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     

On the equivalence and range of applicability of graph-based representations of logic programs

Logic programs under Answer Sets semantics can be studied, and actual computation can be carried out, by means of representing them by directed graphs. Several reductions of logic programs to directed graphs are now available. We compare our proposed representation, called Extended Dependency Graph, to the Block Graph representation recently defined by Linke [Proc. IJCAI-2001, 2001, pp. 641-648]. On the relevant fragment of well-founded irreducible programs, extended dependency and block graph turns out to be isomorphic. So, we argue that graph representation of general logic programs should be abandoned in favor of graph representation of well-founded irreducible programs, which are more concise, more uniform in structure while being equally expressive.     

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.     

Verifying local stratifiability of logic programs and databases

In this paper, we deal with the problem of verifying local stratifiability of logic programs and databases presented by Przymusinski. The notion of dependency graphs is generalized from representing the priority relation between predicate symbols to representing the priority between atoms. Necessary and sufficient conditions for the local stratifiability of logic programs are presented and algorithms for performing the verification are developed. Finally, we prove that a database DB containing clauses with disjunctive consequents can easily be converted into a logic program P such that DB is locally stratified iff P is locally stratified. Yi-Dong Shen, Dr.: Department of Computer Science, Chongqing University, Chongqing, 630044, P.R. China (Present Address) c/o Ping Ran, Department of Heat Power Engineering, Chongqing UniversityResearch interests: Artificial Intelligence, Deductive Databases, Logic Programming, Non-Monotonic Reasoning, Parallel Processing     

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.     

Well-founded semantics and stratification for ordered logic programs

This paper present an extension of traditional logic programming, called ordered logic (OL) programming, to support classical negation as well as constructs from the object-oriented paradigm. In particular, such an extension allows to cope with the notions of object, multiple inheritance and non-monotonic reasoning. The contribution of the work is mainly twofold. First, a rich wellfounded semantics for ordered logic programs is defined. Second, an efficient method for the well-founded model computation of a meaningful class of ordered logic programs, called stratified programs, is provided.     

An extended variant of atoms loop check for positive logic programs

The Equality check and the Subsumption check are weakly sound, but are not complete even for function-free logic programs. Although the OverSize (OS) check is complete for positive logic programs, it is too general in the sense that it prunes SLD-derivations merely based on the depth-bound of repeated predicate symbols and the size of atoms, regardless of the inner structure of the atoms, so it may make wrong conclusions even for some simple programs. In this paper, we explore complete loop checking mechanisms for positive logic programs. We develop an extended Variant of Atoms (VA) check that has the following features: (1) it generalizes the concept of “variant” from “the same up to variable renaming” to “the same up to variable renaming except possibly with some arguments whose size recursively increases”, (2) it makes use of the depth-bound of repeated variants of atoms instead of depth-bound of repeated predicate symbols, (3) it combines the Equality/Subsumption check with the VA check, (4) it is complete w. r. t. the leftmost selection rule for positive logic programs, and (5) it is more sound than both the OS check and all the existing versions of the VA check. The research was completed when the author visited the University of Maryland Institute for Advanced Computer Studies. Yi-Dong Shen, Ph. D: He is a professor of Computer Science at Chongqing University, China. He received the Ph. D degree in computer Science from Chongqing University in 1991. He was a visiting researcher at the University of Valenciennes, France (1992–1993) and the University of Maryland Institute for Advanced Computer Studies (UMIACS), U. S. A. (1995–1996), respectively. His present interests include: Artificial Intelligence, Deductive and Object-Oriented Databases, Logic Programming and Parallel Processing.     

A parallel execution model of logic programs

A parallel-execution model that can concurrently exploit AND and OR parallelism in logic programs is presented. This model employs a combination of techniques in an approach to executing logic problems in parallel, making tradeoffs among number of processes, degree of parallelism, and combination bandwidth. For interpreting a nondeterministic logic program, this model (1) performs frame inheritance for newly created goals, (2) creates data-dependency graphs (DDGs) that represent relationships among the goals, and (3) constructs appropriate process structures based on the DDGs. (1) The use of frame inheritance serves to increase modularity. In contrast to most previous parallel models that have a large single process structure, frame inheritance facilitates the dynamic construction of multiple independent process structures, and thus permits further manipulation of each process structure. (2) The dynamic determination of data dependency serves to reduce computational complexity. In comparison to models that exploit brute-force parallelism and models that have fixed execution sequences, this model can reduce the number of unification and/or merging steps substantially. In comparison to models that exploit only AND parallelism, this model can selectively exploit demand-driven computation, according to the binding of the query and optional annotations. (3) The construction of appropriate process structures serves to reduce communication complexity. Unlike other methods that map DDGs directly onto process structures, this model can significantly reduce the number of data sent to a process and/or the number of communication channels connected to a process     

