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Calculus

The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform

Kentaro Kikuchi – 1st expert on this subject based on the ideXlab platform

  • FLOPS – A Direct Proof of Strong Normalization for an Extended Herbelin’s Calculus
    Functional and Logic Programming, 2004
    Co-Authors: Kentaro Kikuchi

    Abstract:

    Herbelin presented (at CSL’94) an explicit substitution Calculus with a sequent Calculus as a type system, in which reduction steps correspond to cut-elimination steps. The Calculus, extended with some rules for substitution propagation, simulates β-reduction of ordinary λ-Calculus. In this paper we present a proof of strong normalization for the typable terms of the Calculus. The proof is a direct one in the sense that it does not depend on the result of strong normalization for the simply typed λ-Calculus, unlike an earlier proof by Dyckhoff and Urban.

  • a direct proof of strong normalization for an extended herbelin s Calculus
    Lecture Notes in Computer Science, 2004
    Co-Authors: Kentaro Kikuchi

    Abstract:

    Herbelin presented (at CSL’94) an explicit substitution Calculus with a sequent Calculus as a type system, in which reduction steps correspond to cut-elimination steps. The Calculus, extended with some rules for substitution propagation, simulates β-reduction of ordinary A-Calculus. In this paper we present a proof of strong normalization for the typable terms of the Calculus. The proof is a direct one in the sense that it does not depend on the result of strong normalization for the simply typed A-Calculus, unlike an earlier proof by Dyckhoff and Urban.

Silvia Likavec – 2nd expert on this subject based on the ideXlab platform

  • strong normalization of the dual classical sequent Calculus
    International Conference on Logic Programming, 2005
    Co-Authors: Daniel J Dougherty, Silvia Ghilezan, Pierre Lescanne, Silvia Likavec

    Abstract:

    We investigate some syntactic properties of Wadler’s dual Calculus, a term Calculus which corresponds to classical sequent logic in the same way that Parigot’s λμ Calculus corresponds to classical natural deduction. Our main result is strong normalization theorem for reduction in the dual Calculus; we also prove some confluence results for the typed and untyped versions of the system.

  • LPAR – Strong normalization of the dual classical sequent Calculus
    Logic for Programming Artificial Intelligence and Reasoning, 2005
    Co-Authors: Daniel J Dougherty, Silvia Ghilezan, Pierre Lescanne, Silvia Likavec

    Abstract:

    We investigate some syntactic properties of Wadler’s dual Calculus, a term Calculus which corresponds to classical sequent logic in the same way that Parigot’s λμ Calculus corresponds to classical natural deduction. Our main result is strong normalization theorem for reduction in the dual Calculus; we also prove some confluence results for the typed and untyped versions of the system.

Ravi Palla – 3rd expert on this subject based on the ideXlab platform

  • reformulating the situation Calculus and the event Calculus in the general theory of stable models and in answer set programming
    Journal of Artificial Intelligence Research, 2012
    Co-Authors: Ravi Palla

    Abstract:

    Circumscription and logic programs under the stable model semantics are two wellknown nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation Calculus, the event Calculus and temporal action logics; the latter has served as a basis of a family of action languages, such as language A and several of its descendants. Based on the discovery that circumscription and the stable model semantics coincide on a class of canonical formulas, we reformulate the situation Calculus and the event Calculus in the general theory of stable models. We also present a translation that turns the reformulations further into answer set programs, so that efficient answer set solvers can be applied to compute the situation Calculus and the event Calculus.