Temporal disjunctive logic programming

In this paper we introduce the logic programming languageDisjunctive Chronolog which combines the programming paradigms of temporal and disjunctive logic programming. Disjunctive Chronolog is capable of expressing dynamic behaviour as well as uncertainty, two notions that are very common in a variety of real systems. We present the minimal temporal model semantics and the fixpoint semantics for the new programming language and demonstrate their equivalence. We also show how proof procedures developed for disjunctive logic programs can be easily extended to apply to Disjunctive Chronolog programs. Manolis Gergatsoulis, Ph.D.: He received his B.Sc. in Physics in 1983, the M.Sc. and the Ph.D. degrees in Computer Science in 1986 and 1995 respectively all from the University of Athens, Greece. Since 1996 he is a Research Associate in the Institute of Informatics and Telecommunications, NCSR ‘Demokritos’, Athens. His research interests include logic and temporal programming, program transformations and synthesis, as well as theory of programming languages. Panagiotis Rondogiannis, Ph.D.: He received his B.Sc. from the Department of Computer Engineering and Informatics, University of Patras, Greece, in 1989, and his M.Sc. and Ph.D. from the Department of Computer Science, University of Victoria, Canada, in 1991 and 1994 respectively. From 1995 to 1996 he served in the Greek army. From 1996 to 1997 he was a visiting professor in the Department of Computer Science, University of Ioannina, Greece, and since 1997 he is a Lecturer in the same Department. In January 2000 he was elected Assistant Professor in the Department of Informatics at the University of Athens. His research interests include functional, logic and temporal programming, as well as theory of programming languages. Themis Panayiotopoulos, Ph.D.: He received his Diploma on Electrical Engineering from the Department of Electrical Engineering, National Technical Univesity of Athens, in 1984, and his Ph.D. on Artificial Intelligence from the above mentioned department in 1989. From 1991 to 1994 he was a visiting professor at the Department of Mathematics, University of the Aegean, Samos, Greece and a Research Associate at the Institute of Informatics and Telecommunications of “Democritos” National Research Center. Since 1995 he is an Assistant Prof. at the Department of Computer Science, University of Piraeus. His research interests include temporal programming, logic programming, expert systems and intelligent agent architectures.     

Overview of disjunctive logic programming

The field of disjunctive programming started approximately in 1982 and has reached its first decade. The first result in the field was the development of the Generalized Closed World Assumption (GCWA). Major results have been made in this field since 1986. An overview is presented of the developments that have taken place, which include model theoretic, proof theoretic and fixpoint semantics for disjunctive, and extended normal disjunctive theories including alternative forms of negation.Dedicated to Chitta Baral, José Alberto Fernández, Jorge Lobo and Arcot Rajasekar.     

On look-ahead heuristics in disjunctive logic programming

Disjunctive logic programming (DLP), also called answer set programming (ASP), is a convenient programming paradigm which allows for solving problems in a simple and highly declarative way. The language of DLP is very expressive and able to represent even problems of high complexity (every problem in the complexity class ${{\Sigma}_{2}^{P}} = {\rm NP}^{{\rm NP}}$ ). During the last decade, efficient systems supporting DLP have become available. Virtually all of these systems internally rely on variants of the Davis–Putnam procedure (for deciding propositional satisfiability [SAT]), combined with a suitable model checker. The heuristic for the selection of the branching literal (i.e., the criterion determining the literal to be assumed true at a given stage of the computation) dramatically affects the performance of a DLP system. While heuristics for SAT have received a fair deal of research, only little work on heuristics for DLP has been done so far. In this paper, we design, implement, optimize, and experiment with a number of heuristics for DLP. We focus on different look-ahead heuristics, also called “dynamic heuristics” (the DLP equivalent of unit propagation [UP] heuristics for SAT). These are branching rules where the heuristic value of a literal Q depends on the result of taking Q true and computing its consequences. We motivate and formally define a number of look-ahead heuristics for DLP programs. Furthermore, since look-ahead heuristics are computationally expensive, we design two techniques for optimizing the burden of their computation. We implement all the proposed heuristics and optimization techniques in DLV—the state-of-the-art implementation of disjunctive logic programming, and we carry out experiments, thoroughly comparing the heuristics and optimization techniques on a large number of instances of well-known benchmark problems. The results of these experiments are very interesting, showing that the proposed techniques significantly improve the performance of the DLV system.     