Multiprocessor execution of functional programs

Functional languages have recently gained attention as vehicles for programming in a concise and elegant manner. In addition, it has been suggested that functional programming provides a natural methodology for programming multiprocessor computers. This paper describes research that was performed to demonstrate that multiprocessor execution of functional programs on current multiprocessors is feasible, and results in a significant reduction in their execution times.Two implementations of the functional language ALFL were built on commercially available multiprocessors.Alfalfa is an implementation on the Intel iPSC hypercube multiprocessor, andBuckwheat is an implementation on the Encore Multimax shared-memory multiprocessor. Each implementation includes a compiler that performs automatic decomposition of ALFL programs and a run-time system that supports their execution. The compiler is responsible for detecting the inherent parallelism in a program, and decomposing the program into a collection of tasks, calledserial combinators, that can be executed in parallel.The abstract machine model supported by Alfalfa and Buckwheat is calledheterogeneous graph reduction, which is a hybrid of graph reduction and conventional stack-oriented execution. This model supports parallelism, lazy evaluation, and highe order functions while at the same time making efficient use of the processors in the system. The Alfalfa and Buckwheat runtime systems support dynamic load balancing, interprocessor communication (if required), and storage management. A large number of experiments were performed on Alfalfa and Buckwheat for a variety of programs. The results of these experiments, as well as the conclusions drawn from them, are presented.This research was supported in part by National Science Foundation grants DCR-8302018 and DCR-8521451, by a DARPA subcontract with SDC/Unisys, and by gifts from Burroughs Austin Research Center and the Intel Corporation.     

Parallel execution of Prolog with granularity control

This paper presents a system for parallel execution of Prolog supporting both independent conjunctive and disjunctive parallelism. The system is intended for distributed memory architecture and is composed of a set of workers with a hierarchical structure scheduler. The execution model has been designed in such a way that each worker's environment does not contain references to terms in other environments, thus reducing communication overhead. In order to guarantee the improvement of the performance by the parallelism exploitation, a granularity control has been introduced for each kind of parallelism. For conjunctive parallelism PDP applies a control based on the estimation provided by CASLOG. The features of the system allow to introduce this control without adding overhead. For disjunctive parallelism PDP controls granularity by applying a heuristic-based method, which can be adapted to other parallel Prolog systems. Different scheduling policies have also been tested. The system has been implemented on a transputer network and performance results show that it provides a high speedup for coarse grain parallel programs.     

Constructive negation and constraint logic programming with sets

The aim of this paper is to extend theConstructive Negation technique to the case ofCLP(SεT), a Constraint Logic Programming (CLP) language based on hereditarily (and hybrid) finite sets. The challenging aspects of the problem originate from the fact that the structure on whichCLP(SεT) is based is notadmissible closed, and this does not allow to reuse the results presented in the literature concerning the relationships betweenCLP and constructive negation. We propose a new constraint satisfaction algorithm, capable of correctly handling constructive negation for large classes ofCLP(SεT) programs; we also provide a syntactic characterization of such classes of programs. The resulting algorithm provides a novel constraint simplification procedure to handle constructive negation, suitable to theories where unification admits multiple most general unifiers. We also show, using a general result, that it is impossible to construct an interpreter forCLP(SεT) with constructive negation which is guaranteed to work for any arbitrary program; we identify classes of programs for which the implementation of the constructive negation technique is feasible. Agostino Dovier, Ph.D.: He is a researcher in the Department of Science and Technology at the University of Verona, Italy. He obtained his master degree in Computer Science from the University of Udine, Italy, in 1991 and his Ph.D. in Computer Science from the University of Pisa, Italy, in 1996. His research interests are in Programming Languages and Constraints over complex domains, such as Sets and Multisets. He has published over 20 research papers in International Journals and Conferences. He is teaching a course entitled “Special Languages and Techniques for Programming” at the University of Verona. Enrico Pontelli, Ph.D.: He is an Assistant Professor in the Department of Computer Science at the New Mexico State University. He obtained his Laurea degree from the University of Udine (Italy) in 1991, his Master degree from the University of Houston in 1992, and his Ph.D. degree from New Mexico State University in 1997. His research interests are in Programming Languages, Parallel Processing, and Constraint Programming. He has published over 50 papers and served on the program committees of different conferences. He is presently the Associate Director of the Laboratory for Logic, Databases, and Advanced Programming. Gianfranco Rossi, Ph.D.: He received his degree in Computer Science from the University of Pisa in 1979. From 1981 to 1983 he was employed at Intecs Co. System House in Pisa. From November 1983 to February 1989 he was a researcher at the Dipartimento di Informatica of the University of Turin. Since March 1989 he is an Associate Professor of Computer Science, currently with the University of Parma. He is the author of several papers dealing mainly with programming languages, in particular logic programming languages and Prolog, and extended unification algorithms. His current research interests are (logic) programming languages with sets and set unification algorithms.     

