Related papers: Fuzzy Lattice-based Description Logic
We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical…
This paper presents a method of optimization, based on both Bayesian Analysis technical and Galois Lattice of Fuzzy Semantic Network. The technical System we use learns by interpreting an unknown word using the links created between this…
Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion.…
"Episodic Logic:Unscoped Logical Form" (EL-ULF) is a semantic representation capturing predicate-argument structure as well as more challenging aspects of language within the Episodic Logic formalism. We present the first learned approach…
This works is motivated by a real-world case study where it is necessary to integrate and relate existing ontologies through meta- modelling. For this, we introduce the Description Logic ALCQM which is obtained from ALCQ by adding…
In this paper we show that the problem of checking consistency of a knowledge base in the Description Logic ALCM is ExpTime-complete. The M stands for meta-modelling as defined by Motz, Rohrer and Severi. To show our main result, we define…
We give the first ExpTime (complexity-optimal) tableau decision procedure for checking satisfiability of a knowledge base in the description logic SHOQ, which extends the basic description logic ALC with transitive roles, hierarchies of…
This article presents iALC, an intuitionistic version of the classical description logic ALC, based on the framework for constructive modal logics presented by Simpson \cite{simpson95} and related to description languages, via hybrid…
This paper develops a category-theoretic approach to uncertainty, informativeness and decision-making problems. It is based on appropriate first order fuzzy logic in which not only logical connectives but also quantifiers have fuzzy…
We introduce two-dimensional logics based on \L{}ukasiewicz and G\"{o}del logics to formalize paraconsistent fuzzy reasoning. The logics are interpreted on matrices, where the common underlying structure is the bi-lattice (twisted) product…
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…
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…
Artificial intelligence systems often address fairness concerns by evaluating and mitigating measures of group discrimination, for example that indicate biases against certain genders or races. However, what constitutes group fairness…
Pattern recognition systems implemented using deep neural networks achieve better results than linear models. However, their drawback is the black box property. This property means that one with no experience utilising nonlinear systems may…
This paper proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this paper we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and…
Modern applications combine information from a great variety of sources. Oftentimes, some of these sources, like Machine-Learning systems, are not strictly binary but associated with some degree of (lack of) confidence in the observation.…
In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics).…
Autonomous systems (AS) powered by AI components are increasingly integrated into the fabric of our daily lives and society, raising concerns about their ethical and social impact. To be considered trustworthy, AS must adhere to ethical…
We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes…
Neuro-symbolic artificial intelligence aims to combine neural architectures with symbolic approaches that can represent knowledge in a human-interpretable formalism. Continual learning concerns with agents that expand their knowledge over…