We propose a new declarative semantics for logic programs with negation. Its formulation is quite simple; at the same time, it is more general than the iterated fixed point semantics for stratied programs, and is applicable to some useful programs that are not stratified.

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This paper presents for the first time the semantic foundations of CLP in a self-contained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and complete proofs for the main lemmas. Importantly, we clarify which theorems depend on conditions such as solution compactness, satisfaction completeness and independence of constraints. Second, we generalize the original results to allow for incompleteness of the constraint solver. This is important since almost all CLP systems use an incomplete solver. Third, we give conditions on the (possibly incomplete) solver which ensure that the operational semantics is confluent, that is, has independence of literal scheduling.

Bilattices, due to M. Ginsberg, are a family of truth value spaces that allow elegantly for missing or conflicting information. The simplest example is Belnap's four-valued logic, based on classical two-valued logic. Among other examples are those based on finite many-valued logics, and on probabilistic valued logic. A fixed point semantics is developed for logic programming, allowing any bilattice as the space of truth values. The mathematics is little more complex than in the classical two-valued setting, but the result provides a natural semantics for distributed logic programs, including those involving confidence factors. The classical two-valued and the Kripke/Kleene three-valued semantics become special cases, since the logics involved are natural sublogics of Belnap's logic, the logic given by the simplest bilattice. 1 Introduction Often useful information is spread over a number of sites ("Does anybody know, did Willie wear a hat when he left this morning?") that can be speci...

A proof-theoretic characterization of logical languages that form suitable bases for Prolog-like programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its operational meaning, provided by interpreting logical connectives as simple and fixed search instructions. The operational semantics is formalized by the identification of a class of cut-free sequent proofs called uniform proofs. A uniform proof is one that can be found by a goal-directed search that respects the interpretation of the logical connectives as search instructions. The concept of a uniform proof is used to define the notion of an abstract logic programming language, and it is shown that first-order and higher-order Horn clauses with classical provability are examples of such a language. Horn clauses are then generalized to hereditary Harrop formulas and it is shown that first-order and higher-order versions of this new class of formulas are also abstract logic programming languages if the inference rules are those of either intuitionistic or minimal logic. The programming language significance of the various generalizations to first-order Horn clauses is briefly discussed.

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The unification problem in first-order predicate calculus is described in general terms as the solution of a system of equations, and a nondeterministic algorithm is given. A new unification algorithm, characterized by having the acyclicity test efficiently embedded into it, is derived from the nondeterministic one, and a PASCAL implementation is given. A comparison with other well-known unification algorithms shows that the algorithm described here performs well in all cases.

This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.

This paper attempts to define an object-oriented database system. It describes the main features and characteristics that a system must have to qualify as an objectoriented database system. We have separated these characteristics into three groups: ffl Mandatory, the ones the system must satisfy in order to be termed an objectoriented database system. These are complex objects, object identity, encapsulation, types or classes, inheritance, overriding combined with late binding, extensibility, computational completeness, persistence, secondary storage management, concurrency, recovery and an ad hoc query facility. ffl Optional, the ones that can be added to make the system better, but which are not mandatory. These are multiple inheritance, type checking and inferencing, distribution, design transactions and versions. ffl Open, the points where the designer can make a number of choices. These are the programming paradigm, the representation system, the type system, and uniformity. We...

In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting alternative to more traditional logic programming styles of Horn logic programming, stratified logic programming and logic programming with well-founded semantics. The proposed approach is based on the interpretation of program clauses as constraints. In this setting programs do not describe a single intended model, but a family of stable models. These stable models encode solutions to the constraint satisfaction problem described by the program. Our approach imposes restrictions on the syntax of logic programs. In particular, function symbols are eliminated from the language. We argue that the resulting logic programming system is well-attuned to problems in the class NP, has a well-defined domain of applications, and an emerging methodology of programming. We point out that what makes the whole approach viable is recent progress in implementations of algorithms to compute stable models of propositional logic programs. 1