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Jan Paredaens - One of the best experts on this subject based on the ideXlab platform.

  • a study of a Positive Fragment of path queries
    The Computer Journal, 2011
    Co-Authors: Dirk Van Gucht, Marc Gyssens, Jan Paredaens
    Abstract:

    We study the expressiveness of a Positive Fragment of path queries, denoted Path+, on documents that can be represented as node-labeled trees. The expressiveness of Path+ is studied from two angles. First, we establish that Path+ is equivalent in expressive power to two particular subFragments, as well as to the class of tree queries, a subclass of the first-order conjunctive queries defined over the label, parent–child and child–parent predicates. The translation algorithm from tree queries to Path+ yields a normal form for Path+ queries. Using this normal form, we can decompose a Path+ query into subqueries that can be expressed in a very small Fragment of Path+ for which efficient evaluation strategies are available. Second, we characterize the expressiveness of Path+ in terms of its ability to resolve nodes in a document. This result is used to show that each tree query can be translated to a unique, equivalent and minimal tree query. The combination of these results yields an effective strategy to evaluate a large class of path queries on documents.

  • a study of a Positive Fragment of path queries expressiveness normal form and minimization
    British National Conference on Databases, 2009
    Co-Authors: Dirk Van Gucht, Marc Gyssens, Jan Paredaens
    Abstract:

    We study the expressiveness of a Positive Fragment of path queries, denoted Path$\mathstrut^+$, on node-labeled trees documents. The expressiveness of Path$\mathstrut^+$ is studied from two angles. First, we establish that Path$\mathstrut^+$ is equivalent in expressive power to a particular sub-Fragment as well as to the class of tree queries, a sub-class of the first-order conjunctive queries defined over label, parent-child, and child-parent predicates. The translation algorithm from tree queries to Path$\mathstrut^+$ yields a normal form for Path$\mathstrut^+$ queries. Using this normal form, we can decompose a Path$\mathstrut^+$ query into sub-queries that can be expressed in a very small sub-Fragment of Path$\mathstrut^+$ for which efficient evaluation strategies are available. Second, we characterize the expressiveness of Path$\mathstrut^+$ in terms of its ability to resolve nodes in a document. This result is used to show that each tree query can be translated to a unique, equivalent, and minimal tree query. The combination of these results yields an effective strategy to evaluate a large class of path queries on documents.

Dirk Van Gucht - One of the best experts on this subject based on the ideXlab platform.

  • a study of a Positive Fragment of path queries
    The Computer Journal, 2011
    Co-Authors: Dirk Van Gucht, Marc Gyssens, Jan Paredaens
    Abstract:

    We study the expressiveness of a Positive Fragment of path queries, denoted Path+, on documents that can be represented as node-labeled trees. The expressiveness of Path+ is studied from two angles. First, we establish that Path+ is equivalent in expressive power to two particular subFragments, as well as to the class of tree queries, a subclass of the first-order conjunctive queries defined over the label, parent–child and child–parent predicates. The translation algorithm from tree queries to Path+ yields a normal form for Path+ queries. Using this normal form, we can decompose a Path+ query into subqueries that can be expressed in a very small Fragment of Path+ for which efficient evaluation strategies are available. Second, we characterize the expressiveness of Path+ in terms of its ability to resolve nodes in a document. This result is used to show that each tree query can be translated to a unique, equivalent and minimal tree query. The combination of these results yields an effective strategy to evaluate a large class of path queries on documents.

  • a study of a Positive Fragment of path queries expressiveness normal form and minimization
    British National Conference on Databases, 2009
    Co-Authors: Dirk Van Gucht, Marc Gyssens, Jan Paredaens
    Abstract:

    We study the expressiveness of a Positive Fragment of path queries, denoted Path$\mathstrut^+$, on node-labeled trees documents. The expressiveness of Path$\mathstrut^+$ is studied from two angles. First, we establish that Path$\mathstrut^+$ is equivalent in expressive power to a particular sub-Fragment as well as to the class of tree queries, a sub-class of the first-order conjunctive queries defined over label, parent-child, and child-parent predicates. The translation algorithm from tree queries to Path$\mathstrut^+$ yields a normal form for Path$\mathstrut^+$ queries. Using this normal form, we can decompose a Path$\mathstrut^+$ query into sub-queries that can be expressed in a very small sub-Fragment of Path$\mathstrut^+$ for which efficient evaluation strategies are available. Second, we characterize the expressiveness of Path$\mathstrut^+$ in terms of its ability to resolve nodes in a document. This result is used to show that each tree query can be translated to a unique, equivalent, and minimal tree query. The combination of these results yields an effective strategy to evaluate a large class of path queries on documents.

