Related papers: Reasoning within Fuzzy Description Logics
We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…
In this paper we introduce a fuzzy constraint linear discriminant analysis (FC-LDA). The FC-LDA tries to minimize misclassification error based on modified perceptron criterion that benefits handling the uncertainty near the decision…
General Type-2 (GT2) Fuzzy Logic Systems (FLSs) are perfect candidates to quantify uncertainty, which is crucial for informed decisions in high-risk tasks, as they are powerful tools in representing uncertainty. In this paper, we travel…
Description Logics (DLs) are a family of languages used for the representation and reasoning on the knowledge of an application domain, in a structured and formal manner. In order to achieve this objective, several provers, such as RACER…
Ontology is a popular method for knowledge representation in different domains, including the legal domain, and description logics (DL) is commonly used as its description language. To handle reasoning based on inconsistent DL-based legal…
The paper introduces fuzzy linguistic logic programming, which is a combination of fuzzy logic programming, introduced by P. Vojtas, and hedge algebras in order to facilitate the representation and reasoning on human knowledge expressed in…
While large language models (LLMs) have demonstrated impressive capabilities across various natural language processing tasks by acquiring rich factual knowledge from their broad training data, their ability to synthesize and logically…
Aiming to harmonise finite and infinite model reasoning, we initiate the study of partially finite models, where the reasoning task comes with a formula that specifies a part of the model that must be finite. We focus on the problem of…
Order-Sorted Feature (OSF) logic is a knowledge representation and reasoning language based on function-denoting feature symbols and set-denoting sort symbols ordered in a subsumption lattice. OSF logic allows the construction of…
An analysis description language is a domain specific language capable of describing the contents of an LHC analysis in a standard and unambiguous way, independent of any computing framework. It is designed for use by anyone with an…
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…
Within the framework proposed in this paper, we address the issue of extending the certain networks to a fuzzy certain networks in order to cope with a vagueness and limitations of existing models for decision under imprecise and uncertain…
Deep learning (DL) libraries, widely used in AI applications, often contain vulnerabilities like buffer overflows and use-after-free errors. Traditional fuzzing struggles with the complexity and API diversity of DL libraries such as…
Formal methods are widely recognized as a powerful engineering method for the specification, simulation, development, and verification of distributed interactive systems. However, most formal methods rely on a two-valued logic, and are…
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…
The aim of this paper is to show how we can handle the Recognising Textual Entailment (RTE) task by using Description Logics (DLs). To do this, we propose a representation of natural language semantics in DLs inspired by existing…
Differential Linear Logic (DiLL) is a sequent calculus that expresses differentiation via symmetries between linear and non-linear formulas. In this paper, we express categorical models of DiLL as a pair of Grothendieck fibrations equipped…
We introduce Riesz Logic, whose models are abelian lattice ordered groups, which generalise Riesz spaces (vector lattices), and show soundness and completeness. Our motivation is to provide a logic for distributional semantics of natural…
There is increased interest in assisting non-expert audiences to effectively interact with machine learning (ML) tools and understand the complex output such systems produce. Here, we describe user experiments designed to study how…
Following the development of fuzzy logic theory by Lotfi Zadeh, its applications were investigated by researchers in different fields. Presenting and working with uncertain data is a complex problem. To solve for such a complex problem, the…