A novel logic program like language, weight constraint rules, is developed for answer set programming purposes. It generalizes normal logic programs by allowing weight constraints in place of literals to represent, e.g., cardinality and resource constraints and by providing optimization capabilities. A declarative semantics is developed which extends the stable model semantics of normal programs. The computational complexity of the language is shown to be similar to that of normal programs under the stable model semantics. A simple embedding of general weight constraint rules to a small subclass of the language called basic constraint rules is devised. An implementation of the language, the smodels system, is developed based on this embedding. It uses a two level architecture consisting of a front-end and a kernel language implementation. The front-end allows restricted use of variables and functions and compiles general weight constraint rules to basic constraint rules. A major part of the work is the development of an ecient search procedure for computing stable models for this kernel language. The procedure is compared with and empirically tested against satis ability checkers and an implementation of the stable model semantics. It offers a competitive implementation of the stable model semantics for normal programs and attractive performance for problems where the new types of rules provide a compact representation.

The Gelfond-Lifschitz operator [GL88] associated with a logic program (and likewise the operator associated with default theories by Reiter) exhibits oscillating behavior. In the case of logic programs, there is always at least one finite, non-empty collection of Herbrand interpretations around which the Gelfond-Lifschitz [GL88] operator "bounces around". The same phenomenon occurs with default logic when Reiter's operator \Gamma \Delta is considered. Based on this, a "stable class" semantics and "extension class" semantics was proposed in [BS90]. The main advantage of this semantics was that it was defined for all logic programs (and default theories), and that this definition was modelled using the standard operators existing in the literature such as Reiter's \Gamma \Delta operator. In this paper, our primary aim is to prove that there is a very interesting duality between stable class theory and the well founded semantics for logic programming. In the stable class semantics, class...

Disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning. This paper focuses on stable model semantics, currently the most widely acknowledged semantics for disjunctive logic programs. After presenting a new notion of unfounded sets for disjunctive logic programs, we provide two declarative characterizations of stable models in terms of unfounded sets. One shows that the set of stable models coincides with the family of unfounded-free models (i.e., a model is stable iff it contains no unfounded atoms). The other proves that stable models can be defined equivalently by a property of their false literals, as a model is stable iff the set of its false literals coincides with its greatest unfounded set. We then generalize the well-founded WP operator to disjunctive logic programs, give a fixpoint semantics for disjunctive stable models and present an algorithm for computing the stable models of function-free programs. The algor...

Though the declarative semantics of both explicit and nonmonotonic negation in logic programs has been studied extensively, relatively little work has been done on computation and implementation of these semantics. In this paper, we study three different approaches to computing stable models of logic programs based on mixed integer linear programming methods for automated deduction introduced by R. Jeroslow. We subsequently discuss the relative efficiency of these algorithms. The results of experiments with a prototype compiler implemented by us tend to confirm our theoretical discussion. In contrast to resolution, the mixed integer programming methodology is both fully declarative and handles reuse of old computations gracefully. We also introduce, compare, implement, and experiment with linear constraints corresponding to four semantics for "explicit" negation in logic programs: the four-valued annotated semantics [3], the Gelfond-Lifschitz semantics [12], the over-determined models ...

We propose a modification L 1 of the action description language A. The language L 1 allows representation of hypothetical situations and hypothetical occurrence of actions (as in A) as well as representation of actual occurrences of actions and observations of the truth values of fluents in actual situations. The corresponding entailment relation formalizes various types of common-sense reasoning about actions and their effects not modeled by previous approaches. As an application of L 1 we also present an architecture for intelligent agents capable of observing, planning and acting in a changing environment based on the entailment relation of L 1 and use logic programming approximation of this entailment to implement a planning module for this architecture. We prove the soundness of our implementation and give a sucient condition for its completeness.

