In this paper we review the definition of {log} 1, a logic language with sets, from the viewpoint of CLP. We show that starting with a CLP-scheme allows a more uniform treatment of the built-in set operations (namely, =, ∈ and their negative counterparts), and allows all the theoretical results of CLP to be immediately exploitable. We prove this by precisely defining the privileged interpretation domain and the axioms of the selected set theory. Then we define a non-deterministic procedure for checking constraint satisfiability based on the reduction of a given constraint to a collection of constraint in a suitable canonical form, which is provable to be sound and complete w.r.t. the given theory. Algorithms for trasforming each one of the set constraints the language provides (=, �=, ∈ and �∈) into their corresponding canonical forms are described in details. It is also shown that the resulting language is powerful enough to allow all the usual operations on sets (such as ⊆, ∪, etc.) to be effectively programmed in the language itself. 1

A unification algorithm is said to be minimal for a unification problem if it generates exactly a (minimal) complete set of most-general unifiers, without instances, and without repetitions. The aim of this paper is to present a combinatorial minimality study for a significant collection of sample problems that can be used as benchmarks for testing any set-unification algorithm. Based on this combinatorial study, a new Set-Unification Algorithm (named SUA) is also described and proved to be minimal for all the analyzed problems. Furthermore, an existing nave set-unification algorithm has also been tested to show its bad behavior for most of the sample problems.

Constructive negation has been proved to be a valid alternative to negation as failure, especially when negation is required to have, in a sense, an ‘active’ role. In this paper we analyze an extension of the original constructive negation in order to gracefully integrate with the management of set-constraints in the context of a Constraint Logic Programming Language dealing with finite sets. We show that the marriage between CLP with sets and constructive negation gives us the possibility of representing a general class of intensionally defined sets without any further extension to the operational semantics of the language. The presence of intensional sets allows a definite increase in the expressive power and abstraction level offered by the host logic language. 1

Machine (WAM) to implement the paradigm and that these changes blend well with the overall machinery of the WAM. A central feature in the implementation of subset-logic programs is that of a monotonic memo-table, i.e., a memo-table whose entries can monotonically grow or shrink in an appropriate partial order. We present in stages the paradigm of subset-logic progams, showing the effect of each feature on the implementation. The implementation has been completed, and we present performance figures to show the efficiency and costs of memoization. Our conclusion is that the monotonic memo-tables are a practical tool for implementing a set-oriented logic programming language. We also compare this system with other closely related systems, especially XSB and CORAL. Keywords: subset and relational program clauses, sets, set matching and unification, memo tables, monotonic aggregation, Warren Abstract Machine, run-time structures, performance analysis / Address correspondence to...

Subset-logic programs are built up of three kinds of program clauses: subset, equational, and relational clauses. Using these clauses, we can program solutions to a broad range of problems of interest in logic programming and deductive databases. In an earlier paper [Jay92], we discussed the implementation of subset and equational program clauses. This paper substantially extends that work, and focuses on the more expressive paradigm of subset and relational clauses. This paradigm supports setof operations, transitive closures, monotonic aggregation as well as incremental and lazy eager enumeration of sets. Although the subset-logic paradigm differs substantially from that of Prolog, we show that few additional changes are needed to the WAM [War83] to implement the paradigm and that these changes blend well with the overall machinery of the WAM. A central feature in the implementation of subset-logic programs is that of a "monotonic memo-table," i.e., a memo-table who entries can monot...

Constructive negation has been proved to be a valid alternative to negation as failure, especially when negation is required to have, in a sense, an active role. In this paper we analyze an extension of the original constructive negation in order to gracefully integrate with the management of set-constraints in the context of a Constraint Logic Programming Language dealing with finite sets. We show that the marriage between CLP with sets and constructive negation gives us the possibility of representing a general class of intensionally defined sets without any further extension to the operational semantics of the language. The presence of intensional sets allows a definite increase in the expressive power and abstraction level offered by the host logic language. 1 Introduction In [7] we have shown that an increase in expressivity and abstraction capability can be obtained by embedding the basic notion of set in a logic programming language. By adding simple set constructors (fg and ...