DWAM — A WAM model extension for disjunctive logic programming

Answering queries in disjunctive logic programming requires the use of ancestry-resolution. The resulting complication makes it difficult to implement a Prolog-type query answering procedure for disjunctive logic programs. However, SLO-resolution provides a mechanism which is similar to SLD-resolution and hence offers a solution to this problem. The Warren Abstract Machine has been a very effective model for implementing Prolog. In this paper, we extend the WAM model of Prolog and adapt it for DISLOG — a language for disjunctive logic programming. We describe the extensions and additional instructions needed to make WAM viable for modeling and executing DISLOG. The extension is made in such a way that the original architecture is not disturbed and a Prolog program will execute as efficiently as it does in the original WAM.This work was done while the author was at the University of Kentucky.     

On the computational cost of disjunctive logic programming: Propositional case

This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of well-known semantics, as well as the complexity of deciding whether a propositional formula is satisfied by all models according to a given semantics. We concentrate on finite propositional disjunctive programs with as well as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is ₂ ^p -complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is ₂ ^p -complete; analogous results are derived for the answer sets semantics of extended disjunctive logic programs. Besides, we generalize previously derived complexity results for the generalized closed world assumption and other more sophisticated variants of the closed world assumption. Furthermore, we use the close ties between the logic programming framework and other nonmonotonic formalisms to provide new complexity results for disjunctive default theories and disjunctive autoepistemic literal theories.Parts of the results in this paper appeared in form of an abstract in the Proceedings of the Twelfth ACM SIGACT SIGMOD-SIGART Symposium on Principles of Database Systems (PODS-93), pp. 158–167. Other parts appeared in shortened form in the Proceedings of the International Logic Programming Symposium, Vancouver, October 1993 (ILPS-93), pp. 266–278. MIT Press.     

Propositional semantics for disjunctive logic programs

In this paper we study the properties of the class of head-cycle-free extended disjunctive logic programs (HEDLPs), which includes, as a special case, all nondisjunctive extended logic programs. We show that any propositional HEDLP can be mapped in polynomial time into a propositional theory such that each model of the latter corresponds to an answer set, as defined by stable model semantics, of the former. Using this mapping, we show that many queries over HEDLPs can be determined by solving propositional satisfiability problems. Our mapping has several important implications: It establishes the NP-completeness of this class of disjunctive logic programs; it allows existing algorithms and tractable subsets for the satisfiability problem to be used in logic programming; it facilitates evaluation of the expressive power of disjunctive logic programs; and it leads to the discovery of useful similarities between stable model semantics and Clark's predicate completion.     

Generalized disjunctive well-founded semantics for logic programs

Generalized disjunctive well-founded semantics (GDWFS) is a refined form of the generalized well-founded semantics (GWFS) of Baral, Lobo and Minker, to disjunctive logic programs. We describe fixpoint, model theoretic and procedural characterizations of GDWFS and show their equivalence. The fixpoint semantics is similar to the fixpoint semantics of the GWFS, except that it iterates over state-pairs (a pair of sets; one a set of disjunctions of atoms and the other a pair of conjunctions of atoms), rather than partial interpretations. The model theoretic semantics is based on a dynamic stratification of the program. The procedural semantics is based on SLIS refutations, + trees and SLISNF trees.     

Defeasible logic versus Logic Programming without Negation as Failure

Recently there has been increased interest in logic programming-based default reasoning approaches which are not using negation-as-failure in their object language. Instead, default reasoning is modelled by rules and a priority relation among them. In this paper we compare the expressive power of two approaches in this family of logics: Defeasible Logic, and sceptical Logic Programming without Negation as Failure (LPwNF). Our results show that the former has a strictly stronger expressive power. The difference is caused by the latter logic's failure to capture the idea of teams of rules supporting a specific conclusion.     

