Some Proof Theory of First Order Logic Programming

Logic programming languages, such as Prolog, provide a high-level, declarative approach to programming. Logic Programming offers great potential for implicit parallelism, thus allowing parallel systems to often reduce a program's execution time without programmer intervention. We believe that for complex applications that take several hours, if not days, to return an answer, even limited speedups from parallel execution can directly translate to very significant productivity gains. It has been argued that Prolog's evaluation strategy – SLD resolution – often limits the potential of the logic programming paradigm. The past years have therefore seen widening efforts at increasing Prolog's declarativeness and expressiveness. Tabling has proved to be a viable technique to efficiently overcome SLD's susceptibility to infinite loops and redundant subcomputations. Our research demonstrates that implicit or-parallelism is a natural fit for logic programs with tabling. To substantiate this belief, we have designed and implemented an or-parallel tabling engine – OPTYap – and we used a shared-memory parallel machine to evaluate its performance. To the best of our knowledge, OPTYap is the first implementation of a parallel tabling engine for logic programming systems. OPTYap builds on Yap's efficient sequential Prolog engine. Its execution model is based on the SLG-WAM for tabling, and on the environment copying for or-parallelism. Preliminary results indicate that the mechanisms proposed to parallelize search in the context of SLD resolution can indeed be effectively and naturally generalized to parallelize tabled computations, and that the resulting systems can achieve good performance on shared-memory parallel machines. More importantly, it emphasizes our belief that through applying or-parallelism and tabling to logic programs the range of applications for Logic Programming can be increased.

Logic Programming languages, such as Prolog, provide a highlevel, declarative approach to programming. Despite the power, flexibility and good performance that Prolog systems have achieved, some deficiencies in Prolog?s evaluation strategy - SLD resolution - limit the potential of the logic programming paradigm. Tabled evaluation is a recognized and powerful technique that overcomes SLD?s susceptibility in dealing with recursion and redundant sub-computations. In a tabled evaluation, there are several points where we may have to choose between different tabling operations. The decision on which operation to perform is determined by the scheduling algorithm. The two most successful tabling scheduling algorithms are local scheduling and batched scheduling. In previous work, we have developed a framework, on top of the Yap Prolog system, that supports the combination of different linear tabling strategies for local scheduling. In this work, we propose the extension of our framework to support batched scheduling. In particular, we are interested in the two most successful linear tabling strategies, the DRA and DRE strategies. To the best of our knowledge, no other Prolog system supports both strategies simultaneously for batched scheduling. Our experimental results show that the combination of the DRA and DRE strategies can effectively reduce the execution time for batched evaluation.

Relating defeasible and normal logic programming through transformation properties

Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this article, we will survey the use ofstructural proof theoryas an alternative foundation. Researchers have been using this foundation for the past 35 years to elevate logic programming from its roots in first-order classical logic into higher-order versions of intuitionistic and linear logic. These more expressive logic programming languages allow for capturing stateful computations and rich forms of abstractions, including higher-order programming, modularity, and abstract data types. Term-level bindings are another kind of abstraction, and these are given an elegant and direct treatment within both proof theory and these extended logic programming languages. Logic programming has also inspired new results in proof theory, such as those involving polarity and focused proofs. These recent results provide a high-level means for presenting the differences between forward-chaining and backward-chaining style inferences. Anchoring logic programming in proof theory has also helped identify its connections and differences with functional programming, deductive databases, and model checking.

We study the relationship between argumentation (abduction) and disjunctive logic programming. Based on the paradigm of argumentation, an abductive semantic framework for disjunctive logic programming is presented, in which the disjunctions of negative literals are taken as possible assumptions rather than only negative literals as the case of non-disjunctive logic programming. In our framework, three semantics PDH, CDH and WFDH are defined by three kinds of acceptable hypotheses to represent credulous reasoning, moderate reasoning and skeptical reasoning in AI, respectively. On the other hand, our semantic framework could be established in a broader class than that of disjunctive programs (called bi-disjunctive logic programs) and, hence, the corresponding abductive framework is abbreviated as BDAS (Bi-Disjunctive Argumentation-theoretic Semantics). Besides its rich expressive power and nondeterminism, BDAS integrates and naturally extends many key semantics, such as the minimal models, EGCWA, the well-founded model, and the stable models. In particular, a novel and interesting argumentation-theoretic characterization of EGCWA is shown. Thus the framework in this paper does not only provides a new way of performing argumentation (abduction) in disjunctive logic programming, but also is a simple, intuitive and unifying semantic framework for disjunctive logic programming.KeywordsLogic ProgramLogic ProgrammingArgument FrameworkDisjunctive ProgramDisjunctive LogicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A meta-program, regardless of the nature of the programming language, is a program whose data denotes another (object) program. The importance of meta-programming can be gauged from its large number of applications. These include compilers, interpreters, program analysers, and program transformers. Furthermore, if the object program is a logic or functional program formalizing some knowledge, then the meta-program may be regarded as a meta-reasoner for reasoning about this knowledge. In this chapter, the meta-program is assumed to be a logic program. The object program does not have to be a logic program although much of the work in this chapter assumes this. We have identified three major topics for consideration. These are the theoretical foundations of meta-programming, the suitability of the alternative meta-programming techniques for different applications, and methods for improving the efficiency of meta-programs. As with logic programs generally, meta-programs have declarative and procedural semantics. The theoretical study of meta-programming shows that both aspects of the semantics depend crucially on the manner in which object programs are represented as data in a meta-program. The second theme of the paper is the problem of designing and choosing appropriate ways of specifying important meta-programming problems, including dynamic metaprogramming and problems involving self-application. The third theme concerns efficient implementation of meta-programs. Meta-programming systems require representations with facilities that minimize the overhead of interpreting the object program. In addition, efficiency can be gained by transforming the meta-program, specializing it for the particular object program it is reasoning about. This chapter, which concentrates on these aspects of meta-programming, is not intended to be a survey of the field. A more complete survey of meta-programming for logic programming can be found in [Barklund, 1995]. Many issues in meta-programming have their roots in problems in logic which have been studied for several decades. This chapter emphasizes meta-programming solutions. It is not intended to give a full treatment of the underlying logical problems, though we try to indicate some connections to wider topics in meta-logic. The meta-programs in this chapter are logic programs based on first order logic.

