Independence in constraint logic programs

Studying independence of literals, variables, and substitutions has proven very useful in the context of logic programming (LP). Here we study independence in the broader context of constraint logic programming (CLP). We show that a naive extrapolation of the LP definitions of independence to CLP is unsatisfactory (in fact, wrong) for two reasons. First, because interaction between variables through constraints is more complex than in the case of logic programming. Second, in order to ensure the efUciency of several optimizations not only must independence of the search space be considered, but also an orthogonal issue - "independence of constraint solving." We clarify these issues by proposing various types of search independence and constraint solver independence, and show how they can be combined to allow different independence-related optimizations, from parallelism to intelligent backtracking. Sufficient conditions for independence which can be evaluated "a-priori" at run-time are also proposed. Our results suggest that independence, provided a suitable definition is chosen, is even more useful in CLP than in LP

Residuation and guarded rules for constraint logic programming

A major difficulty with logic programming is combinatorial explosion: since goals are solved with possibly indeterminate (i.e., branching) reductions, the resulting search trees may grow wildly. Constraint logic programming systems try to avoid combinatorial explosion by building in strong determinate (i.e., non-branching) reduction in the form of constraint simplification. In this paper we present two concepts, residuation and guarded rules, for further strengthening determinate reduction. Both concepts apply to constraint logic programming in general and yield an operational semantics that coincides with the declarative semantics. Residuation is a control strategy giving priority to determinate reductions. Guarded rules are logical consequences of programs adding otherwise unavailable determinate reductions

Implementing global constraints as graphs of elementary constraints

Global constraints are cardinal concepts of CLP (FD), a constraint programming language. They are means to find a set of integers that satisfy certain relations. The fact that defining global constraints often requires the knowledge of a specification language makes sharing constraints between scientists and programmers difficult. Nicolas Beldiceanu presented a theory that could solve this problem, because it depicts global constraints as graphs: an abstraction that everyone understands. The abstract description language defined by the theory may also be interpreted by a computer program. This paper deals with the problematic issues of putting the theory into practice by implementing such a program. It introduces a concrete syntax of the language and presents three programs understanding that syntax. These case studies represent two different approaches of propagation. One of these offers exhausting pruning with poor efficiency, the other, yet unfinished attempt provides a better alternative at the cost of being a lot more complicated

An algorithm for linear constraint solving: its incorporation in a prolog meta-interpreter for CLP

AbstractThe paper presents an incremental and efficient algorithm for testing the satisfiability of systems of linear equalities, inequalities (strict or unrestricted), and disequalities. In addition, it describes the incorporation of that algorithm into a metalevel interpreter capable of processing both tree constraints and the mentioned linear constraints in the domain of rationals. Important characteristics of the described algorithm are (1) detection of fixed variables within the context of Gaussian elimination, including the simplex method. (2) efficient dereferencing by considering subclasses of solved forms, and (3) efficient testing of inconsistencies between equality and disequality subclasses. The metalevel interpreter is written in Prolog. Examples of its usage are provided. Finally, the paper outlines how the approach may be generalized to consider the efficient and incremental testing of constraint satisfiability in various domains

The role of computational logic as a hinge paradigm among deduction, problem solving, programming, and parallelism

This paper presents some brief considerations on the role of Computational Logic in the construction of Artificial Intelligence systems and in programming in general. It does not address how the many problems in AI can be solved but, rather more modestly, tries to point out some advantages of Computational Logic as a tool for the AI scientist in his quest. It addresses the interaction between declarative and procedural views of programs (deduction and action), the impact of the intrinsic limitations of logic, the relationship with other apparently competing computational paradigms, and finally discusses implementation-related issues, such as the efficiency of current implementations and their capability for efficiently exploiting existing and future sequential and parallel hardware. The purpose of the discussion is in no way to present Computational Logic as the unique overall vehicle for the development of intelligent systems (in the firm belief that such a panacea is yet to be found) but rather to stress its strengths in providing reasonable solutions to several aspects of the task

Independence in CLP Languages

Studying independence of goals has proven very useful in the context of logic programming. In particular, it has provided a formal basis for powerful automatic parallelization tools, since independence ensures that two goals may be evaluated in parallel while preserving correctness and eciency. We extend the concept of independence to constraint logic programs (CLP) and prove that it also ensures the correctness and eciency of the parallel evaluation of independent goals. Independence for CLP languages is more complex than for logic programming as search space preservation is necessary but no longer sucient for ensuring correctness and eciency. Two additional issues arise. The rst is that the cost of constraint solving may depend upon the order constraints are encountered. The second is the need to handle dynamic scheduling. We clarify these issues by proposing various types of search independence and constraint solver independence, and show how they can be combined to allow dierent optimizations, from parallelism to intelligent backtracking. Sucient conditions for independence which can be evaluated \a priori" at run-time are also proposed. Our study also yields new insights into independence in logic programming languages. In particular, we show that search space preservation is not only a sucient but also a necessary condition for ensuring correctness and eciency of parallel execution

Some considerations on the compile-time analysis of constraint logic programs

This paper discusses some issues which arise in the dataflow analysis of constraint logic programming (CLP) languages. The basic technique applied is that of abstract interpretation. First, some types of optimizations possible in a number of CLP systems (including efficient parallelization) are presented and the information that has to be obtained at compile-time in order to be able to implement such optimizations is considered. Two approaches are then proposed and discussed for obtaining this information for a CLP program: one based on an analysis of a CLP metainterpreter using standard Prolog analysis tools, and a second one based on direct analysis of the CLP program. For the second approach an abstract domain which approximates groundness (also referred to as "definiteness") information (i.e. constraint to a single valué) and the related abstraction functions are presented

Proving the existence of solutions in logical arithmetic

Logical arithmetic is a logically correct technique for real arithmetic in Prolog which uses constraints over interval representations for its implementation. Four problems with the technique are considered: answers are conditional and uninformative; iterative computations may lead to unboundedly large constraint networks; it is difficult and ineffective to deal with negation; and computing extrema is often not effective. A solution to these problems is proposed in the form of "existential intervals" which record the existence of a solution to a set of constraints within an interval. It is shown how to operate on existential intervals and how they solve the four problems