Related papers: Reasoning in Infinitely Valued G-IALCQ

Fuzzy implication functions are a key area of study in fuzzy logic, extending the classical logical conditional to handle truth degrees in the interval $[0,1]$. While existing literature often focuses on a limited number of families, in the…

Fuzzy description logics serve the representation of vague knowledge, typically letting concepts take truth degrees in the unit interval. Expressiveness, logical properties, and complexity vary strongly with the choice of propositional…

We present a fuzzy version of description logics with concrete domains. Main features are: (i) concept constructors are based on t-norm, t-conorm, negation and implication; (ii) concrete domains are fuzzy sets; (iii) fuzzy modifiers are…

The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…

Defeasible rules are used in providing computable representations of legal documents and, more recently, have been suggested as a basis for explainable AI. Such applications draw attention to the scalability of implementations. The…

Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator [18] was introduced to formalise programs running in parallel. In other direction, other authors proposed a systematic…

Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates…

We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…

In this paper we prove soundness and completeness of some epistemic extensions of G\"odel fuzzy logic, based on Kripke models in which both propositions at each state and accessibility relations take values in [0,1]. We adopt belief as our…

Temporal logics are extensively used for the specification of on-going behaviours of reactive systems. Two significant developments in this area are the extension of traditional temporal logics with modalities that enable the specification…

This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…

We propose a formalism for representation of finite languages, referred to as the class of IDL-expressions, which combines concepts that were only considered in isolation in existing formalisms. The suggested applications are in natural…

This paper employs the linear nested sequent framework to design a new cut-free calculus LNIF for intuitionistic fuzzy logic--the first-order G\"odel logic characterized by linear relational frames with constant domains. Linear nested…

One of the main challenges in the area of Neuro-Symbolic AI is to perform logical reasoning in the presence of both neural and symbolic data. This requires combining heterogeneous data sources such as knowledge graphs, neural model…

Difference Logic (DL) is a fragment of linear arithmetics where atoms are constraints x+k <= y for variables x,y (ranging over Q or Z) and integer k. We study the complexity of deciding the truth of existential DL sentences. This problem…

In this paper we analyse the benefits of incorporating interval-valued fuzzy sets into the Bousi-Prolog system. A syntax, declarative semantics and im- plementation for this extension is presented and formalised. We show, by using potential…

In fuzzy propositional logic, to a proposition a partial truth in [0,1] is assigned. It is well known that under certain circumstances, fuzzy logic collapses to classical logic. In this paper, we will show that under dual conditions, fuzzy…

Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a…