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A framework for a modular multi-concept lexicographic closure semantics

arXiv.org Artificial Intelligence

We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality. The idea is that of distributing the defeasible properties of concepts into different modules, according to their subject, and of defining a notion of preference for each module based on the lexicographic closure semantics. The preferential semantics of the knowledge base can then be defined as a combination of the preferences of the single modules. The range of possibilities, from fine grained to coarse grained modules, provides a spectrum of alternative semantics.


Defeasible Inheritance-Based Description Logics

AAAI Conferences

Defeasible inheritance networks are a non-monotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics, a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is build on top of the classical entailment relation.


On the KLM properties of a fuzzy DL with Typicality

arXiv.org Artificial Intelligence

The paper investigates the properties of a fuzzy logic of typicality. The extension of fuzzy logic with a typicality operator was proposed in recent work to define a fuzzy multipreference semantics for Multilayer Perceptrons, by regarding the deep neural network as a conditional knowledge base. In this paper, we study its properties. First, a monotonic extension of a fuzzy ALC with typicality is considered (called ALCFT) and a reformulation the KLM properties of a preferential consequence relation for this logic is devised. Most of the properties are satisfied, depending on the reformulation and on the fuzzy combination functions considered. We then strengthen ALCFT with a closure construction by introducing a notion of faithful model of a weighted knowledge base, which generalizes the notion of coherent model of a conditional knowledge base previously introduced, and we study its properties.


Theoretical Foundations of Defeasible Description Logics

arXiv.org Artificial Intelligence

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 case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in DLs. Indeed, we also analyse the problem of non-monotonic reasoning in DLs at the level of entailment and present an algorithm for the computation of rational closure of a defeasible ontology. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of reasoning in the underlying classical DL ALC.


Defeasible Inheritance-Based Description Logics

Journal of Artificial Intelligence Research

Defeasible inheritance networks are a non-monotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach to non-monotonic reasoning. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics (DLs), a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is built on top of the classical entailment relation and, thus, is amenable of an implementation based on existing reasoners. Eventually, we evaluate our approach on well-known landmark test examples.