Static semantics for normal and disjunctive logic programs

In this paper, we propose a newsemantic framework for disjunctive logic programming by introducingstatic expansions of disjunctive programs. The class of static expansions extends both the classes of stable, well-founded and stationary models of normal programs and the class of minimal models of positive disjunctive programs. Any static expansion of a programP provides the corresponding semantics forP consisting of the set of all sentences logically implied by the expansion. We show that among all static expansions of a disjunctive programP there is always theleast static expansion, which we call thestatic completion ¯P ofP. The static completion¯P can be defined as the least fixed point of a naturalminimal model operator and can be constructed by means of a simpleiterative procedure. The semantics defined by the static completion¯P is called thestatic semantics ofP. It coincides with the set of sentences that are true inall static expansions ofP. For normal programs, it coincides with the well-founded semantics. The class of static expansions represents a semantic framework which differs significantly from the other semantics proposed recently for disjunctive programs and databases. It is also defined for a much broader class of programs.Dedicated to Jack MinkerPartially supported by the National Science Foundation grant # IRI-9313061.     

The Least Fixpoint Transformation for Disjunctive Logic Programs

The paradigm of disjunctive logic programming(DLP)enhances greatly the expressive power of normal logic programming(NLP)and many(declarative)semantics have been defined for DLP to cope with various problems of knowledge representation in artificial intelligence.However,the expressive ability of the semantics and the soundness of program transformations for DLP have been rarely explored.This paper defines an immediate consequence operatro T^GP for each disjunctive program and shows that T^GP has the least and computable fixpoint Lft(P),Lft is,in fact,a program transformation for DLP,which transforms all disjunctive programs into negative programs.It is shown that Lft preserves many key semantics,including the disjunctive stable models,well-founded model,disjunctive argunent semantics DAS,three-valued models,ect.Thic means that every disjunctive program P has a unique canonical form Lft(P)with respect to these semantics.As a result,the work in this paper provides a unifying framework for studying the expressive ability of various semantics for DLP On the other hand,the computing of the above semantics for negative programs is ust a trivial task,therefore,Lft(P)is also an optimization method for DLP.Another application of Lft is to derive some interesting semantic results for DLP.     

Negation as failure: Careful closure procedure

The aim of this paper is a modification of Minker's Generalized Closed World Assumption that would allow application of the “negation as failure rule” with respect to a set P of (not necessarily all) predicates of a database DB. A careful closure procedure is introduced which, when applied to a database DB, produces a new database DB*, that is used to answer queries about predicates from DB. It is shown that DB* is consistent iff DB is consistent. If P is the set of all predicates from DB and DB does not contain functional symbols, then DB* coincides with Minker's GCWA. The soundness and completeness of the careful closure procedure with respect to a minimal model style semantic is shown. As an inference engine associated with DB* we propose a query evaluation procedure QEP* which is a combination of a method of splitting an indefinite database DB into a disjunction of Horn databases and Clark's query evaluation procedure QEP. Soundness of QEP* with respect to DB* is shown for a broad class of databases.     

Tableaux for logic programming

We present a logic programming language, which we call Proflog, with an operational semantics based on tableaux and a denotational semantics based on supervaluations. We show the two agree. Negation is well behaved, and semantic noncomputability issues do not arise. This is accomplished essentially by dropping a domain closure requirement. The cost is that intuitions developed through the use of classical logic may need modification, though the system is still classical at a level once removed. Implementation problems are discussed very briefly; the thrust of the paper is primarily theoretical.Research partly supported by NSF Grant CCR-9104015.     

LMNtal as a hierarchical logic programming language

LMNtal (pronounced “elemental”) is a simple language model based on hierarchical graph rewriting that uses logical variables to represent connectivity and membranes to represent hierarchy. LMNtal is an outcome of the attempt to unify constraint-based concurrency and Constraint Handling Rules (CHR), the two notable extensions to concurrent logic programming. LMNtal is intended to be a substrate language of various computational models, especially those addressing concurrency, mobility and multiset rewriting. Although the principal objective of LMNtal was to provide a unifying computational model, it is of interest to equip the formalism with a precise logical interpretation. In this paper, we show that it is possible to give LMNtal a simple logical interpretation based on intuitionistic linear logic and a flattening technique. This enables us to call LMNtal a hierarchical, concurrent linear logic language.     

Classical negation in logic programs and disjunctive databases

An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter.