1,721,005 research outputs found
A reconstruction of multipreference closure
No full textThe paper describes a preferential approach for dealing with exceptions in KLM preferential logics, based on the rational closure. It is well known that rational closure does not allow an independent handling of inheritance of different defeasible properties of concepts. In this work, we consider an alternative closure construction, called Multi Preference closure (MP-closure), which has been first considered for reasoning with exceptions in DLs. We reconstruct the notion of MP-closure in the propositional case and show that it is a natural (weaker) variant of Lehmann's lexicographic closure, which appears to be too bold in some cases. The MP-closure defines a preferential consequence relation that, although weaker than lexicographic closure, is stronger than Relevant Closure
Reasoning about Exceptions in Ontologies: From the Lexicographic Closure to the Skeptical Closure
No full textReasoning about exceptions in ontologies is nowadays one of the challenges the description logics community is facing. The paper describes a preferential approach for dealing with exceptions in Description Logics, based on the rational closure. The rational closure has the merit of providing a simple and efficient approach for reasoning with exceptions, but it does not allow independent handling of the inheritance of different defeasible properties of concepts. In this work we outline a possible solution to this problem by introducing a weaker variant of the lexicographical closure, that we call skeptical closure, which requires to construct a single base. We develop a bi-preference semantics for defining a characterization of the skeptical closure
Towards a Rational Closure for Expressive Description Logics: The Case of SHIQ
No full textWe explore the extension of the notion of rational closure to logics lacking the finite model property, considering the logic SHIQ. We provide a semantic characterization of rational closure in SHIQ in terms of a preferential semantics, based on a finite rank characterization of minimal models. We show that the rational closure of a KB can be computed in EXPTIME based on a polynomial encoding of the rational extension of SHIQ into entailment in SHIQ. We discuss the extension of rational closure to more expressive description logics.
The research that led to the present paper was partially supported by a grant of the group GNCS of INdAM
On a plausible concept-wise multipreference semantics and its relations with self-organising maps
No full textIn this paper we describe a concept-wise multi-preference semantics for description logic which has its root in the preferential approach for modeling defeasible reasoning in knowledge representation. We argue that this proposal, beside satisfying some desired properties, such as KLM postulates, and avoiding the drowning problem, also defines a plausible notion of semantics. We motivate the plausibility of the concept-wise multi-preference semantics by developing a logical semantics of self-organising maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category generalisation, in terms of multi-preference interpretations
Preferential reasoning with typicality and neural network models (Extended abstract)
No full textIn this extended abstract we report some results concerning the relationships between a multipreferentia semantics for defeasible reasoning in knowledge representation and some neural network models, namel Self-Organising Maps and Multilayer Perceptrons
A multipreference semantics from common sense reasoning to neural network models: An overview
No full textIn this short paper we report about a "concept-wise" multipreference semantics for weighted conditionals and its use to provide a logical interpretation to some neural network models, Self-Organising Maps (SOMs) and Multilayer Perceptrons (MLPs). For MLPs, a deep network can be regarded as a conditional knowledge base, in which the synaptic connections correspond to weighted conditionals
Proof Methods and Theorem Proving for Conditional Logics with Strong Centering
No full textIn this work we continue our investigation on proof methods and theorem proving for Conditional Logics with the selection function semantics. Conditional Logics recently have received a renewed attention and have found several applications in knowledge representation and artificial intelligence. We present a labelled sequent calculus for systems including the axiom of strong centering CS, as well as a theorem prover implementing the sequent calculus in Prolog
Towards a conditional interpretation of self organizing maps
No full textIn this paper we aim at establishing a link between the preferential semantics for conditionals and self-organising maps (SOMs). We show that a concept-wise multipreference semantics, recently proposed for defeasible description logics, which takes into account preferences with respect to different concepts, can be used to to provide a logical interpretation of SOMs
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