Zhiguang Zhao - One of the best experts on this subject based on the ideXlab platform.

  • Z.: Positive formulas in intuitionistic and minimal logic. Submitted to this volume (2014) On duality and universal models 19
    2020
    Co-Authors: Dick De Jongh, Zhiguang Zhao
    Abstract:

    Abstract. In this article we investigate the Positive, i.e. ¬, ⊥-free formulas of intuitionistic propositional and predicate logic, IPC and IQC, and minimal logic, MPC and MQC. For each formula ϕ of IQC we define the Positive formula ϕ + that represents the Positive content of ϕ. The formulas ϕ and ϕ + exhibit the same behavior on top models, models with a largest world that makes all atomic sentences true. We characterize the Positive formulas of IPC and IQC as the formulas that are immune to the operation of turning a model into a top model. With the +-operation we show, using the uniform interpolation theorem for IPC, that both the Positive Fragment of IPC and MPC respect a revised version of uniform interpolation. In propositional logic the well-known theorem that KC is conservative over the Positive Fragment of IPC is shown to generalize to many logics with Positive axioms. In first-order logic, we show that IQC + DNS (double negation shift) + KC is conservative over the Positive Fragment of IQC and similar results as for IPC

  • universal models for the Positive Fragment of intuitionistic logic
    Tbilisi Symposium on Logic Language and Computation, 2015
    Co-Authors: Nick Bezhanishvili, Dick De Jongh, Apostolos Tzimoulis, Zhiguang Zhao
    Abstract:

    We describe the n-universal model $$\mathcal {U}^\star n$$ of the Positive Fragment of the intuitionistic propositional calculus $$\mathsf {IPC}$$. We show that $$\mathcal {U}^\star n$$ is isomorphic to a generated submodel of $$\mathcal {U}n$$ --- the n-universal model of $$\mathsf {IPC}$$. Using $$\mathcal {U}^\star n$$, we give an alternative proof of Jankov's theorem stating that the intermediate logic $$\mathsf {KC}$$, the logic of the weak law of excluded middle, is the greatest intermediate logic extending $$\mathsf {IPC}$$ that proves exactly the same Positive formulas as $$\mathsf {IPC}$$.

  • Positive formulas in intuitionistic and minimal logic
    Tbilisi Symposium on Logic Language and Computation, 2013
    Co-Authors: Dick De Jongh, Zhiguang Zhao
    Abstract:

    In this article we investigate the Positive, i.e. $$\lnot ,\bot $$-free formulas of intuitionistic propositional and predicate logic, IPC and IQC, and minimal logic, MPC and MQC. For each formula $$\varphi $$ of IQC we define the Positive formula $$\varphi ^+$$ that represents the Positive content of $$\varphi $$. The formulas $$\varphi $$ and $$\varphi ^+$$ exhibit the same behavior on top models, models with a largest world that makes all atomic sentences true. We characterize the Positive formulas of IPC and IQC as the formulas that are immune to the operation of turning a model into a top model. With the +-operation on formulas we show, using the uniform interpolation theorem for IPC, that both the Positive Fragment of IPC and MPC respect a revised version of uniform interpolation. In propositional logic the well-known theorem that KC is conservative over the Positive Fragment of IPC is shown to generalize to many logics with Positive axioms. In first-order logic, we show that IQC + DNS double negation shift + KC is conservative over the Positive Fragment of IQC and similar results as for IPC.

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

  • a study of a Positive Fragment of path queries
    The Computer Journal, 2011
    Co-Authors: Dirk Van Gucht, Marc Gyssens, Jan Paredaens
    Abstract:

    We study the expressiveness of a Positive Fragment of path queries, denoted Path+, on documents that can be represented as node-labeled trees. The expressiveness of Path+ is studied from two angles. First, we establish that Path+ is equivalent in expressive power to two particular subFragments, as well as to the class of tree queries, a subclass of the first-order conjunctive queries defined over the label, parent–child and child–parent predicates. The translation algorithm from tree queries to Path+ yields a normal form for Path+ queries. Using this normal form, we can decompose a Path+ query into subqueries that can be expressed in a very small Fragment of Path+ for which efficient evaluation strategies are available. Second, we characterize the expressiveness of Path+ in terms of its ability to resolve nodes in a document. This result is used to show that each tree query can be translated to a unique, equivalent and minimal tree query. The combination of these results yields an effective strategy to evaluate a large class of path queries on documents.

