Related papers: Encoding de Finetti's coherence within Lukasiewicz…
The first system of many-valued logic was introduced by J. Lukasiewicz, his motivation was of philosophical nature as he was looking for an interpretation of the concepts of possibility and necessity. Since then, plenty of research has been…
We investigate four well-known negative translations of classical logic into intuitionistic logic within a substructural setting. We find that in affine logic the translation schemes due to Kolmogorov and G\"odel both satisfy Troelstra's…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
The G\"odel translation provides an embedding of the intuitionistic logic $\mathsf{IPC}$ into the modal logic $\mathsf{Grz}$, which then embeds into the modal logic $\mathsf{GL}$ via the splitting translation. Combined with Solovay's…
We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory…
In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is…
In this paper (propositional) probability logic ($PL$) is investigated from model theoretic point of view. First of all, the ultraproduct construction is adapted for $\sigma$-additive probability models, and subsequently when this class of…
The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…
We generalize methods, developed by S. Ghilardi, and apply them to a subsystem J$_2$ of bimodal provability logic GLB. We describe projective formulas in J$_2$ in terms of Kripke semantics and prove that logic J$_2$ has finitary unification…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…
We explore the problem of explaining observations in contexts involving statements with truth degrees such as `the lift is loaded', `the symptoms are severe', etc. To formalise these contexts, we consider infinitely-valued {\L}ukasiewicz…
In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the…
A focused proof system provides a normal form to cut-free proofs that structures the application of invertible and non-invertible inference rules. The focused proof system of Andreoli for linear logic has been applied to both the proof…
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…
We introduce the logics GLP(\Lambda), a generalization of Japaridze's polymodal provability logic GLP(\omega) where \Lambda is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall…
The paper explores properties of the {\L}ukasiewicz {\mu}-calculus, or {\L}{\mu} for short, an extension of {\L}ukasiewicz logic with scalar multiplication and least and greatest fixed-point operators (for monotone formulas). We observe…