The Experts below are selected from a list of 96 Experts worldwide ranked by ideXlab platform

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

  • Defeasible inheritance-based description logics
    Journal of Artificial Intelligence Research, 2013
    Co-Authors: Giovanni Casini, Umberto Straccia
    Abstract:

    Defeasible inheritance networks are a non-monotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach to non-monotonic reasoning. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics (DLs), a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is built on top of the classical Entailment Relation and, thus, is amenable of an implementation based on existing reasoners. Eventually, we evaluate our approach on well-known landmark test examples.

  • defeasible inheritance based description logics
    International Joint Conference on Artificial Intelligence, 2011
    Co-Authors: Giovanni Casini, Umberto Straccia
    Abstract:

    Defeasible inheritance networks are a nonmonotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics, a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is build on top of the classical Entailment Relation.

Giovanni Casini - One of the best experts on this subject based on the ideXlab platform.

  • Defeasible inheritance-based description logics
    Journal of Artificial Intelligence Research, 2013
    Co-Authors: Giovanni Casini, Umberto Straccia
    Abstract:

    Defeasible inheritance networks are a non-monotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach to non-monotonic reasoning. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics (DLs), a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is built on top of the classical Entailment Relation and, thus, is amenable of an implementation based on existing reasoners. Eventually, we evaluate our approach on well-known landmark test examples.

  • defeasible inheritance based description logics
    International Joint Conference on Artificial Intelligence, 2011
    Co-Authors: Giovanni Casini, Umberto Straccia
    Abstract:

    Defeasible inheritance networks are a nonmonotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics, a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is build on top of the classical Entailment Relation.

Yidong Shen - One of the best experts on this subject based on the ideXlab platform.

  • a default approach to semantics of logic programs with constraint atoms
    International Conference on Logic Programming, 2009
    Co-Authors: Yidong Shen
    Abstract:

    We define the semantics of logic programs with (abstract) constraint atoms in a way closely tied to default logic. Like default logic, formulas in rules are evaluated using the classical Entailment Relation, so a constraint atom can be represented by an equivalent propositional formula. Therefore, answer sets are defined in a way closely related to default extensions. The semantics defined this way enjoys two properties generally considered desirable for answer set programming *** minimality and derivability . The derivability property is very important because it guarantees free of self-supporting loops in answer sets. We show that when restricted to basic logic programs, this semantics agrees with the conditional-satisfaction based semantics. Furthermore, answer sets by the minimal-model based semantics can be recast in our approach. Consequently, the default approach gives a unifying account of the major existing semantics for logic programs with constraint atoms. This also makes it possible to characterize, in terms of the minimality and derivability properties, the precise Relationship between them and contrast with others.

Christopher D Manning - One of the best experts on this subject based on the ideXlab platform.

  • modeling semantic containment and exclusion in natural language inference
    International Conference on Computational Linguistics, 2008
    Co-Authors: Bill Maccartney, Christopher D Manning
    Abstract:

    We propose an approach to natural language inference based on a model of natural logic, which identifies valid inferences by their lexical and syntactic features, without full semantic interpretation. We greatly extend past work in natural logic, which has focused solely on semantic containment and monotonicity, to incorporate both semantic exclusion and implicativity. Our system decomposes an inference problem into a sequence of atomic edits linking premise to hypothesis; predicts a lexical Entailment Relation for each edit using a statistical classifier; propagates these Relations upward through a syntax tree according to semantic properties of intermediate nodes; and composes the resulting Entailment Relations across the edit sequence. We evaluate our system on the FraCaS test suite, and achieve a 27% reduction in error from previous work. We also show that hybridizing an existing RTE system with our natural logic system yields significant gains on the RTE3 test suite.

Neuwirth Stefan - One of the best experts on this subject based on the ideXlab platform.

