Deductive System

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Umberto Straccia - One of the best experts on this subject based on the ideXlab platform.

  • A general framework for representing, reasoning and querying with annotated Semantic Web data
    Journal of Web Semantics, 2012
    Co-Authors: Antoine Zimmermann, Nuno Lopes, Axel Polleres, Umberto Straccia
    Abstract:

    We describe a generic framework for representing and reasoning with annotated Semantic Web data, a task becoming more important with the recent increased amount of inconsistent and non-reliable meta-data on the Web. We formalise the annotated language, the corresponding Deductive System and address the query answering problem. Previous contributions on specific RDF annotation domains are encompassed by our unified reasoning formalism as we show by instantiating it on (i) temporal, (ii) fuzzy, and (iii) provenance annotations. Moreover, we provide a generic method for combining multiple annotation domains allowing to represent, e.g., temporally-annotated fuzzy RDF. Furthermore, we address the development of a query language – AnQL – that is inspired by SPARQL, including several features of SPARQL 1.1 (subqueries, aggregates, assignment, solution modifiers) along with the formal definitions of their semantics.

  • A General Framework for Representing, Reasoning and Querying with Annotated Semantic Web Data (updated version)
    2011
    Co-Authors: Antoine Zimmermann, Nuno Lopes, Axel Polleres, Umberto Straccia
    Abstract:

    We describe a generic framework for representing and reasoning with annotated Semantic Web data, a task becoming more important with the recent increased amount of inconsistent and non-reliable meta-data on the web. We formalise the annotated language, the corresponding Deductive System and address the query answering problem. Previous contributions on specific RDF annotation domains are encompassed by our unified reasoning formalism as we show by instantiating it on (i) temporal, (ii) fuzzy, and (iii) provenance annotations. Moreover, we provide a generic method for combining multiple annotation domains allowing to represent, e.g., temporally-annotated fuzzy RDF. Furthermore, we address the development of a query language – AnQL – that is inspired by SPARQL, including several features of SPARQL 1.1 (subqueries, aggregates, assignment, solution modifiers) along with the formal definitions of their semantics.

  • RR - A Minimal Deductive System for General Fuzzy RDF
    Web Reasoning and Rule Systems, 2009
    Co-Authors: Umberto Straccia
    Abstract:

    It is well-known that crisp RDF is not suitable to represent vague information. Fuzzy RDF variants are emerging to overcome this limitations. In this work we provide, under a very general semantics, a Deductive System for a salient fragment of fuzzy RDF. We then also show how we may compute the top-k answers of the union of conjunctive queries in which answers may be scored by means of a scoring function.

Marc Denecker - One of the best experts on this subject based on the ideXlab platform.

  • a Deductive System for fo id based on least fixpoint logic
    International Conference on Logic Programming, 2009
    Co-Authors: Ping Hou, Marc Denecker
    Abstract:

    The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. The goal of this paper is to extend Gentzen's sequent calculus to obtain a Deductive inference method for FO(ID). The main difficulty in building such a proof System is the representation and inference of unfounded sets. It turns out that we can represent unfounded sets by least fixpoint expressions borrowed from stratified least fixpoint logic (SLFP), which is a logic with a least fixpoint operator and characterizes the expressibility of stratified logic programs. Therefore, in this paper, we integrate least fixpoint expressions into FO(ID) and define the logic FO(ID,SLFP). We investigate a sequent calculus for FO(ID,SLFP), which extends the sequent calculus for SLFP with inference rules for the inductive definitions of FO(ID). We show that this proof System is sound with respect to a slightly restricted fragment of FO(ID) and complete for a more restricted fragment of FO(ID).

  • a Deductive System for pc id
    International Conference on Logic Programming, 2007
    Co-Authors: Ping Hou, Johan Wittocx, Marc Denecker
    Abstract:

    The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. This paper studies a Deductive inference method for PC(ID), its propositional fragment.We introduce a formal proof System based on the sequent calculus (Gentzen-style Deductive System) for this logic. As PC(ID) is an integration of classical propositional logic and propositional inductive definitions, our Deductive System integrates inference rules for propositional calculus and definitions.We prove the soundness and completeness of this Deductive System for a slightly restricted fragment of PC(ID). We also give a counter-example to show that cut-elimination does not hold in this proof System.

  • LPNMR - A Deductive System for PC(ID)
    Logic Programming and Nonmonotonic Reasoning, 1
    Co-Authors: Ping Hou, Johan Wittocx, Marc Denecker
    Abstract:

    The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. This paper studies a Deductive inference method for PC(ID), its propositional fragment.We introduce a formal proof System based on the sequent calculus (Gentzen-style Deductive System) for this logic. As PC(ID) is an integration of classical propositional logic and propositional inductive definitions, our Deductive System integrates inference rules for propositional calculus and definitions.We prove the soundness and completeness of this Deductive System for a slightly restricted fragment of PC(ID). We also give a counter-example to show that cut-elimination does not hold in this proof System.

Francesco Scarcello - One of the best experts on this subject based on the ideXlab platform.