Organizational Semiotics is the branch of Semiotics that studies the application of the Theory of Signs in organizational contexts. Organizations are based upon co-coordinated patterns of behavior, including social norms. To achieve the required efficacy, an organization may use both norms and communication to co-ordinate the different agents involved in organizational behavior. The formalization of normative agent behavior can be done using Deontic Agency Logic. The implementation can be done using agent-oriented programming. We propose to combine Ontology Charts, Norm Analysis, Deontic Agency Logic and Agent-Oriented Programming in order to create normative agent-based models of the structure and the dynamics of Virtual Enterprises (VE). This approach seems to be more resistant to organizational change than pure technology-oriented approaches.KeywordsModal LogicVirtual OrganizationDeontic LogicVirtual EnterpriseOntological DependencyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Lawry's label semantics for modeling and computing with linguistic information in natural language provides a clear interpretation of linguistic expressions and thus a transparent model for real-world applications. Meanwhile, annotated logic programs (ALPs) and its fuzzy extension AFLPs have been developed as an extension of classical logic programs offering a powerful computational framework for handling uncertain and imprecise data within logic programs. This paper proposes annotated linguistic logic programs (ALLPs) that embed Lawry's label semantics into the ALP/AFLP syntax, providing a linguistic logic programming formalism for development of automated reasoning systems involving soft data as vague and imprecise concepts occurring frequently in natural language. The syntax of ALLPs is introduced, and their declarative semantics is studied. The ALLP SLD-style proof procedure is then defined and proved to be sound and complete with respect to the declarative semantics of ALLPs. © 2010 Wiley Periodicals, Inc.

Logic programming is one of a batch of new-generation tools derived from the field of artificial intelligence and presenting new challenges and opportunities to those concerned with managing and processing data. This paper is a review of the underlying theory of logic programming, demonstrating how simple spatial problems may be expressed in the language of logic and then transformed into a syntax suitable for automated theorem proving. The implementation of automated theorem proving as a general purpose logic programming language is illustrated by means of PROLOG and examples of PROLOG applications are drawn from the literature. Logic programming is presented both as an elegant programming language and also as a modelling framework with strong theoretical roots offering a fresh approach to the formulation and solution of spatial problems. Pointers are offered to its potential applications in this field.

Translating Multi-Agent Autoepistemic Logic into Logic Program

We show how the language Constraint Handling Rules (CHR), a high-level logic language for the implementation of constraint solvers, can be slightly extended to become a general-purpose logic programming language with an expressive power subsuming the expressive ower of Horn clause programs with SLD resolution. The extended language, called “CHR∀”, retains however the extra features of CHR, e.g., committed choice and matching, which axe important for other purposes, especially for efficiently solving constraints. CHR∀ turns out to be a very flexible query language in the sense that it supports several (constraint) logic programming paradigms and allows to mix them in a single program. In particular, it supports top-down query evaluation and also bottom-up evaluation as it is frequently used in (disjunctive) deductive databases.

This paper describes an extension of Horn clause logic programs by bounded quantifiers. Bounded quantifiers had been extensively used in a part of mathematical logic called theory of admissible sets [2]. Later some variants of bounded quantifiers had been introduced in logic programming languages [12, 19, 21, 9, 6, 7]. We show that an extension of logic programs by bounded quantifiers has several equivalent logical semantics and is efficiently implementable using a variant of SLD-resolution, which we call SLDB-resolution. We give examples showing that introduction of bounded quantifiers results in a high level logical specification language. An expressive power of subsets of Horn clauses and subsets of logic programs with bounded quantifiers is compared. We also show that the use of bounded quantifiers sheds new light on classical negation in logic programming.KeywordsLogic ProgramLogic ProgrammingFunction SymbolUnification AlgorithmPredicate SymbolThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In order to provide performance improvements in the execution of large logic programs, it is highly desirable to investigate the relationships between logic, data-base systems and knowledge-based systems in the context of massively parallel architectures. This paper presents a model for the interpretation of logic programs in this type of environment and overviews the algorithms under development. An interpreter that implements the model has been demonstrated in simulations on a number of small programs. Implementation requires only a small set of hardware primitives be available, these have been successfully implemented on a working prototype machines. DADO Current research aims to develop the model into a practical and efficient logic programming system for use on the machine.

Distribution semantics is one of the most prominent approaches for the combination of logic programming and probability theory. Many languages follow this semantics, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs), and ProbLog. When a program contains functions symbols, the distribution semantics is well–defined only if the set of explanations for a query is finite and so is each explanation. Well–definedness is usually either explicitly imposed or is achieved by severely limiting the class of allowed programs. In this paper, we identify a larger class of programs for which the semantics is well–defined together with an efficient procedure for computing the probability of queries. Since Logic Programs with Annotated Disjunctions offer the most general syntax, we present our results for them, but our results are applicable to all languages under the distribution semantics. We present the algorithm “Probabilistic Inference with Tabling and Answer subsumption” (PITA) that computes the probability of queries by transforming a probabilistic program into a normal program and then applying SLG resolution with answer subsumption. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog,cplint, and CVE. PITA was almost always able to solve larger problems in a shorter time, on domains with and without function symbols.

Argumentation-based abduction in disjunctive logic programming