arXiv subjects

Jérémy Ledent

Publications and source records attributed to Jérémy Ledent.

9 recordsLinked to original sources

arXiv2026

Algebraic Characterization of FO-definable Languages of Higher-Dimensional Automata

Higher-dimensional automata (HDA) are a model of concurrency that models simultaneous execution of events using higher dimensional cells. HDA recognize languages of pomsets, a generalization of finite words whose letters are partially ordered. We prove a new algebraic characterization of HDA languages: a language of pomsets is regular if and only if it is the inverse image of a functor from the category of pomsets into a finite category. Furthermore, the language is definable in first-order logic exactly when it is recognized by an aperiodic category, generalizing the McNaughton-Papert theorem to HDA languages. We also investigate a notion of counter-free HDA, and show that if a language is accepted by a counter-free HDA, it must be definable in first-order logic. The converse, however, is still open.

cs.FL↗

arXiv2026

Distributed Knowledge in Simplicial Models

The usual semantics of multi-agent epistemic logic is based on Kripke models, defined in terms of binary relations on a set of possible worlds. Recently, there has been a growing interest in using simplicial complexes rather than graphs, as models for multi-agent epistemic logic. This approach uses agents' views as the fundamental object instead of worlds. A set of views by different agents about a world forms a simplex, and a set of simplexes defines a simplicial complex, that can serve as a model for multi-agent epistemic logic. This new approach reveals topological information that is implicit in Kripke models, because the binary indistinguishability relations are more clearly seen as n-ary relations in the simplicial complex. This paper, written for an economics audience, introduces simplicial models to non-experts and connects distributed computing, epistemic logic and topology. Our focus is on distributed knowledge and its fixed point, common distributed knowledge. These concepts arise when considering the knowledge that a group of agents would acquire, if they could communicate their local knowledge perfectly. While common knowledge has been shown to be related to consensus, we illustrate how distributed knowledge is related to a task weaker to consensus, called majority consensus. We describe three models of communication, some well-known (immediate snapshot), and others less studied (related to broadcast and test-and-set). When majority consensus is solvable, we describe the distributed knowledge that is used to solve it. When it is not solvable, we present a logical obstruction, a formula that should always be known according to the task specification, but which the players cannot know.

cs.LO↗

arXiv2025

Kamp Theorem for Pomset Languages of Higher Dimensional Automata

Temporal logics are a powerful tool to specify properties of computational systems. For concurrent programs, Higher Dimensional Automata (HDA) are a very expressive model of non-interleaving concurrency. HDA recognize languages of partially ordered multisets, or pomsets. Recent work has shown that Monadic Second Order (MSO) logic is as expressive as HDA for pomset languages. In the case of words, Kamp's theorem states that First Order (FO) logic is as expressive as Linear Temporal Logic (LTL). In this paper, we extend this result to pomsets. To do so, we first investigate the class of pomset languages that are definable in FO. As expected, this is a strict subclass of MSO-definable languages. Then, we define a Linear Temporal Logic for pomsets, and show that it is equivalent to FO.

cs.FL↗

arXiv2023

A many-sorted epistemic logic for chromatic hypergraphs

We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes the standard epistemic logic and is a conservative extension of it. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.

cs.LO↗

arXiv2023

Semi-simplicial Set Models for Distributed Knowledge

In recent years, a new class of models for multi-agent epistemic logic has emerged, based on simplicial complexes. Since then, many variants of these simplicial models have been investigated, giving rise to different logics and axiomatizations. In this paper, we present a further generalization, where a group of agents may distinguish two worlds, even though each individual agent in the group is unable to distinguish them. For that purpose, we generalize beyond simplicial complexes and consider instead simplicial sets. By doing so, we define a new semantics for epistemic logic with distributed knowledge. As it turns out, these models are the geometric counterpart of a generalization of Kripke models, called "pseudo-models". We identify various interesting sub-classes of these models, encompassing all previously studied variants of simplicial models; and give a sound and complete axiomatization for each of them.

cs.LO↗

arXiv2022

A Simplicial Model for $KB4_n$: Epistemic Logic with Agents that May Die

The standard semantics of multi-agent epistemic logic S5 is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive. This one dimensional structure contains implicit higher-dimensional information beyond pairwise interactions, that we formalized as pure simplicial models in a previous work (Information and Computation, 2021). Here we extend the theory to encompass simplicial models that are not necessarily pure. The corresponding class of Kripke models are those where the accessibility relation is symmetric and transitive, but might not be reflexive. Such models correspond to the epistemic logic KB4 . Impure simplicial models arise in situations where two possible worlds may not have the same set of agents. We illustrate it with distributed computing examples of synchronous systems where processes may crash.

cs.LO↗

arXiv2022

Translating Extensive Form Games to Open Games with Agency

We show open games cover extensive form games with both perfect and imperfect information. Doing so forces us to address two current weaknesses in open games: the lack of a notion of player and their agency within open games, and the lack of choice operators. Using the former we construct the latter, and these choice operators subsume previous proposed operators for open games, thereby making progress towards a core, canonical and ergonomic calculus of game operators. Collectively these innovations increase the level of compositionality of open games, and demonstrate their expressiveness.

cs.GT↗

arXiv2021

Compositional Game Theory, Compositionally

We present a new compositional approach to compositional game theory (CGT) based upon Arrows, a concept originally from functional programming, closely related to Tambara modules, and operators to build new Arrows from old. We model equilibria as a bimodule over an Arrow and define an operator to build a new Arrow from such a bimodule over an existing Arrow. We also model strategies as graded Arrows and define an operator which builds a new Arrow by taking the colimit of a graded Arrow. A final operator builds a graded Arrow from a graded bimodule. We use this compositional approach to CGT to show how known and previously unknown variants of open games can be proven to form symmetric monoidal categories.

cs.LO↗

arXiv2018

A Simplicial Complex Model for Dynamic Epistemic Logic to study Distributed Task Computability

The usual epistemic model S5n for a multi-agent system is based on a Kripke frame, which is a graph whose edges are labeled with agents that do not distinguish between two states. We propose to uncover the higher dimensional information implicit in this structure, by considering a dual, simplicial complex model. We use dynamic epistemic logic (DEL) to study how an epistemic simplicial complex model changes after a set of agents communicate with each other. We concentrate on an action model that represents the so called immediate snapshot communication patterns of asynchronous agents, because it is central to distributed computability (but our setting works for other communication patterns). There are topological invariants preserved from the initial epistemic complex to the one after the action model is applied, which determine the knowledge that the agents gain after communication. Finally, we describe how a distributed task specification can be modeled as a DEL action model, and show that the topological invariants determine whether the task is solvable. We thus provide a bridge between DEL and the topological theory of distributed computability, which studies task solvability in a shared memory or message passing architecture.

cs.LO↗