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We describe a simplified categorical approach to Galois descent theory. It is well known that Galois descent is a special case of Grothendieck descent, and that under mild additional conditions the category of Grothendieck descent data…

Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…

This paper proves the existence and uniqueness results (in the sense of maximally defined regularity) as well as the stability analysis for the solutions to a class of nonlocal fully-nonlinear parabolic systems, where the nonlocality stems…

Graphical models in probability and statistics are a core concept in the area of probabilistic reasoning and probabilistic programming-graphical models include Bayesian networks and factor graphs. In this paper we develop a new model of…

We present Polaris, a concurrent separation logic with support for probabilistic reasoning. As part of our logic, we extend the idea of coupling, which underlies recent work on probabilistic relational logics, to the setting of programs…

Conventional game theory assumes that players are perfectly rational. In a realistic situation, however, players are rarely perfectly rational. This bounded rationality is one of the main reasons why the predictions of Nash equilibrium in…

Graph games and Markov decision processes (MDPs) are standard models in reactive synthesis and verification of probabilistic systems with nondeterminism. The class of $\omega$-regular winning conditions; e.g., safety, reachability,…

Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in…

This paper describes Picky, a probabilistic agenda-based chart parsing algorithm which uses a technique called {\em probabilistic prediction} to predict which grammar rules are likely to lead to an acceptable parse of the input. Using a…

Functor coalgebras capture a wide range of transition systems that must however evolve in discrete steps. We introduce graded coalgebras of graded monads and propose them to model continuous-time transition systems. We develop the theory of…

In this paper I give a brief introduction to a family of simple but non-trivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical…

Game comonads, introduced by Abramsky, Dawar and Wang and developed by Abramsky and Shah, give an interesting categorical semantics to some Spoiler-Duplicator games that are common in finite model theory. In particular they expose…

This paper introduces a new approach to represent logic functions in the form of Sierpinski Gaskets. The structure of the gasket allows to manipulate with the corresponding logic expression using recursive essence of fractals. Thus, the…

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…

We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is…

Transformer-based large language models (LLMs) have demonstrated strong reasoning abilities across diverse fields, from solving programming challenges to competing in strategy-intensive games such as chess. Prior work has shown that LLMs…

The logit model is often used to analyze experimental data. However, randomization does not justify the model, so the usual estimators can be inconsistent. A consistent estimator is proposed. Neyman's non-parametric setup is used as a…

This paper generalizes L.S. Shapley's celebrated value allocation theory on coalition games by discovering and applying a fundamental connection between stochastic path integration driven by canonical time-reversible Markov chains and…

We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order to abstract the underlying data structures (e.g. sets or linear…

This paper belongs to the field of probabilistic modal logic, focusing on a comparative analysis of two distinct semantics: one rooted in Kripke semantics and the other in neighbourhood semantics. The primary distinction lies in the…