We present a simple and powerful generalized algebraic semantics for constraint logic programs that is parameterized with respect to the underlying constraint system. The idea is to abstract away from standard semantic objects by focusing on the general properties of any --possibly non-standard -- semantic definition. In constraint logic programming, this corresponds to a suitable definition of the constraint system supporting the semantic definition. An algebraic structure is introduced to formalize the notion of a constraint system, thus making classical mathematical results applicable. Both top-down and bottom-up semantics are considered. Non-standard semantics for constraint logic programs can then be formally specified using the same techniques used to define standard semantics. Different nonstandard semantics for constraint logic languages can be specified in this ...

We present a simple and powerful generalized algebraic semantics for constraint logic programs that is parameterized with respect to the underlying constraint system. "Generalized semantics" abstract away from standard semantics objects, by focusing on the general properties of any (possibly non-standard) semantics definition. In constraint logic programming, this corresponds to a suitable definition of the constraint system supporting the semantics definition. An algebraic structure is introduced to formalize the constraint system notion, thus making applicable classical mathematical results and both a top-down and bottom-up semantics are considered. Non-standard semantics for CLP can then be formally specified by means of the same techniques used to define standard semantics. Different non-standard semantics for constraint logic languages can be specified in this framework: e.g. abstract interpretation, machine level traces and any computation based on an instance of the constraint system.

Abstract. The aim of the paper is discussion of connections between the three kinds of objects named in the title. In a sense, it is a survey of such connections; however, some new directions are also considered. This relates, especially, to sections 3, 4 and 5, where we consider a field that could be understood as an universal algebraic geometry. This geometry is parallel to universal algebra. In the monograph [51] algebraic logic was used for building up a model of a database. Later on, the structures arising there turned out to be useful for solving several problems from algebra. This is the position which the present paper is written from.

. In this paper, we are developing a new logical semantics of CLP. It is shown that CLP is based on an amalgamated logic embedding the entailment relation of constraints into a fragment of intuitionistic logic. Constrained SLD resolution corresponds to a complete proof search in the amalgamated logic. The framework provides not only the logical account on the definitional semantics towards CLP but also a general way to integrate constraints into various logic programming systems. 1 Introduction Constraint logic programming has recently attracted much research actively. Intuitively, constraint logic programming languages are designed by replacing unification with constraint solving over a computational domain. Therefore, logic programming can be pursued over any intended domain of discourse. Many CLP languages has been designed [JL87, Col87] and implemented [JL87, Col87]. Their computational domains include linear arithmetic[JL87], boolean algebra [KS89] and finite sets [MHS88]. Since ...

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