Performance of an OR-parallel logic programming system

The research focus in parallel logic programming is shifting rapidly from theoretical considerations and simulation on uniprocessors to implementation on true multiprocessors. This report presents performance figures from such a system,Boplog, for OR-parallel Horn clause logic programs on the BBN Butterfly Parallel Processor. Boplog is designed expressly for a large scale shared memory multiprocessor with an Omega interconnect. The target machine and underlying execution model are described briefly. The primary focus of the paper is on detailed statistics taken from the execution of benchmark programs to assess the performance of the model and clarify the impact of design and architecture decisions. They show that while speedup of this implementation on highly OR-parallel problems is very good, overall performance is poor. Despite its speed drawback, many aspcts of the implementation and its performance can prove useful in designing future systems for similar machines. A binding model that prohibits constant time access to bindings, and the inability of the machine to support an ambitious use of machine memory appear to be most damaging factors.This work was carried out at the University of Utah, Salt Lake City, Utah. It was supported by a University of Utah Graduate Research Fellowship, the National Science Foundation under Grant DCR-856000, and by an unrestricted gift from L. M. Ericsson Telefon AB, Stockholm, Sweden, Production of the document was supported by the Rockwell International Science Center.     

Proving termination of GHC programs

A transformational approach for proving termination of parallel logic programs such as GHC programs is proposed. A transformation from GHC programs to term rewriting systems is developed; it exploits the fact that unifications in GHC-resolution correspond to matchings. The termination of a GHC program for a class of queries is implied by the termination of the resulting rewrite system. This approach facilitates the applicability of a wide range of termination techniques developed for rewrite systems in proving termination of GHC programs. The method consists of three steps: (a) deriving moding information from a given GHC program, (b) transforming the GHC program into a term rewriting system using the moding information, and finally (c) proving termination of the resulting rewrite system. Using this method, the termination of many benchmark GHC programs such as quick-sort, merge-sort, merge, split, fair-split and append, etc., can be proved. This is a revised and extended version of Ref. 12). The work was partially supported by the NSF Indo-US grant INT-9416687 Kapur was partially supported by NSF Grant nos. CCR-8906678 and INT-9014074. M. R. K. Krishna Rao, Ph.D.: He currently works as a senior research fellow at Griffith University, Brisbane, Australia. His current interests are in the areas of logic programming, modular aspects and noncopying implementations of term rewriting, learning logic programs from examples and conuterexamples and dynamics of mental states in rational agent architectures. He received his Ph.D in computer science from Tata Institute of Fundamental Research (TIFR), Bombay in 1993 and worked at TIFR and Max Planck Institut für Informatik, Saarbrücken until January 1997. Deepak Kapur, Ph.D.: He currently works as a professor at the State University of New York at Albany. His research interests are in the areas of automated reasoning, term rewriting, constraint solving, algebraic and geometric reasoning and its applications in computer vision, symbolic computation, formal methods, specification and verification. He obtained his Ph.D. in Computer Science from MIT in 1980. He worked at General Electric Corporate Research and Development until 1987. Prof. Kapur is the editor-in-chief of the Journal of Automated Reasoning. He also serves on the editorial boards of Journal of Logic Programming, Journal on Constraints, and Journal of Applicable Algebra in Engineering, Communication and Computer Science. R. K. Shyamasundar, Ph.D.: He currently works as a professor at Tata Institute of Fundamental Research (TIFR), Bombay. His current intersts are in the areas of logic programming, reactive and real time programming, constraint solving, formal methods, specification and verification. He received his Ph.D in computer science from Indian Institute of Science, Bangalore in 1975 and has been a faculty member at Tata Institute of Fundamental Research since then. He has been a visiting/regular faculty member at Technological University of Eindhoven, University of Utrecht, IBM TJ Watson Research Centre, Pennsylvania State University, University of Illinois at Urbana-Champaign, INRIA and ENSMP, France. He has served on (and chaired) Program Committees of many International Conferences and has been on the Editorial Committees.     

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     

On the complexity of some inductive logic programming problems

The bounded ILP-consistency problem for function-free Horn clauses is described as follows. Given at setE ⁺ andE ^? of function-free ground Horn clauses and an integerk polynomial inE ⁺∪E ^?, does there exist a function-free Horn clauseC with no more thank literals such thatC subsumes each element inE ⁺ andC does not subsume any element inE ^?? It is shown that this problem is Σ ₂ ^P complete. We derive some related results on the complexity of ILP and discuss the usefulness of such complexity results.     