  • Regular Entailment Relations
    Springer International Publishing, 2021
    Co-Authors: Coquand Thierry, Lombardi Henri, Neuwirth Stefan
    Abstract:

    International audienceInspired by the work of Lorenzen on the theory of preordered groups in the forties and fifties, we define regular Entailment Relations and show a crucial theorem for this structure. We also describe equivariant systems of ideals à la Lorenzen and show that the remarkable regularisation process invented by him yields a regular Entailment Relation. By providing constructive objects and arguments, we pursue Lorenzen's aim of ``bringing to light the basic, pure concepts in their simple and transparent clarity'

  • Groupes réticulés engendrés par un groupe ordonné et systèmes réguliers d'idéaux
    'Rocky Mountain Mathematics Consortium', 2019
    Co-Authors: Coquand Thierry, Lombardi Henri, Neuwirth Stefan
    Abstract:

    International audienceUnbounded Entailment Relations, introduced by Paul Lorenzen (1951), are a slight variant of a notion which plays a fundamental rôle in logic (see Scott 1974) and in algebra (see Lombardi and Quitté 2015). We call “systems of ideals” their single-conclusion counterpart. If they preserve the order of a commutative ordered monoid G and are equivariant w.r.t. its law, we call them “equivariant systems of ideals for G”: they describe all morphisms from G to meet-semilattice-ordered monoids generated by (the image of) G. Taking an article by Lorenzen (1953) as a starting point, we also describe all morphisms from a commutative ordered group G to lattice-ordered groups generated by G through unbounded Entailment Relations that preserve its order, are equivariant, and satisfy a regularity property invented by Lorenzen (1950); we call them “regular Entailment Relations”. In particular, the free lattice-ordered group generated by G is described through the finest regular Entailment Relation for G, and we provide an explicit description for it; it is order-reflecting if and only if the morphism is injective, so that the Lorenzen-Clifford-Dieudonné theorem fits into our framework. Lorenzen’s research in algebra starts as an inquiry into the system of Dedekind ideals for the divisibility group of an integral domain R, and specifically into Wolfgang Krull’s “Fundamentalsatz” that R may be represented as an intersection of valuation rings if and only if R is integrally closed: his constructive substitute for this representation is the “regularisation” of the system of Dedekind ideals, i.e. the lattice-ordered group generated by it when doing as if its elements are comparable

  • Lattice-ordered groups generated by an ordered group and regular systems of ideals
    2018
    Co-Authors: Coquand Thierry, Lombardi Henri, Neuwirth Stefan
    Abstract:

    Unbounded Entailment Relations, introduced by Paul Lorenzen (1951), are a slight variant of a notion which plays a fundamental r\^ole in logic (see Scott 1974) and in algebra (see Lombardi and Quitt\'e 2015). We call systems of ideals their single-conclusion counterpart. If they preserve the order of a commutative ordered monoid G and are equivariant w.r.t. its law, we call them equivariant systems of ideals for G: they describe all morphisms from G to meet-semilattice-ordered monoids generated by (the image of) G. Taking an article by Lorenzen (1953) as a starting point, we also describe all morphisms from a commutative ordered group G to lattice-ordered groups generated by G through unbounded Entailment Relations that preserve its order, are equivariant, and satisfy a regularity property invented by Lorenzen (1950); we call them regular Entailment Relations. In particular, the free lattice-ordered group generated by G is described through the finest regular Entailment Relation for G, and we provide an explicit description for it; it is order-reflecting if and only if the morphism is injective, so that the Lorenzen-Clifford-Dieudonn\'e theorem fits into our framework. Lorenzen's research in algebra starts as an inquiry into the system of Dedekind ideals for the divisibility group of an integral domain R, and specifically into Wolfgang Krull's "Fundamentalsatz" that R may be represented as an intersection of valuation rings if and only if R is integrally closed: his constructive substitute for this representation is the regularisation of the system of Dedekind ideals, i.e. the lattice-ordered group generated by it when one proceeds as if its elements are comparable