  • a Deductive System for non monotonic reasoning
    International Conference on Logic Programming, 1997
    Co-Authors: Thomas Eiter, Nicola Leone, Cristinel Mateis, Gerald Pfeifer, Francesco Scarcello
    Abstract:

    Disjunctive Deductive Databases (DDDBs) — function-free disjunctive logic programs with negation in rule bodies allowed — have been recently recognized as a powerful tool for knowledge representation and commonsense reasoning. Much research has been spent on issues like semantics and complexity of DDDBs, but the important area of implementing DDDBs has been less addressed so far. However, a thorough investigation thereof is a basic requirement for building Systems which render previous foundational work on DDDBs useful for practice.

Ping Hou - One of the best experts on this subject based on the ideXlab platform.

  • a Deductive System for fo id based on least fixpoint logic
    International Conference on Logic Programming, 2009
    Co-Authors: Ping Hou, Marc Denecker
    Abstract:

    The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. The goal of this paper is to extend Gentzen's sequent calculus to obtain a Deductive inference method for FO(ID). The main difficulty in building such a proof System is the representation and inference of unfounded sets. It turns out that we can represent unfounded sets by least fixpoint expressions borrowed from stratified least fixpoint logic (SLFP), which is a logic with a least fixpoint operator and characterizes the expressibility of stratified logic programs. Therefore, in this paper, we integrate least fixpoint expressions into FO(ID) and define the logic FO(ID,SLFP). We investigate a sequent calculus for FO(ID,SLFP), which extends the sequent calculus for SLFP with inference rules for the inductive definitions of FO(ID). We show that this proof System is sound with respect to a slightly restricted fragment of FO(ID) and complete for a more restricted fragment of FO(ID).

  • a Deductive System for pc id
    International Conference on Logic Programming, 2007
    Co-Authors: Ping Hou, Johan Wittocx, Marc Denecker
    Abstract:

    The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. This paper studies a Deductive inference method for PC(ID), its propositional fragment.We introduce a formal proof System based on the sequent calculus (Gentzen-style Deductive System) for this logic. As PC(ID) is an integration of classical propositional logic and propositional inductive definitions, our Deductive System integrates inference rules for propositional calculus and definitions.We prove the soundness and completeness of this Deductive System for a slightly restricted fragment of PC(ID). We also give a counter-example to show that cut-elimination does not hold in this proof System.

  • LPNMR - A Deductive System for PC(ID)
    Logic Programming and Nonmonotonic Reasoning, 1
    Co-Authors: Ping Hou, Johan Wittocx, Marc Denecker
    Abstract:

    The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. This paper studies a Deductive inference method for PC(ID), its propositional fragment.We introduce a formal proof System based on the sequent calculus (Gentzen-style Deductive System) for this logic. As PC(ID) is an integration of classical propositional logic and propositional inductive definitions, our Deductive System integrates inference rules for propositional calculus and definitions.We prove the soundness and completeness of this Deductive System for a slightly restricted fragment of PC(ID). We also give a counter-example to show that cut-elimination does not hold in this proof System.

Antoine Zimmermann - One of the best experts on this subject based on the ideXlab platform.

  • A general framework for representing, reasoning and querying with annotated Semantic Web data
    Journal of Web Semantics, 2012
    Co-Authors: Antoine Zimmermann, Nuno Lopes, Axel Polleres, Umberto Straccia
    Abstract:

    We describe a generic framework for representing and reasoning with annotated Semantic Web data, a task becoming more important with the recent increased amount of inconsistent and non-reliable meta-data on the Web. We formalise the annotated language, the corresponding Deductive System and address the query answering problem. Previous contributions on specific RDF annotation domains are encompassed by our unified reasoning formalism as we show by instantiating it on (i) temporal, (ii) fuzzy, and (iii) provenance annotations. Moreover, we provide a generic method for combining multiple annotation domains allowing to represent, e.g., temporally-annotated fuzzy RDF. Furthermore, we address the development of a query language – AnQL – that is inspired by SPARQL, including several features of SPARQL 1.1 (subqueries, aggregates, assignment, solution modifiers) along with the formal definitions of their semantics.

  • A General Framework for Representing, Reasoning and Querying with Annotated Semantic Web Data (updated version)
    2011
    Co-Authors: Antoine Zimmermann, Nuno Lopes, Axel Polleres, Umberto Straccia
    Abstract:

    We describe a generic framework for representing and reasoning with annotated Semantic Web data, a task becoming more important with the recent increased amount of inconsistent and non-reliable meta-data on the web. We formalise the annotated language, the corresponding Deductive System and address the query answering problem. Previous contributions on specific RDF annotation domains are encompassed by our unified reasoning formalism as we show by instantiating it on (i) temporal, (ii) fuzzy, and (iii) provenance annotations. Moreover, we provide a generic method for combining multiple annotation domains allowing to represent, e.g., temporally-annotated fuzzy RDF. Furthermore, we address the development of a query language – AnQL – that is inspired by SPARQL, including several features of SPARQL 1.1 (subqueries, aggregates, assignment, solution modifiers) along with the formal definitions of their semantics.