A survey of parallel execution strategies for transitive closure and logic programs

An important feature of database technology of the nineties is the use of parallelism for speeding up the execution of complex queries. This technology is being tested in several experimental database architectures and a few commercial systems for conventional select-project-join queries. In particular, hash-based fragmentation is used to distribute data to disks under the control of different processors in order to perform selections and joins in parallel. With the development of new query languages, and in particular with the definition of transitive closure queries and of more general logic programming queries, the new dimension of recursion has been added to query processing. Recursive queries are complex; at the same time, their regular structure is particularly suited for parallel execution, and parallelism may give a high efficiency gain. We survey the approaches to parallel execution of recursive queries that have been presented in the recent literature. We observe that research on parallel execution of recursive queries is separated into two distinct subareas, one focused on the transitive closure of Relational Algebra expressions, the other one focused on optimization of more general Datalog queries. Though the subareas seem radically different because of the approach and formalism used, they have many common features. This is not surprising, because most typical Datalog queries can be solved by means of the transitive closure of simple algebraic expressions. We first analyze the relationship between the transitive closure of expressions in Relational Algebra and Datalog programs. We then review sequential methods for evaluating transitive closure, distinguishing iterative and direct methods. We address the parallelization of these methods, by discussing various forms of parallelization. Data fragmentation plays an important role in obtaining parallel execution; we describe hash-based and semantic fragmentation. Finally, we consider Datalog queries, and present general methods for parallel rule execution; we recognize the similarities between these methods and the methods reviewed previously, when the former are applied to linear Datalog queries. We also provide a quantitative analysis that shows the impact of the initial data distribution on the performance of methods. Recommended by: Patrick Valduriez     

A backtracking algorithm for the stream AND-parallel execution of logic programs

We present the first backtracking algorithm for stream AND-parallel logic programs. It relies on compile-time knowledge of the dataflow graph of each clause to let it figure out efficiently which goals to kill or restart when a goal fails. This crucial information, which we derive from mode declarations, was not available at compile-time in any previous stream AND-parallel system. We show that modes can increase the precision of the backtracking algorithm, though our algorithm allows this precision to be traded off against overhead on a procedure-by-procedure and call-by-call basis. The modes also allow our algorithm to handle efficiently programs that manipulate partially instantiated data structures and an important class of programs with circular dependency graphs. On code that does not need backtracking, the efficiency of our algorithm approaches that of the committed-choice languages; on code that does need backtracking its overhead is comparable to that of the independent AND-parallel backtracking algorithms.     

A residualizing semantics for the partial evaluation of functional logic programs

Recent proposals for multi-paradigm declarative programming combine the most important features of functional, logic and concurrent programming into a single framework. The operational semantics of these languages is usually based on a combination of narrowing and residuation. In this paper, we introduce a non-standard, residualizing semantics for multi-paradigm declarative programs and prove its equivalence with a standard operational semantics. Our residualizing semantics is particularly relevant within the area of program transformation where it is useful, e.g., to perform computations during partial evaluation. Thus, the proof of equivalence is a crucial result to demonstrate the correctness of (existing) partial evaluation schemes.     

N-Prolog and equivalence of logic programs

The aim of this work is to develop a declarative semantics for N-Prolog with negation as failure. N-Prolog is an extension of Prolog proposed by Gabbay and Reyle (1984, 1985), which allows for occurrences of nested implications in both goals and clauses. Our starting point is an operational semantics of the language defined by means of top-down derivation trees. Negation as finite failure can be naturally introduced in this context. A goal-G may be inferred from a database if every top-down derivation of G from the database finitely fails, i.e., contains a failure node at finite height.Our purpose is to give a logical interpretation of the underlying operational semantics. In the present work (Part 1) we take into consideration only the basic problems of determining such an interpretation, so that our analysis will concentrate on the propositional case. Nevertheless we give an intuitive account of how to extend our results to a first order language. A full treatment of N-Prolog with quantifiers will be deferred to the second part of this work.Our main contribution to the logical understanding of N-Prolog is the development of a notion of modal completion for programs, or databases. N-Prolog deductions turn out to be sound and complete with respect to such completions. More exactly, we introduce a natural modal three-valued logic PK and we prove that a goal is derivable from a propositional program if and only if it is implied by the completion of the program in the logic PK. This result holds for arbitrary programs. We assume no syntactic restriction, such as stratification (Apt et al. 1988; Bonner and McCarty 1990). In particular, we allow for arbitrary recursion through negation.Our semantical analysis heavily relies on a notion of intensional equivalence for programs and goals. This notion is naturally induced by the operational semantics, and is preserved under substitution of equivalent subexpressions. Basing on this substitution property we develop a theory of normal forms of programs and goals. Every program can be effectively transformed into an equivalent program in normal form. From the simple and uniform structure of programs in normal form one may directly define the completion.