, we can elicit the full range of human behaviors in a variety of different scenarios in classic economic games. By analyzing which prompts elicit which behaviors, we can categorize and compare…
Presheaf models provide a formulation of labelled transition systems that is useful for, among other things, modelling concurrent computation. This paper aims to extend such models further to represent stochastic dynamics such as shown in…
The traditional mathematical model for an impartial combinatorial game is defined recursively as a set of the options of the game, where the options are games themselves. We propose a model called gamegraph, together with its generalization…
Logic-based models can be used to build verification tools for machine learning classifiers employed in the legal field. ML classifiers predict the outcomes of new cases based on previous ones, thereby performing a form of case-based…
This thesis explores how concepts of formal language theory can be used to study left-orderable groups. It analyses the languages formed by their positive cones and demonstrates how the abstract families of languages (AFLs) in the Chomsky…
The primary goal of this paper is to recast the semantics of modal logic, and dynamic epistemic logic (DEL) in particular, in category-theoretic terms. We first review the category of relations and categories of Kripke frames, with…
The rapid advancements in large language models (LLMs) have presented challenges in evaluating those models. Existing evaluation methods are either reference-based or preference based, which inevitably need human intervention or introduce…
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
Lov\'asz (1967) showed that two finite relational structures A and B are isomorphic if, and only if, the number of homomorphisms from C to A is the same as the number of homomorphisms from C to B for any finite structure C. Soon after,…
In this report, we propose a game semantics model of intuitionistic linear logic with a notion of brackets and a trace operator. This model is a revised version of Conway games augmented with an algebraicly defined gain which enable to…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
We propose a unifying additive theory for standard conventions in Combinatorial Game Theory, including normal-, mis\`ere- and scoring-play, studied by Berlekamp, Conway, Dorbec, Ettinger, Guy, Larsson, Milley, Neto, Nowakowski, Renault,…
The advent of large language models (LLMs) has spurred the development of numerous jailbreak techniques aimed at circumventing their security defenses against malicious attacks. An effective jailbreak approach is to identify a domain where…