The Experts below are selected from a list of 69 Experts worldwide ranked by ideXlab platform

Phan Huy Tu - One of the best experts on this subject based on the ideXlab platform.

  • answer sets for logic programs with arbitrary abstract constraint atoms
    Journal of Artificial Intelligence Research, 2007
    Co-Authors: Enrico Pontelli, Phan Huy Tu
    Abstract:

    In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer set semantics of normal logic programs to the case of logic programs with arbitrary types of c-atoms. The results are four different answer set definitions which are equivalent when applied to normal logic programs. The standard fixpoint-based semantics of logic programs is generalized in two directions, called answer set by reduct and answer set by complement. These definitions, which differ from each other in the treatment of negation-as-failure (naf) atoms, make use of an immediate Consequence Operator to perform answer set checking, whose definition relies on the notion of conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The other two definitions, called strongly and weakly well-supported models, are generalizations of the notion of well-supported models of normal logic programs to the case of programs with c-atoms. As for the case of fixpoint-based semantics, the difference between these two definitions is rooted in the treatment of naf atoms. We prove that answer sets by reduct (resp. by complement) are equivalent to weakly (resp. strongly) well-supported models of a program, thus generalizing the theorem on the correspondence between stable models and well-supported models of a normal logic program to the class of programs with c-atoms. We show that the newly defined semantics coincide with previously introduced semantics for logic programs with monotone c-atoms, and they extend the original answer set semantics of normal logic programs. We also study some properties of answer sets of programs with c-atoms, and relate our definitions to several semantics for logic programs with aggregates presented in the literature.

  • answer sets for logic programs with arbitrary abstract constraint atoms
    National Conference on Artificial Intelligence, 2006
    Co-Authors: Enrico Pontelli, Phan Huy Tu
    Abstract:

    We present two equivalent approaches for defining answer sets for logic programs with arbitrary abstract constraint atoms (c-atoms). The first approach uses an immediate Consequence Operator for answer set checking. whose definition relies on the notion of conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The second approach generalizes the notion of well-supported models of normal logic programs to programs with c-atoms. We prove that the newly defined semantics coincides with previously introduced semantics for logic programs with monotone c-atoms and extends the original answer set semantics for normal logic programs. We discuss different possibilities for treating negation-as-failure c-atoms and characterize situations in which they yield the same answer sets. We study some properties of answer sets of programs with c-atoms and relate our definition to several semantics for logic programs with aggregates.

Enrico Pontelli - One of the best experts on this subject based on the ideXlab platform.

  • a constructive semantic characterization of aggregates in answer set programming
    Theory and Practice of Logic Programming, 2007
    Co-Authors: Tran Cao Son, Enrico Pontelli
    Abstract:

    This technical note describes a monotone and continuous fixpoint Operator to compute the answer sets of programs with aggregates. The fixpoint Operator relies on the notion of aggregate solution. Under certain conditions, this Operator behaves identically to the three-valued immediate Consequence Operator PaggrP for aggregate programs, independently proposed in Pelov (2004) and Pelov et al. (2004). This Operator allows us to closely tie the computational complexity of the answer set checking and answer sets existence problems to the cost of checking a solution of the aggregates in the program. Finally, we relate the semantics described by the Operator to other proposals for logic programming with aggregates.

  • answer sets for logic programs with arbitrary abstract constraint atoms
    Journal of Artificial Intelligence Research, 2007
    Co-Authors: Enrico Pontelli, Phan Huy Tu
    Abstract:

    In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer set semantics of normal logic programs to the case of logic programs with arbitrary types of c-atoms. The results are four different answer set definitions which are equivalent when applied to normal logic programs. The standard fixpoint-based semantics of logic programs is generalized in two directions, called answer set by reduct and answer set by complement. These definitions, which differ from each other in the treatment of negation-as-failure (naf) atoms, make use of an immediate Consequence Operator to perform answer set checking, whose definition relies on the notion of conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The other two definitions, called strongly and weakly well-supported models, are generalizations of the notion of well-supported models of normal logic programs to the case of programs with c-atoms. As for the case of fixpoint-based semantics, the difference between these two definitions is rooted in the treatment of naf atoms. We prove that answer sets by reduct (resp. by complement) are equivalent to weakly (resp. strongly) well-supported models of a program, thus generalizing the theorem on the correspondence between stable models and well-supported models of a normal logic program to the class of programs with c-atoms. We show that the newly defined semantics coincide with previously introduced semantics for logic programs with monotone c-atoms, and they extend the original answer set semantics of normal logic programs. We also study some properties of answer sets of programs with c-atoms, and relate our definitions to several semantics for logic programs with aggregates presented in the literature.