Over the years, many different agent programming languages have been proposed. In this paper, we propose a concept called Agent Programs using which, the way an agent should act in various situations can be declaratively specified by the creator of that agent. Agent Programs may be built on top of arbitrary pieces of software code and may be used to specify what an agent is obliged to do, what an agent may do, and what an agent may not do. In this paper, we define several successively more sophisticated and epistemically satisfying declarative semantics for agent programs. We further show that agent programs cleanly extend well understood semantics for logic programs, and thus are clearly linked to existing results on logic programming and nonmonotonic reasoning.

Logic programs with the stable model semantics can be thought of as a new paradigm for constraint satisfaction, where the rules of a program are seen as constraints on the stable models. In this work the paradigm is realized by developing an efficient procedure for computing the stable models of ground logic programs. A strong pruning technique based on two deductive closures is introduced. The technique is further strengthened by the introduction of backjumping, which is an improvement over chronological backtracking, and lookahead, a new pruning method. Moreover, a strong heuristic is derived. The two deductive closures are given linear-time implementations that provide a linear-space implementation method for the decision procedure. A high lower bound on the least upper bound on the complexity of the procedure is found. In order to generalize the procedure such that it can handle programs with variables, an algorithm for grounding a function-free range restricted logic program that...

The focus of this paper is nonmonotonic reasoning as it relates to logic programming. I discuss the pre-history of nonmonotonic reasoning starting from approximately 1958. I then review the research that has been accomplished in the areas of circumscription, default theory, modal theories and logic programming. The overview includes the major results developed including complexity results that are known about the various theories. I then provide a summary which includes an assessment of the field and what must be done to further research in nonmonotonic reasoning and logic programming. 1 Introduction Classical logic has played a major role in computer science. It has been an important tool both for the development of architecture and of software. Logicians have contended that reasoning, as performed by humans, is also amenable to analysis using classical logic. However, workers in the field of artificial 1 This paper is an updated version of an invited Banquet Address, First Interna...

Representing and reasoning about narratives together with the ability to do hypothetical reasoning is important for agents in a dynamic world. These agents need to record their observations and action executions as a narrative and at the same time, to achieve their goals against a changing environment, they need to make plans (or re-plan) from the current situation. The early action formalisms did one or the other. For example, while the original situation calculus was meant for hypothetical reasoning and planning, the event calculus was more appropriate for narratives. Recently, there have been some attempts at developing formalisms that do both. Independently, there has also been a lot of recent research in reasoning about actions using circumscription. Of particular interest to us is the research on using high-level languages and their logical representation using nested abnormality theories (NATs)---a form of circumscription with blocks that make knowledge representation modular. Starting from theories in the high-level language L, which is extended to allow concurrent actions, we define a translation to NATs that preserves both narrative and hypothetical reasoning. We initially use the high level language L, and then extend it to allow concurrent actions. In the process, we study several knowledge representation issues such as filtering, and restricted monotonicity with respect to NATs. Finally, we compare our formalization with other approaches, and discuss how our use of NATs makes it easier to incorporate other features of action theories, such as constraints, to our formalization. 1998 Elsevier Science B.V. All rights reserved. Keywords: Narratives; Nested abnormality theories; Circumscription; Reasoning about actions; Value minimization # Corresponding a...

We show that stable models of logic programs may be viewed as minimal models of programs that satisfy certain additional constraints. To do so, we transform the normal programs into disjunctive logic programs and sets of integrity constraints. We show that the stable models of the normal program coincide with the minimal models of the disjunctive program that satisfy the integrity constraints. As a consequence, the stable model semantics can be characterized using the Extended Generalized Closed World Assumption for disjunctive logic programs. Using this result, we develop a bottom-up algorithm for function free logic programs to find all stable models of a normal program by computing the perfect models of a disjunctive stratified logic program and checking them for consistency with the integrity constraints. The integrity constraints provide a rationale as to why some normal logic programs have no stable models. 1 Introduction We consider the problem of finding the stable models o...