Abductive logic programming oers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming oers a computational mechanism that provides a level of declarativity superior to that of Prolog, and which has supported successful applications in elds such as parsing, program analysis, and model checking. In this paper we show how to use tabled logic programming to evaluate queries to abductive frameworks with integrity constraints when these frameworks contain both default and explicit negation. The result is the ability to compute abduction over well-founded semantics with explicit negation and answer sets. Our approach consists of a transformation and an evaluation method. The transformation adjoins to each objective literal O in a program, an objective literal not(O) along with rules that ensure that not(O) will be true if and only if O is false. We call the resulting program a dual program. The evaluation method, Abdual, then operates on the dual program. Abdual is sound and complete for evaluating queries to abductive frameworks whose entailment method is based on either the well-founded semantics with explicit negation, or on answer sets. Further, Abdual is asymptotically as ecient as any known method for either class of problems. In addition, when abduction is not desired, Abdual operating on a dual program provides a novel tabling method for evaluating queries to ground extended programs whose complexity and termination properties are similar to those of the best tabling methods for the well-founded semantics. A publicly available meta-interpreter has been developed for Abdual using the XSB system.

Abductive Logic Programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled Logic Programming offers a computational mechanism that provides a level of declarativity above that of Prolog, and which has supported successful applications in fields such as parsing, program analysis, and model checking. In this paper we show how to use tabled logic programming to evaluate queries to abductive frameworks with integrity constraints when these frameworks contain both default and explicit negation. Our approach consists of a transformation and an evaluation method. The transformation adjoins to each rule R of a finite ground program a new rule that is true if and only if R is false. We call the resulting program a dual program. The evaluation method, Abdual, then operates on the dual program. Abdual is sound and complete for evaluating queries to abductive frameworks whose entailment method ...

Abstract. We consider the problem of exploring the search tree of a CLP goal in pursuit of a target property. Essential to such a process is a method of tabling to prevent duplicate exploration. Typically, only actually traversed goals are memoed in the table. In this paper we present a method where, upon the successful traversal of a subgoal, a generalization of the subgoal is memoed. This enlarges the record of already traversed goals, thus providing more pruning in the subsequent search process. The key feature is that the abstraction computed is guaranteed not to give rise to a spurious path that might violate the target property. A driving application area is the use of CLP to model the behavior of other programs. We demonstrate the performance of our method on a benchmark of program verfication problems. 1

Abstract. Tabled evaluations can incorporate a number of features, including tabled negation, reduction with respect to the well-founded model, tabled constraints and answer subsumption. Many of these features are most efficiently evaluated using the Local evaluation strategy, which fully evaluates each mutually dependent set of tabled subgoals before returning answers to other subgoals outside of that set. In this paper, we introduce a formalism, Concurrent Local SLG by which multiple threads of computation concurrently perform Local evaluation of the well-founded semantics, and which is a framework for multi-threaded tabling in the XSB system. We prove several properties of Local evaluation within single-threaded tabled computation. We then extend SLG to a model of concurrency and show that the completeness and complexity of SLG are retained when computed by multiple threads. Finally, we extend Local evaluation to concurrent SLG, and show that the properties of Local evaluation continue to hold under concurrency.

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this document |intended to be the user manual| reects the current status (Version 2.2) of our system. While we have taken great eort to create a robust and ecient system, we would like to emphasize that XSB is also a research system and is to some degree experimental. When the research features of XSB | tabling, HiLog, and Indexing Techniques | are discussed in this manual, we also cite documents where they are fully explained. All of these documents can be found via the world-wide web or anonymous ftp from fwww/ftpg.cs.sunysb.edu, the same host from which XSB can be obtained.

Probabilistic Logic Programming is an active field of research, with many proposals for languages, semantics and reasoning algorithms. One such proposal, Logic Programming with Annotated Disjunctions (LPADs) represents probabilistic information in a sound and simple way. This paper presents two contributions to the evaluation of LPADs. The first is the definition of a semantics for LPADs with function symbols, which is needed for many domains (including some standard benchmarks used in this paper). The second is the algorithm “Probabilistic Inference with Tabling and Answer subsumption” (PITA) for computing the probability of queries. Answer subsumption is a feature of tabling that allows the combination of different answers for the same subgoal in the case in which a partial order can be defined over them. We have applied it in our case since probabilistic explanations (stored as BDDs in PITA) possess a natural lattice structure. PITA has been implemented in XSB and compared with the ProbLog, cplint and CVE systems. The results show that in almost all cases, PITA is able to solve larger problems and is faster than competing algorithms.

The paradigm of Tabled Logic Programming (TLP) is now supported by a number of Prolog systems, including XSB, YAP, B Prolog, Mercury, ALS, and Ciao. The reasons for this are partly theoretical: tabling ensures termination and optimal known complexity for queries to a large class of programs. However the overriding reasons are practical. TLP allows sophisticated programs to be written concisely and efficiently, especially when mechanisms such as tabled negation and call and answer subsumption are supported. As a result TLP has now been used in a variety of applications from program analysis to querying over the semantic web. This paper provides a survey of TLP and its applications as implemented in XSB Prolog, along with discussion of how XSB supports tabling with