  • answer sets for logic programs with arbitrary abstract constraint atoms
    National Conference on Artificial Intelligence, 2006
    Co-Authors: Enrico Pontelli, Phan Huy Tu
    Abstract:

    We present two equivalent approaches for defining answer sets for logic programs with arbitrary abstract constraint atoms (c-atoms). The first approach uses an immediate Consequence Operator for answer set checking. whose definition relies on the notion of conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The second approach generalizes the notion of well-supported models of normal logic programs to programs with c-atoms. We prove that the newly defined semantics coincides with previously introduced semantics for logic programs with monotone c-atoms and extends the original answer set semantics for normal logic programs. We discuss different possibilities for treating negation-as-failure c-atoms and characterize situations in which they yield the same answer sets. We study some properties of answer sets of programs with c-atoms and relate our definition to several semantics for logic programs with aggregates.

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

  • Grounded fixpoints
    AAAI Press, 2015
    Co-Authors: Bogaerts Bart, Vennekens Joost, Denecker Marc
    Abstract:

    Algebraical fixpoint theory is an invaluable instrument for studying semantics of logics. For example, all major semantics of logic programming, autoepistemic logic, default logic and more recently, abstract argumentation have been shown to be induced by the different types of+fixpoints defined in approximation fixpoint theory (AFT). In this paper, we add a new type of fixpoint to AFT: a grounded fixpoint of lattice Operator O : L → L is defined as a lattice element x ∈ L such that O(x) = x and for all v ∈ L such that O(v ∧ x) ≤ v, it holds that x ≤ v. On the algebraical level, we show that all grounded fixpoints are minimal fixpoints approximated by the well-founded fixpoint and that all stable fixpoints are grounded. On the logical level, grounded fixpoints provide a new mathematically simple and compact type of semantics for any logic with a (possibly non-monotone) semantic Operator. We explain the intuition underlying this semantics in the context of logic programming by pointing out that grounded fixpoints of the immediate Consequence Operator are interpretations that have no non-trivial unfounded sets. We also analyse the complexity of the induced semantics. Summarised, grounded fixpoint semantics is a new, probably the simplest and most compact, element in the family of semantics that capture basic intuitions and principles of various non-monotonic logics.status: publishe

  • Grounded fixpoints
    Leuven Belgium, 2014
    Co-Authors: Bogaerts Bart, Vennekens Joost, Denecker Marc
    Abstract:

    Algebraical fixpoint theory is an invaluable instrument for studying semantics of logics. For example, all major semantics of logic programming, autoepistemic logic, default logic and more recently, abstract argumentation have been shown to be induced by the different types of fixpoints defined in approximation fixpoint theory (AFT). In this paper, we add a new type of fixpoint to AFT: a grounded fixpoint of lattice Operator O : L → L is defined as a lattice element x ∈ L such that O(x) = x and for all v ∈ L such that O(v ∧ x) ≤ v, it holds that x ≤ v. On the algebraical level, we show that all grounded fixpoints are minimal fixpoints approximated by the well-founded fixpoint and that all stable fixpoints are grounded. On the logical level, grounded fixpoints provide a new mathematically simple and compact type of semantics for any logic with a (possibly non-monotone) semantic Operator. We explain the intuition underlying this semantics in the context of logic programming by pointing out that grounded fixpoints of the immediate Consequence Operator are interpretations that have no non-trivial unfounded sets. We also analyse the complexity of the induced semantics. Summarised, grounded fixpoint semantics is a new, probably the simplest and most compact, element in the family of semantics that capture basic intuitions and principles of various non-monotonic logics.nrpages: 9status: publishe

Andreas Behrend - One of the best experts on this subject based on the ideXlab platform.

