Nicola Olivetti

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A uniform proof-theoretic reconstruction of the major nonmonotonic logics is introduced. It consists of analytic sequent calculi where the details of nonmonotonic assumption making are modelled by an axiomatic rejection method. Another distinctive feature of the calculi is the use of provability constraints that make reasoning largely independent of any(More)
Minimal entailment is the semantical counterpart of Circumscription and Closed World Assumption. In this paper we show that it is possible to formalize minimal entailment at the propositional level, using standard deduction methods. Firstly we present a tableau procedure which is a natural reformulation of Smullyan's Analytic Tableaux. Then we introduce the(More)
We define the notion of rational closure in the context of Description Logics. We start from an extension of ALC with a typicality operator T allowing to express concepts of the form T(C), whose meaning is to select the “most normal” instances of a concept C. The semantics we consider is based on rational models and exploits a minimal models mechanism based(More)
We extend the Description Logic ALC with a “typicality” operator T that allows us to reason about the prototypical properties and inheritance with exceptions. The resulting logic is called ALC + T. The typicality operator is intended to select the “most normal” or “most typical” instances of a concept. In our framework, knowledge bases may then contain, in(More)
We present two embeddings of in nite-valued Lukasiewicz logic L into Meyer and Slaney’s abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding systems for L. These include: hypersequent calculi for A and L and terminating versions of these calculi; labelled single(More)
We extend the Description Logic ALC with a “typicality” operator T that allows us to reason about the prototypical properties and inheritance with exceptions. The resulting logic is called ALC +T. The typicality operator is intended to select the “most normal” or “most typical” instances of a concept. In our framework, knowledge bases may then contain, in(More)
In this paper we present a cut-free sequent calculus, called SeqS, for some standard conditional logics. The calculus uses labels and transition formulas and can be used to prove decidability and space complexity bounds for the respective logics. We also show that these calculi can be the base for uniform proof systems. Moreover, we present CondLean, a(More)