  • a study of a Positive Fragment of path queries expressiveness normal form and minimization
    British National Conference on Databases, 2009
    Co-Authors: Dirk Van Gucht, Marc Gyssens, Jan Paredaens
    Abstract:

    We study the expressiveness of a Positive Fragment of path queries, denoted Path$\mathstrut^+$, on node-labeled trees documents. The expressiveness of Path$\mathstrut^+$ is studied from two angles. First, we establish that Path$\mathstrut^+$ is equivalent in expressive power to a particular sub-Fragment as well as to the class of tree queries, a sub-class of the first-order conjunctive queries defined over label, parent-child, and child-parent predicates. The translation algorithm from tree queries to Path$\mathstrut^+$ yields a normal form for Path$\mathstrut^+$ queries. Using this normal form, we can decompose a Path$\mathstrut^+$ query into sub-queries that can be expressed in a very small sub-Fragment of Path$\mathstrut^+$ for which efficient evaluation strategies are available. Second, we characterize the expressiveness of Path$\mathstrut^+$ in terms of its ability to resolve nodes in a document. This result is used to show that each tree query can be translated to a unique, equivalent, and minimal tree query. The combination of these results yields an effective strategy to evaluate a large class of path queries on documents.

Dick De Jongh - One of the best experts on this subject based on the ideXlab platform.

  • Z.: Positive formulas in intuitionistic and minimal logic. Submitted to this volume (2014) On duality and universal models 19
    2020
    Co-Authors: Dick De Jongh, Zhiguang Zhao
    Abstract:

    Abstract. In this article we investigate the Positive, i.e. ¬, ⊥-free formulas of intuitionistic propositional and predicate logic, IPC and IQC, and minimal logic, MPC and MQC. For each formula ϕ of IQC we define the Positive formula ϕ + that represents the Positive content of ϕ. The formulas ϕ and ϕ + exhibit the same behavior on top models, models with a largest world that makes all atomic sentences true. We characterize the Positive formulas of IPC and IQC as the formulas that are immune to the operation of turning a model into a top model. With the +-operation we show, using the uniform interpolation theorem for IPC, that both the Positive Fragment of IPC and MPC respect a revised version of uniform interpolation. In propositional logic the well-known theorem that KC is conservative over the Positive Fragment of IPC is shown to generalize to many logics with Positive axioms. In first-order logic, we show that IQC + DNS (double negation shift) + KC is conservative over the Positive Fragment of IQC and similar results as for IPC

  • universal models for the Positive Fragment of intuitionistic logic
    Tbilisi Symposium on Logic Language and Computation, 2015
    Co-Authors: Nick Bezhanishvili, Dick De Jongh, Apostolos Tzimoulis, Zhiguang Zhao
    Abstract:

    We describe the n-universal model $$\mathcal {U}^\star n$$ of the Positive Fragment of the intuitionistic propositional calculus $$\mathsf {IPC}$$. We show that $$\mathcal {U}^\star n$$ is isomorphic to a generated submodel of $$\mathcal {U}n$$ --- the n-universal model of $$\mathsf {IPC}$$. Using $$\mathcal {U}^\star n$$, we give an alternative proof of Jankov's theorem stating that the intermediate logic $$\mathsf {KC}$$, the logic of the weak law of excluded middle, is the greatest intermediate logic extending $$\mathsf {IPC}$$ that proves exactly the same Positive formulas as $$\mathsf {IPC}$$.

  • Positive formulas in intuitionistic and minimal logic
    Tbilisi Symposium on Logic Language and Computation, 2013
    Co-Authors: Dick De Jongh, Zhiguang Zhao
    Abstract:

    In this article we investigate the Positive, i.e. $$\lnot ,\bot $$-free formulas of intuitionistic propositional and predicate logic, IPC and IQC, and minimal logic, MPC and MQC. For each formula $$\varphi $$ of IQC we define the Positive formula $$\varphi ^+$$ that represents the Positive content of $$\varphi $$. The formulas $$\varphi $$ and $$\varphi ^+$$ exhibit the same behavior on top models, models with a largest world that makes all atomic sentences true. We characterize the Positive formulas of IPC and IQC as the formulas that are immune to the operation of turning a model into a top model. With the +-operation on formulas we show, using the uniform interpolation theorem for IPC, that both the Positive Fragment of IPC and MPC respect a revised version of uniform interpolation. In propositional logic the well-known theorem that KC is conservative over the Positive Fragment of IPC is shown to generalize to many logics with Positive axioms. In first-order logic, we show that IQC + DNS double negation shift + KC is conservative over the Positive Fragment of IQC and similar results as for IPC.