The research on systems of logicprogramming with modules has followed two mainstreams, programming-in-the-large, where compositional operators are provided for combining separate and independent modules, and programm...
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ISBN:
(纸本)3540632557
The research on systems of logicprogramming with modules has followed two mainstreams, programming-in-the-large, where compositional operators are provided for combining separate and independent modules, and programming-in-the-small, which aims at enhancing logicprogramming with new logical connectives. In this paper, we present a general model theoretic approach to modular logic programming which combines programming in-the-large and in-the-small in a satisfactory way. Rather than inventing completely new constructs, however, we resort to a well-known concept in formal logic: generalized quantifiers. We show how generalized quantifiers can be incorporated into logic programs, both for Horn logic programs as well as in the presence of negation. Our basic observation is then that a logic program can be seen as a generalized quantifier, and we obtain a semantics for modularlogic programs this way. Generalized quantifiers in logic programs gives rise to interesting classes of logic programs. We present a taxonomy of natural such classes, and investigate their properties. In particular, their expressive power over finite structures is analyzed.
With the recent development of a new ubiquitous nature of data and the profusity of available knowledge, there is nowadays the need to reason from multiple sources of often incomplete and uncertain knowledge. Our goal...
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With the recent development of a new ubiquitous nature of data and the profusity of available knowledge, there is nowadays the need to reason from multiple sources of often incomplete and uncertain knowledge. Our goal was to provide a way to combine declarative knowledge bases – represented as logicprogramming modules under the answer set semantics – as well as the individual results one already inferred from them, without having to recalculate the results for their composition and without having to explicitly know the original logicprogramming encodings that produced such results. This posed us many challenges such as how to deal with fundamental problems of modular frameworks for logicprogramming, namely how to define a general compositional semantics that allows us to compose unrestricted modules. Building upon existing logicprogramming approaches, we devised a framework capable of composing generic logicprogramming modules while preserving the crucial property of compositionality, which informally means that the combination of models of individual modules are the models of the union of modules. We are also still able to reason in the presence of knowledge containing incoherencies, which is informally characterised by a logic program that does not have an answer set due to cyclic dependencies of an atom from its default negation. In this thesis we also discuss how the same approach can be extended to deal with probabilistic knowledge in a modular and compositional way. We depart from the modular logic programming approach in Oikarinen & Janhunen (2008); Janhunen et al. (2009) which achieved a restricted form of com- positionality of answer set programming modules. We aim at generalising this framework of modular logic programming and start by lifting restrictive conditions that were originally imposed, and use alternative ways of combining these (so called by us) Generalised modularlogic Programs. We then deal with conflicts arising in generalised modular lo
Recently, enabling modularity aspects in Answer Set programming (ASP) has gained increasing interest to ease the composition of program parts to an overall program. In this paper, we focus on modular nonmonotonic logi...
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ISBN:
(纸本)9783642028458
Recently, enabling modularity aspects in Answer Set programming (ASP) has gained increasing interest to ease the composition of program parts to an overall program. In this paper, we focus on modular nonmonotonic logic programs (MLP) under the answer set semantics, whose modules may have contextually dependent input provided by other modules. Moreover, (Mutually) recursive module calls are allowed. We define a model-theoretic semantics for this extended setting, show that many desired properties of ordinary logicprogramming generalize to our modular ASP, and determine the computational complexity of the new formalism. We investigate the relationship of modular programs to disjunctive logic programs with well-defined input/output interface (DLP-functions) and show that they can be embedded into MLPs.
Lambda calculus offers a natural representation of syntactic structures involving higher-order constructs and local variables, and supports flexible manipulation of such concepts. Thus an integration of logic programm...
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Lambda calculus offers a natural representation of syntactic structures involving higher-order constructs and local variables, and supports flexible manipulation of such concepts. Thus an integration of logicprogramming with lambda-terms would provide more direct support for meta-programming. While it is conceptually straightforward to replace first-order terms with lambda-terms, the extra search space in unification with respect to lambda-conversions cannot be ignored from a practical point of view. Our objective is to explore useful alternatives with weaker conversions that are computationally more tractable. In this paper, we study predicate abstractions, in which lambda-abstractions are used to provide anonymous predicates and functions that return predicates. The framework is based upon a simple logic of (untyped) lambda-calculus, called L(alpha). L(alpha) has a general model-theoretic semantics and an equality theory that corresponds to alpha-equivalence. Intended meanings of predicate abstractions are formalized by equivalence axioms over atomic formulas. We show that under certain conditions, computing with predicate abstractions does not incur any extra search space. Furthermore, programs in this language can be compiled statically into efficient Prolog programs and all most general answers are still preserved.
Disjunctive logicprogramming is nowadays a mature formalism which has been successfully applied to a variety of practical problems, such as information integration, knowledge representation, planning, diagnosis, opti...
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Disjunctive logicprogramming is nowadays a mature formalism which has been successfully applied to a variety of practical problems, such as information integration, knowledge representation, planning, diagnosis, optimization and configuration. Although current DLP systems have been extended in many directions, they still miss features which may be helpful towards industrial applications, like the capability of quickly introducing new predefined constructs or of dealing with modules. Indeed, in spite of the fact that a wide literature about modular logic programming is known, code reusability has never been considered as a critical point in Disjunctive logicprogramming. In this work we extend Disjunctive logicprogramming, under stable model semantics, with the notion of "template" predicates. A template predicate may be instantiated to an ordinary predicate by means of template atoms, thus allowing to define reusable modules, to define new constructs and aggregates without any syntactic limitation.
This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposi...
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This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for arbitrary programs. We show that the immediate consequence operator of a program can be represented via composition which allows us to compute its least model without any explicit reference to operators. This bridges the conceptual gap between the syntax and semantics of a propositional logic program in a mathematically satisfactory way.
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