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.     

Interpreting disjunctive logic programs based on a strong sense of disjunction

This paper studies a strong form of disjunctive information in deductive databases. The basic idea is that a disjunctionA B should be considered true only in the case when neitherA norB can be inferred, but the disjunctionA B is true. Under this interpretation, databases may be inconsistent. For those databases that are consistent, it is shown that a unique minimal model exists. We study a fixpoint theory and present a sound and complete proof procedure for query processing in consistent databases. For a class of inconsistent databases, we obtain a declarative semantics by selecting an interpretation that maximizes satisfaction, and minimizes indefiniteness. Two notions of negation are introduced.     

On stratified disjunctive programs

We address the problem of a consistent fixpoint semantics for general disjunctive programs restricted to stratifiable programs which do not recurse through negative literals. We apply the nonmonotonic fixpoint theory developed by Apt, Blair and Walker to a closure operatorT ^c and develop a fixpoint semantics for stratified disjunctive programs. We also provide an iterative definition for negation, called the Generalized Closed World Assumption for Stratified programs (GCWAS), and show that our semantics captures this definition. We develop a model-theoretic semantics for stratified disjunctive programs and show that the least state characterized by the fixpoint semantics corresponds to a stable-state defined in a manner similar to the stable-models of Gelfond and Lifschitz. We also discuss a weaker stratification semantics for general disjunctive programs based on the Weak Generalized Closed World Assumption.     

An execution model for exploiting AND-parallelism in logic programs

This paper presents a parallel execution model for exploiting AND-parallelism in Horn Clause logic programs. The model is based upon the generator-consumer approach, and can be implemented efficiently with small run-time overhead. Other related models that have been proposed to minimize the run-time overhead are unable to exploit the full parallelism inherent in the generator-consumer approach. Furthermore, our model performs backtracking more intelligently than these models. We also present two implementation schemes to realize our model: one has a coordinator to control the activities of processes solving different literals in the same clause; and the other achieves synchronization by letting processes pass messages to each other in a distributed fashion. Trade-offs between these two schemes are then discussed. This work was supported by Army Research Office grant #DAAG29-84-K-0060 to the Artificial Intelligence Laboratory at the University of Texas at Austin.     

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.     

优先归纳逻辑程序的极限行为

虽然对归纳逻辑程序的极限行为至今并没有深入的研究，但是通常在分析正在执行的增量式或在线归纳学习算法时，必须考虑这种程序的极限行为．某些归纳学习算法如果不考虑极限行为可能运行到最后会发生错误．如果给定一个递增的例子集合序列，一个归纳逻辑程序会产生一个相应的具有集合论极限的Horn逻辑程序序列，则此归纳逻辑程序是收敛的，并且如果该Horn逻辑程序序列关于例子集合序列的极限是极限正确的，则此归纳逻辑程序是极限正确的，还说明GOLEM系统不是极限正确的．为了解决这个问题，提出了一个极限正确的称为优先GOLEM系统的归纳逻辑系统，并证明了在一定的限制下，优先GOLEM系统的算法是极限正确的．     

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.     

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.     

Most specific logic programs

More specific versions of definite logic programs are introduced. These are versions of a program in which each clause is further instantiated or removed and which have an equivalent set of successful derivations to those of the original program, but a possibly increased set of finitely failed goals. They are better than the original program because failure in a non-successful derivation may be detected more quickly. Furthermore, information about allowed variable bindings which is hidden in the original program may be made explicit in a more specific version of it. This allows better static analysis of the program's properties and may reveal errors in the original program. A program may have several more specific versions but there is always a most specific version which is unique up to variable renaming. Methods to calculate more specific versions are given and it is characterized when they give the most specific version.     

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.     

Compositional model-theoretic semantics for logic programs

We present a compositional model-theoretic semantics for logic programs, where the composition of programs is modelled by the composition of the admissible Herbrand models of the programs. An Herbrand model is admissible if it is supported by the assumption of a set of hypotheses. On one hand, the hypotheses supporting a model correspond to an open interpretation of the program intended to capture possible compositions with other programs. On the other hand, admissible models provide a natural model-theory for a form of hypothetical reasoning, called abduction. The application of admissibel models to programs with negation is discussed. Antonio Brogi: Dipartimento di Informatica, Università di Pisa, Corso Italia 40, 56125 Pisa, ItalyResearch interests: Programming Language Design and Semantics, Logic Programming and Artificial Intelligence     

View updates in stratified disjunctive databases

The view update problem is considered in the context of deductive databases where the update of an intensional predicate is accomplished by modifying appropriately the underlying relations in the extensional database. Two classes of disjunctive databases are considered. The first class contains those disjunctive databases which allow only definite rules in the intensional database and disjunctive facts in the extensional database. The second class contains stratified disjunctive databases so that in addition to the first class, negation is allowed in the bodies of the rules, but the database must be stratified. Algorithms are given both for the insertion of an intensional predicate into and the deletion of an intensional predicate from the database. The algorithms use SLD resolution and the concept of minimal models of the extensional database. The algorithms are proved to be correct and best according to the criterion of causing minimal change to the database, where we give first priority to minimizing deletions.Research supported by the National Science Foundation under grant numbers IRI-8916059, IRI-8921591, IRI-9200898, and IRI-9210220.     

Completeness of hyper-resolution via the semantics of disjunctive logic programs

We present a proof of completeness of hyper-resolution based on the fixpoint semantics of disjunctive logic programs. This shows that hyper-resolution can be studied from the point of view of logic programming.     

Grammar-related transformations of logic programs

We investigate a simple transformation of logic programs capable of inverting the order of computation. Several examples are given which illustrate how this transformation may serve such purposes as left-recursion elimination, loop-elimination, simulation of forward reasoning, isotopic modification of programs and simulation of abductive reasoning.     

A new approach to hybrid probabilistic logic programs

This paper presents a novel revision of the framework of Hybrid Probabilistic Logic Programming, along with a complete semantics characterization, to enable the encoding of and reasoning about real-world applications. The language of Hybrid Probabilistic Logic Programs framework is extended to allow the use of non-monotonic negation, and two alternative semantical characterizations are defined: stable probabilistic model semantics and probabilistic well-founded semantics. These semantics generalize the stable model semantics and well-founded semantics of traditional normal logic programs, and they reduce to the semantics of Hybrid Probabilistic Logic programs for programs without negation. It is the first time that two different semantics for Hybrid Probabilistic Programs with non-monotonic negation as well as their relationships are described. This proposal provides the foundational grounds for developing computational methods for implementing the proposed semantics. Furthermore, it makes it clearer how to characterize non-monotonic negation in probabilistic logic programming frameworks for commonsense reasoning. An erratum to this article can be found at