Works by Nicola Olivetti

4

Conditional Beliefs: From Neighbourhood Semantics to Sequent Calculus.Marianna Girlando, Sara Negri, Nicola Olivetti & Vincent Risch - forthcoming - Review of Symbolic Logic:1-44.

Logic and Philosophy of Logic

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44

Analytic Calculi for Product Logics.George Metcalfe, Nicola Olivetti & Dov Gabbay - 2004 - Archive for Mathematical Logic 43 (7):859-889.

Product logic Π is an important t-norm based fuzzy logic with conjunction interpreted as multiplication on the real unit interval [0,1], while Cancellative hoop logic CHL is a related logic with connectives interpreted as for Π but on the real unit interval with 0 removed (0,1]. Here we present several analytic proof systems for Π and CHL, including hypersequent calculi, co-NP labelled calculi and sequent calculi.

Fuzzy Logic in Logic and Philosophy of Logic

Proof Theory in Logic and Philosophy of Logic

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28

Tableaux for Łukasiewicz Infinite-Valued Logic.Nicola Olivetti - 2003 - Studia Logica 73 (1):81 - 111.

In this work we propose a labelled tableau method for ukasiewicz infinite-valued logic L . The method is based on the Kripke semantics of this logic developed by Urquhart [25] and Scott [24]. On the one hand, our method falls under the general paradigm of labelled deduction [8] and it is rather close to the tableau systems for sub-structural logics proposed in [4]. On the other hand, it provides a CoNP decision procedure for L validity by reducing the check of (...)

Nonclassical Logics in Logic and Philosophy of Logic

Proof Theory in Logic and Philosophy of Logic

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22

Algorithmic Proof Methods and Cut Elimination for Implicational Logics Part I: Modal Implication.Dov M. Gabbay & Nicola Olivetti - 1998 - Studia Logica 61 (2):237-280.

In this work we develop goal-directed deduction methods for the implicational fragment of several modal logics. We give sound and complete procedures for strict implication of K, T, K4, S4, K5, K45, KB, KTB, S5, G and for some intuitionistic variants. In order to achieve a uniform and concise presentation, we first develop our methods in the framework of Labelled Deductive Systems [Gabbay 96]. The proof systems we present are strongly analytical and satisfy a basic property of cut admissibility. We (...)

Modal Logic in Logic and Philosophy of Logic

Proof Theory in Logic and Philosophy of Logic

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37

Iterated Belief Revision and Conditional Logic.Laura Giordano, Valentina Gliozzi & Nicola Olivetti - 2002 - Studia Logica 70 (1):23-47.

In this paper we propose a conditional logic called IBC to represent iterated belief revision systems. We propose a set of postulates for iterated revision which are a small variant of Darwiche and Pearl''s ones. The conditional logic IBC has a standard semantics in terms of selection function models and provides a natural representation of epistemic states. We establish a correspondence between iterated belief revision systems and IBC-models. Our representation theorem does not entail Gärdenfors'' Triviality Result.

Belief Revision in Epistemology

Logic and Philosophy of Logic

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Laura Giordano Iterated Belief Revision.Nicola Olivetti & Conditional Logic - 2002 - Studia Logica 70:23-47.

Epistemic Logic in Logic and Philosophy of Logic

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2

The Logic of Conditional Beliefs: Neighbourhood Semantics and Sequent Calculus.Marianna Girlando, Sara Negri, Nicola Olivetti & Vincent Risch - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 322-341.

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19

Automated Reasoning for Conditional Logics: The Theorem Prover Condlean 3.1.Nicola Olivetti & Gian Luca Pozzato - 2007 - In Jean-Yves Béziau & Alexandre Costa-Leite (eds.), Perspectives on Universal Logic.

Areas of Mathematics in Philosophy of Mathematics

Mathematical Proof in Philosophy of Mathematics

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18

Theorem Proving for Conditional Logics: CondLean and GOALD U CK.Nicola Olivetti & Gian Luca Pozzato - 2008 - Journal of Applied Non-Classical Logics 18 (4):427-473.

Logic and Philosophy of Logic

Logics in Logic and Philosophy of Logic

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15

Preferential Semantics for the Logic of Comparative Similarity Over Triangular and Metric Models.Régis Alenda & Nicola Olivetti - 2012 - In Luis Farinas del Cerro, Andreas Herzig & Jerome Mengin (eds.), Logics in Artificial Intelligence. Springer. pp. 1--13.

Logic and Philosophy of Logic

Logics in Logic and Philosophy of Logic

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17

N-Prolog and Equivalence of Logic Programs.Nicola Olivetti & Lea Terracini - 1992 - Journal of Logic, Language and Information 1 (4):253-340.

The aim of this work is to develop a declarative semantics for N-Prolog with negation as failure. N-Prolog is an extension of Prolog proposed by Gabbay and Reyle, which allows for occurrences of nested implications in both goals and clauses. Our starting point is an operational semantics of the language defined by means of top-down derivation trees. Negation as finite failure can be naturally introduced in this context. A goal-G may be inferred from a database if every top-down derivation of (...)

Logic and Philosophy of Logic

Science, Logic, and Mathematics

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7

Łukasiewicz Logic: From Proof Systems To Logic Programming.George Metcalfe, Nicola Olivetti & Dov Gabbay - 2005 - Logic Journal of the IGPL 13 (5):561-585.

We present logic programming style “goal-directed” proof methods for Łukasiewicz logic Ł that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goal-directed calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational Pavelka logic RPL, an extension of Ł with rational constants.

Fuzzy Logic in Logic and Philosophy of Logic

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A Language For Handling Hypothetical Updates And Inconsistency.Dov Gabbay, Laura Giordano, Alberto Martelli & Nicola Olivetti - 1996 - Logic Journal of the IGPL 4 (3):385-416.

In this paper we propoee a logic programming language which supports hypothetical updates together with integrity constraints. The language makes use of a revision mechanism, which is needed to restore consistency when an update violates some integrity constraint. The revision policy adopted is based on the simple idea that more recent information is preferred to earlier one. We show how this language can be used to represent and perform several types of defeasible reasoning. We develop a logical characterization of the (...)

Logic and Philosophy of Logic

Science, Logic, and Mathematics

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