We represent properties of actions in a logic programming language that uses both classical negation and negation as failure. The method is applicable to temporal projection problems with incomplete information, as well as to reasoning about the past. It is proved to be sound relative to a semantics of action based on states and transition functions. 1 Introduction This paper extends the work of Eshghi and Kowalski [6], Evans [7] and Apt and Bezem [1] on representing properties of actions in logic programming languages with negation as failure. Our goal is to overcome some of the limitations of the earlier work. The existing formalizations of action in logic programming are adequate for only the simplest kind of temporal reasoning---"temporal projection." In a temporal projection problem, we are given a description of the initial state of the world, and use properties of actions to determine what the world will look like after a series of actions is performed. Moreover, the existing ...

SLD resolution with negation as finite failure (SLDNF) reflects the procedural interpretation of predicate calculus as a programming language and forms the computational basis for Prolog systems. Despite its advantages for stack-based memory management, SLDNF is often not appropriate for query evaluation for three reasons: a) it may not terminate due to infinite positive recursion; b) it may not terminate due to infinite recursion through negation; c) it may repeatedly evaluate the same literal in a rule body, leading to unacceptable performance. We address three problems fir a goal-oriented query evaluation of general logic programs by presenting tabled evaluation with delaying (SLG resolution).

We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the proof-theoretic and model-theoretic issues and the relationships between them.

The well-founded model provides a natural and robust semantics for logic programs with negative literals in rule bodies. Although various procedural semantics have been proposed for query evaluation under the well-founded semantics, the practical issues of implementation for effective and efficient computation of queries have been rarely discussed. This paper investigates two major implementation issues of query evaluation under the well-founded semantics, namely (a) to ensure that negative literals be resolved only after their positive counterparts have been completely evaluated, and (b) to detect and handle potential negative loops. We present efficient incremental algorithms for maintaining positive and negative dependencies among subgoals in a top-down evaluation. Both completely evaluated subgoals and potential negative loops are detected by inspecting the dependency information of a single subgoal. Our implementation can be viewed as an effective successor to SLDNF resolution, ex...

The precise probability of a compound event (e.g. e1 e2 ; e1 e2) depends upon the known relationships (e.g. independence, mutual exclusion, ignorance of any relationship, etc.) between the primitive events that constitute the compound event. To date, most research on probabilistic logic programming [20, 19, 22, 23, 24] has assumed that we are ignorant of the relationship between primitive events. Likewise, most research in AI (e.g. Bayesian approaches) have assumed that primitive events are independent. In this paper, we propose a hybrid probabilistic logic programming language in which the user can explicitly associate, with any given probabilistic strategy, a conjunction and disjunction operator, and then write programs using these operators. We describe the syntax of hybrid probabilistic programs, and develop a model theory and fixpoint theory for such programs. Last, but not least, we develop three alternative procedures to answer queries, each of which is guaranteed to be sound ...

. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...

Based on the search forest for positive programs as defined by Bol and Degerstedt, we define a tabulated version of SLS-resolution that is sound and complete w.r.t. well founded semantics. In contrast to SLS-resolution as proposed by Przymusinski and by Ross, a positivistic computation rule is not required. This proposal is closely related to that of Chen and Warren, but it relies on tabulation for both positive and negative recursion. In this way, only one forest needs to be constructed, rather than a forest for each negative context. For function-free programs, the resulting search forest is finite. Keywords: logic programming, deductive databases, well founded semantics, tabulation, search forest, SLS-resolution, implementation. 1 Introduction It was shown in [5, 24] that bottom-up computation with magic templates [2, 22] and tabulated SLD-resolution [9, 26, 27] perform `essentially' the same computation. This result is made more precise in [4], where a common framework for both ...

The well-founded semantics and the stable model semantics capture intuitions of the skeptical and credulous semantics in nonmonotonic reasoning, respectively. They represent the two dominant proposals for the declarative semantics of deductive databases and logic programs. However, neither semantics seems to be suitable for all applications. We have developed an efficient implementation of goal-oriented effective query evaluation under the well-founded semantics. It produces a residual program for subgoals that are relevant to a query, which contains facts for true instances and clauses with body literals for undefined instances. This paper presents a simple method of stable model computation that can be applied to the residual program of a query to derive answers with respect to stable models. The method incorporates both forward and backward chaining to propagate the assumed truth values of ground atoms, and derives multiple stable models through backtracking. Users are ab...

The main aim of this paper is to present a framework for tabulated SLDresolution that allows a strict separation between search space and search. We introduce the notion of a search forest to model the search space, and we define what we understand by a search strategy for it. We present some basic search strategies and discuss how a particular tabulation technique, OLDT-resolution, and a particular transformation technique, Magic Templates, relate to our approach. This comparison also reveals an inherent difference between the tabulation and the transformation approach. 1 Introduction Resolution is the main technique used by query answering systems for logic programs. It can be applied in two different ways, usually called "bottomup " and "top-down". The top-down methods are perhaps the most intuitive ones, because their starting point is the query: they are goal-oriented . As a result they will not compute irrelevant facts, but intermediate results that are needed several times ca...

We define and study a high-level language for describing actions that extends the language A introduced by Gelfond and Lifschitz. The new language, AR 0 , allows us to describe actions with indirect effects (ramifications) and simple forms of nondeterminism. A translation from AR 0 into a formalism based on circumscription is proved to be sound and complete. 1 Introduction Describing properties of actions and their effects on the state of the world has long been considered one of the central problems in the theory of knowledge representation. The approaches proposed in the literature differ by the temporal ontologies they use (linear or branching time, time points or intervals, situations, events or histories), by the logic used (classical logic, its nonmonotonic extensions, logic programming), and by other details of the formalization (which objects are reified, which circumscription policy is used, etc.). In this area of research, it turned out to be difficult to discuss the possi...