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Constructive Negation Without Subsidiary Trees
 of LSI Department, Univ. Politécnica de Catalunya
, 2000
"... In this paper we propose a new operational semantics, called BCN, which is sound and complete with respect to ClarkKunen's completion for the unrestricted class of Normal Logic Programs. BCN is based on constructive negation and can be seen as an operational semantics for the class of Norm ..."
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In this paper we propose a new operational semantics, called BCN, which is sound and complete with respect to ClarkKunen's completion for the unrestricted class of Normal Logic Programs. BCN is based on constructive negation and can be seen as an operational semantics for the class of Normal Constraint Logic Programs (NCLP) over the Herbrand universe. The main features of BCN making it a useful operational mechanism are twofold: First, BCN improves the existing proposals because it is more amenable to a practical implementation. The point is that, instead of computing subsidiary trees, the process of constructing answers for negative goals is reduced to a simple symbolic manipulation plus a constraint satisfaction checking process. Essentially, our approach exploits the definition of negative literals in the completion to interpret the constructive negation metarule. Second, the way in which BCN is defined makes it an extensible scheme to NCLP over arbitrary constraint domains. 1
Tight and Loose Semantics for Transformation Systems
 Recent Trends in Algebraic Development Techniques, Springer LNCS 2267 (2001
, 2001
"... Abstract. When defining the requirements of a system, specification units typically are partial or incomplete descriptions of a system component. In this context, providing a complete description of a component means integrating all the existing partial views for that component. However, in many cas ..."
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Abstract. When defining the requirements of a system, specification units typically are partial or incomplete descriptions of a system component. In this context, providing a complete description of a component means integrating all the existing partial views for that component. However, in many cases defining the semantics of this integration operation is not an easy task. In particular, this is the case when the framework used at the specification level is, in some sense, an “operational ” one (e.g. a Petri net or a statechart). Moreover, this problem may also apply to the definition of compositional semantics for modular constructs for this kind of frameworks. In this paper, we study this problem, at a general level. First, we define a general notion of framework whose semantics is defined in terms of transformations over states represented as algebras and characterize axiomatically the standard tight semantics. Then, inspired in the doublepullback approach defined for graph transformation, we axiomatically present a loose semantics for this class of transformation systems, exploring their compositional properties. In addition, we see how this approach may be applied to a number of formalisms. 1
A Functorial Framework for Constraint Normal Logic Programming
"... Abstract. The semantic constructions and results for definite programs do not extend when dealing with negation. The main problem is related to a wellknown problem in the area of algebraic specification: if we fix a constraint domain as a given model, its free extension by means of a set of Horn cl ..."
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Abstract. The semantic constructions and results for definite programs do not extend when dealing with negation. The main problem is related to a wellknown problem in the area of algebraic specification: if we fix a constraint domain as a given model, its free extension by means of a set of Horn clauses defining a set of new predicates is semicomputable. However, if the language of the extension is richer than Horn clauses its free extension (if it exists) is not necessarily semicomputable. In this paper we present a framework that allows us to deal with these problems in a novel way. This framework is based on two main ideas: a reformulation of the notion of constraint domain and a functorial presentation of our semantics. In particular, the semantics of a logic program P is defined in terms of three functors: (OP P,ALG P,LOG P) that apply to constraint domains and provide the operational, the least fixpoint and the logical semantics of P, respectively. To be more concrete, the idea is that the application of OP P to a specific constraint solver, provides the operational semantics of P that uses this solver; the application of ALG P to a specific domain, provides the least fixpoint of P over this domain; and, the application of LOG P to a theory of constraints, provides the logic theory associated to P. In this context, we prove that these three functors are in some sense equivalent. 1
An Implementation of Constructive Negation ⋆
"... Abstract. In this paper, we present a new procedural interpretation for constructive negation which is sound and complete with respect to threevalued program completion. Its main features are twofold: first, it gives a uniform treatment to positive and negative literals in goals; second, it provide ..."
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Abstract. In this paper, we present a new procedural interpretation for constructive negation which is sound and complete with respect to threevalued program completion. Its main features are twofold: first, it gives a uniform treatment to positive and negative literals in goals; second, it provides an incremental way to detect failure. This mechanism is a refinement of an operational semantics that does not require subsidiary computation trees to compute answers for negative goals. Instead, such answers are built by solving equality constraints which are directly obtained from predicate completion definitions. The constraints generated during derivations constitute a particular subclass of general equality constraints. We provide an implementation based on a specialized solver for this class of constraints.
A Generalization of the Folding Rule for the ClarkKunen Semantics ⋆
"... Abstract. In this paper, we propose more flexible applicability conditions for the folding rule that increase the power of existing unfold/fold systems for normal logic programs. Our generalized folding rule enables new transformation sequences that, in particular, are suitable for recursion introdu ..."
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Abstract. In this paper, we propose more flexible applicability conditions for the folding rule that increase the power of existing unfold/fold systems for normal logic programs. Our generalized folding rule enables new transformation sequences that, in particular, are suitable for recursion introduction and local variable elimination. We provide some illustrative examples and give a detailed proof of correctness w.r.t. the ClarkKunen semantics. 1
ABSTRACT Constructive Negation by Bottomup Computation of Literal Answers ∗
"... In this paper, we present a new proposal for an efficient implementation of constructive negation. In our approach the answers for a literal are bottomup computed by solving equality constraints, instead of by handling frontiers of subsidiary computation trees. The required equality constraints are ..."
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In this paper, we present a new proposal for an efficient implementation of constructive negation. In our approach the answers for a literal are bottomup computed by solving equality constraints, instead of by handling frontiers of subsidiary computation trees. The required equality constraints are given by Shepherdson’s operators which are, in a sense, similar to bottomup immediate consequence operators. However, in order to make the procedure efficient two main techniques are applied. First, we restrict our constraints to a class of successanswers (resp. failanswers) which are easy to manipulate and to solve (or to prove their unsatisfiability). And, second, we take advantage of the monotonic nature of Shepherdson’s operators to make the procedure incremental and to avoid recalculations that are typical in frontiersbased methods. Then, goal computation is made in the usual topdown CLP scheme of collecting the answers for the selected literal into the constraint of the goal. The procedural mechanism for constructive negation is designed not only to generate every correct answer of a goal, but also to detect failure. That is, in spite of the bottomup nature of the calculation of literal answers, goal computation is not necessarily infinite. The operational semantics that makes use of these ideas, called BCN, is sound and complete with respect to threevalued program completion for the whole class of normal logic programs. A prototype implementation of this approach has been developed and the experimental results are very promising.