A relational query is called finite, or sometimes safe, iff it yields a finite answer in every database state. The set of finite queries of relational calculus is known to be unsolvable. However, in many cases it is possible to impose syntactical restrictions on the class of queries that guarantee finiteness and do not reduce the expressive power of the calculus. We show that unfortunately this is not always the case, as we construct a recursive domain with decidable theory where any solvable (or enumerable, for that matter) subclass of queries either contains an infinite query, or misses a finite one. We show that although any domain can always be extended to a domain with an effective syntax for finite A preliminary version of this paper appeared in the Proc. of the 14th ACM SIGACTSIGMOD -SIGART Symp. on Principles of Database Systems, San Jose, CA, May 2225, 1995. y This work has been partially supported by NSF Grant CCR 9403809. z A part of this research was carried out whil...

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We investigate the defining power of stratified and hierarchical logic programs. As an example for the treatment of negative information in the context of these structured programs we also introduce a stratified and hierarchical closed-world assumption. Our analysis tries to relate the defining power of stratified and hierarchical programs (with and without an appropriate closed-world assumption) very precisely to notions and hierarchies in classical definability theory. Stratified and hierarchical logic programs are two well-known and typical candidates of what one may more generally denote as structured programs. In both cases we have to deal with normal logic programs which satisfy certain syntactic conditions with respect to the occurrence of negative literals. Recently they have gained a lot of importance in connection with the search for nice declarative semantics for logic programs and the treatment of negative information in logic programming (e.g., Lloyd [10]). Stratified programs were introduced into logic programming by Apt, Blair, and Walker [2] and van Gelder [17] not long ago. In mathematical logic, however, theories of this kind have been studied for more than 20 years under the general theme of iterated inductive definability. Indeed, stratified programs can be understood as systems for (finitely) iterated inductive definitions where the definition clauses are of very low logical complexity. The notion of hierarchical program (e.g., Clark [6], Shepherdson [15]), on the other hand, is motivated by database theory and tries to reflect the idea of iterated explicit definability by simple principles. From a conceptual point of view we are interested in the relationship between logic programming, inductive definability and equational definability. By making u...

.)L: TA! Z. Formulae are formed from term literals and integerliterals using logical connectives and quantifications. Term literals are exactly

This paper presents a family of first order feature tree theories, indexed by the theory of the feature labels used to build the trees. A given feature label theory, which is required to carry an appropriate notion of sets, is conservatively extended to a theory of feature trees with the predicates x[t]y (feature t leads from the root of tree x to the tree y), where we have to require t to be a ground term, and xt# (feature t is defined at the root of tree x). In the latter case, t might be a variable. Together with the notion of sets provided by the feature label theory, this yields a first-class status of arities.

We show that T (F )= =E can be completely axiomatized when =E is a quasi-free theory. Quasi-free theories are a wider class of theories than permutative theories of [Mal71] for which Mal'cev gave decision results. As an example of application, we show that the first order theory of T (F )= =E is decidable when E is a set of ground equations. Besides, we prove that the \Sigma 1 -fragment of the theory of T (F )= =E is decidable when E is a compact set of axioms. In particular, the existential fragment of the theory of associative-commutative function symbols is decidable. Introduction Mal'cev studied in the early sixties classes of locally free algebras that can be completely axiomatized [Mal71]. He proved in particular that what is today known as Clark's equality theory is decidable. He also studied some classes of permutative algebras in which, roughly, the axiom f(s 1 ; : : : ; s n ) = f(t 1 ; : : : ; t n ) ) s 1 = t 1 : : : s n = t n is replaced with f(s 1 ; : : : ; s n ) = f(t ...

Lists, multisets, and sets are well-known data structures whose usefulness is widely recognized in various areas of Computer Science. These data structures have been analyzed from an axiomatic point of view with a parametric approach in [12] where the relevant uni cation algorithms have been also parametrically developed. In this paper we extend these results considering more general constraints including not only equality but also membership constraints as well as their negative counterparts. This amounts to de ne the privileged structures for the considered axiomatic theories and to solve the relevant constraint satisfaction problems in each of the theories. We adopt a highly parametric approach which allows all the results obtained separately for each single theory to be easily combined so as to obtain a general framework where it is possible to deal with more than one data structure at a time.

. We address the problem of determining those constraint domains A for which the traditional logic programming semantics and the constraint logic programming semantics CLP (A) coincide. This reduces to a study of non-standard models of Clark's axioms and the notion of solution compactness introduced in the CLP scheme. The results of this study include the proof of the existence of a free product in the class of algebras defined by Clark's axioms, a characterization of when Clark's axioms form a model complete theory, and a limited characterization of those models of Clark's axioms which form solution compact constraint domains. 1 Introduction Appropriate semantics for definite logic programs are now largely agreed upon [17]. They involve a completed program, SLD-resolution, a one-step consequence function, a least Herbrand model and numerous relationships between them: soundness and completeness of SLD-refutations, soundness and completeness of the negation-asfailure rule, .....

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Balanced search trees provide guaranteed worst-case time performance and hence they form a very important class of data structures. However,...