372,380 research outputs found

    Theory of partial-order programming

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    This paper shows the use of partial-order program clauses and lattice domains for declarative programming. This paradigm is particularly useful for expressing concise solutions to problems from graph theory, program analysis, and database querying. These applications are characterized by a need to solve circular constraints and perform aggregate operations, a capability that is very clearly and efficiently provided by partial-order clauses. We present a novel approach to their declarative and operational semantics, as well as the correctness of the operational semantics. The declarative semantics is model-theoretic in nature, but the least model for any function is not the classical intersection of all models, but the greatest lower bound/least upper bound of the respective terms defined for this function in the different models. The operational semantics combines top-down goal reduction with memo-tables. In the partial-order programming framework, however, memoization is primarily needed in order to detect circular circular function calls. In general we need more than simple memoization when functions are defined circularly in terms of one another through monotonic functions. In such cases, we accumulate a set of functional-constraint and solve them by general fixed-point-finding procedure. In order to prove the correctness of memoization, a straightforward induction on the length of the derivation will not suffice because of the presence of the memo-table. However, since the entries in the table grow monotonically, we identify a suitable table invariant that captures the correctness of the derivation. The partial-order programming paradigm has been implemented and all examples shown in this paper have been tested using this implementation

    Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion

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    In this paper, we consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in [10.11], we can investigate the more general stochastic optimal control problems under G-expectation than that were constructed in [28]. Then we obtain a generalized dynamic programming principle and the value function is proved to be a viscosity solution of a fully nonlinear second-order partial differential equation.Comment: 25 page

    Second-order subdifferential calculus with applications to tilt stability in optimization

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    The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the so-called (full and partial) second-order subdifferentials of extended-real-valued functions, which are dual-type constructions generated by coderivatives of frst-order subdifferential mappings. We develop an extended second-order subdifferential calculus and analyze the basic second-order qualification condition ensuring the fulfillment of the principal secondorder chain rule for strongly and fully amenable compositions. The calculus results obtained in this way and computing the second-order subdifferentials for piecewise linear-quadratic functions and their major specifications are applied then to the study of tilt stability of local minimizers for important classes of problems in constrained optimization that include, in particular, problems of nonlinear programming and certain classes of extended nonlinear programs described in composite terms

    Ordinal Measures of the Set of Finite Multisets

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    Well-partial orders, and the ordinal invariants used to measure them, are relevant in set theory, program verification, proof theory and many other areas of computer science and mathematics. In this article we focus on a common data structure in programming, finite multisets of some well partial order. There are two natural orders one can define on the set of finite multisets of a partial order: the multiset embedding and the multiset ordering. Though the maximal order type of these orders is already known, other ordinal invariants remain mostly unknown. Our main contributions are expressions to compute compositionally the width of the multiset embedding and the height of the multiset ordering. Furthermore, we provide a new ordinal invariant useful for characterizing the width of the multiset ordering

    The independence of control structures in abstract programming systems

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    AbstractAn instance of a control structure is a mapping which takes one or more programs into a new program whose behavior is based on that of the original programs. An instance of a control structure is effective iff it is effectively computable. In order to study the interrelationships of control structures, . we consider abstract programming systems (numberings of the partial recursive functions) in which some control structures, effective or otherwise, are present, but others are not. This paper uses the techniques of recursive function theory, including recursion theorems and priority arguments to prove the independence of certain control structures in abstract programming systems. For example, we have obtained the following results. In effective numberings of the partial recursive functions, the one-one effective Kleene recursion theorem and the one-one effective (partial) if-then-else control structure are independent, but together, they yield all effective control structures. In any effective numbering, the effective Kleene form of the double recursion theorem yields all effective control structures

    Towards Closed World Reasoning in Dynamic Open Worlds (Extended Version)

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    The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases composed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve. In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties. To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.Comment: 40 pages; an extended version of the article published in Theory and Practice of Logic Programming, 10 (4-6): 547 - 564, July. Copyright 2010 Cambridge University Pres
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