  • a uniform fixpoint approach to the implementation of inference methods for deductive databases
    arXiv: Databases, 2011
    Co-Authors: Andreas Behrend
    Abstract:

    Within the research area of deductive databases three different database tasks have been deeply investigated: query evaluation, update propagation and view updating. Over the last thirty years various inference mechanisms have been proposed for realizing these main functionalities of a rule-based system. However, these inference mechanisms have been rarely used in commercial DB systems until now. One important reason for this is the lack of a uniform approach well-suited for implementation in an SQL-based system. In this paper, we present such a uniform approach in form of a new version of the soft Consequence Operator. Additionally, we present improved transformation-based approaches to query optimization and update propagation and view updating which are all using this Operator as underlying evaluation mechanism.

  • a fixpoint approach to state generation for stratifiable disjunctive deductive databases
    Advances in Databases and Information Systems, 2007
    Co-Authors: Andreas Behrend
    Abstract:

    In this paper we present a new fixpoint-based approach to bottom-up state generation for stratifiable disjunctive deductive databases. To this end, a new Consequence Operator based on hyperresolution is introduced which extends Minker's Operator for positive disjunctive Datalog rules. In contrast to already existing model generation methods our approach for efficiently computing perfect models is based on state generation. Additionally, it enhances model state computation based on Minker's Operator for positive disjunctive Datalog rules.

Bogaerts Bart - One of the best experts on this subject based on the ideXlab platform.

  • Grounded fixpoints
    AAAI Press, 2015
    Co-Authors: Bogaerts Bart, Vennekens Joost, Denecker Marc
    Abstract:

    Algebraical fixpoint theory is an invaluable instrument for studying semantics of logics. For example, all major semantics of logic programming, autoepistemic logic, default logic and more recently, abstract argumentation have been shown to be induced by the different types of+fixpoints defined in approximation fixpoint theory (AFT). In this paper, we add a new type of fixpoint to AFT: a grounded fixpoint of lattice Operator O : L → L is defined as a lattice element x ∈ L such that O(x) = x and for all v ∈ L such that O(v ∧ x) ≤ v, it holds that x ≤ v. On the algebraical level, we show that all grounded fixpoints are minimal fixpoints approximated by the well-founded fixpoint and that all stable fixpoints are grounded. On the logical level, grounded fixpoints provide a new mathematically simple and compact type of semantics for any logic with a (possibly non-monotone) semantic Operator. We explain the intuition underlying this semantics in the context of logic programming by pointing out that grounded fixpoints of the immediate Consequence Operator are interpretations that have no non-trivial unfounded sets. We also analyse the complexity of the induced semantics. Summarised, grounded fixpoint semantics is a new, probably the simplest and most compact, element in the family of semantics that capture basic intuitions and principles of various non-monotonic logics.status: publishe

  • Grounded fixpoints
    Leuven Belgium, 2014
    Co-Authors: Bogaerts Bart, Vennekens Joost, Denecker Marc
    Abstract:

    Algebraical fixpoint theory is an invaluable instrument for studying semantics of logics. For example, all major semantics of logic programming, autoepistemic logic, default logic and more recently, abstract argumentation have been shown to be induced by the different types of fixpoints defined in approximation fixpoint theory (AFT). In this paper, we add a new type of fixpoint to AFT: a grounded fixpoint of lattice Operator O : L → L is defined as a lattice element x ∈ L such that O(x) = x and for all v ∈ L such that O(v ∧ x) ≤ v, it holds that x ≤ v. On the algebraical level, we show that all grounded fixpoints are minimal fixpoints approximated by the well-founded fixpoint and that all stable fixpoints are grounded. On the logical level, grounded fixpoints provide a new mathematically simple and compact type of semantics for any logic with a (possibly non-monotone) semantic Operator. We explain the intuition underlying this semantics in the context of logic programming by pointing out that grounded fixpoints of the immediate Consequence Operator are interpretations that have no non-trivial unfounded sets. We also analyse the complexity of the induced semantics. Summarised, grounded fixpoint semantics is a new, probably the simplest and most compact, element in the family of semantics that capture basic intuitions and principles of various non-monotonic logics.nrpages: 9status: publishe