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     

Facts, arguments, annotations and reasoning

Reasoning aboutfacts and reasoning aboutarguments regarding facts are distinct activities, and automated reasoning systems should be able to treat them accordingly. In this work, we discuss one precise sense in which this distinction can be envisaged and suggest the use of Annotated Logics to characterise it.     

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.     

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.     

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     

Strong equivalence of logic programs under the infinite-valued semantics

We consider the notion of strong equivalence [V. Lifschitz, D. Pearce, A. Valverde, Strongly equivalent logic programs, ACM Transactions on Computational Logic 2 (4) (2001) 526-541] of normal propositional logic programs under the infinite-valued semantics [P. Rondogiannis, W.W. Wadge, Minimum model semantics for logic programs with negation-as-failure, ACM Transactions on Computational Logic 6 (2) (2005) 441-467] (which is a purely model-theoretic semantics that is compatible with the well-founded one). We demonstrate that two such programs are strongly equivalent under the infinite-valued semantics if and only if they are logically equivalent in the corresponding infinite-valued logic. In particular, we show that strong equivalence of normal propositional logic programs is decidable, and more specifically coNP-complete. Our results have a direct implication for the well-founded semantics since, as we demonstrate, if two programs are strongly equivalent under the infinite-valued semantics, then they are also strongly equivalent under the well-founded semantics.     

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.     

知识工程中使用演绎逻辑的局限性

本文简要归纳了演绎逻辑在知识工程中的作用,着重分析了演绎逻辑在知识表达、推理、问题求解、逻辑程序设计等方面以及作为专家系统说明语言与分析工具的局限性。     

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.     

Inductive inference of logic programs based on algebraic semantics

In this paper we present a new inductive inference algorithm for a class of logic programs, calledlinear monadic logic programs. It has several unique features not found in Shapiro’s Model Inference System. It has been proved that a set of trees isrational if and only if it is computed by a linear monadic logic program, and that the rational set of trees is recognized by a tree automaton. Based on these facts, we can reduce the problem of inductive inference of linear monadic logic programs to the problem of inductive inference of tree automata. Further several efficient inference algorithms for finite automata have been developed. We extend them to an inference algorithm for tree automata and use it to get an efficient inductive inference algorithm for linear monadic logic programs. The correctness, time complexity and several comparisons of our algorithm with Model Inference System are shown.     

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 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.     

The strong semantics for logic programs

Recently, the well-founded semantics of a logic programP has been strengthened to the well-founded semantics-by-case (WF_C) and this in turn has been strengthened to the extended well-founded semantics (WF_E). Both WF_C(P) and WF_E(P) have thelogical consequence property, namely, if an atomAj is true in the theory Th(P), thenAj is true in the semantics as well. However, neither WF_C nor WF_E has the GCWA property, i.e., if an atomAj is false in all minimal models ofP,Aj may not be false in WF_C(P) (resp. WF_E(P)). We extend the ideas in WF_C and WF_E to define a strong well-founded semantics WF_S which has the GCWA property. The strong semantics WF_S(P) is defined by combining GCWA with the notion ofderived rules. Here we use a new Type-III derived rules in addition to those used in WF_C and WF_E. The relationship between WF_S and WF_C is also clarified.     

Dualities between alternative semantics for logic programming and nonmonotonic reasoning

The Gelfond-Lifschitz operator associated with a logic program (and likewise the operator associated with default theories by Reiter) exhibits oscillating behavior. In the case of logic programs, there is always at least one finite, nonempty collection of Herbrand interpretations around which the Gelfond-Lifschitz operator bounces around. The same phenomenon occurs with default logic when Reiter's operator is considered. Based on this, a stable class semantics and extension class semantics has been proposed. The main advantage of this semantics was that it was defined for all logic programs (and default theories), and that this definition was modelled using the standard operators existing in the literature such as Reiter's operator. In this paper our primary aim is to prove that there is a very interestingduality between stable class theory and the well-founded semantics for logic programming. In the stable class semantics, classes that were minimal with respect to Smyth's power-domain ordering were selected. We show that the well-founded semantics precisely corresponds to a class that is minimal w.r.t. Hoare's power domain ordering: the well-known dual of Smyth's ordering. Besides this elegant duality, this immediately suggests how to define a well-founded semantics for default logic in such a way that the dualities that hold for logic programming continue to hold for default theories. We show how the same technique may be applied to strong autoepistemic logic: the logic of strong expansions proposed by Marek and Truszczynski.     

Defaults as restrictions on classical Hilbert-style proofs

Since the earliest formalisation of default logic by Reiter many contributions to this appealing approach to nonmonotonic reasoning have been given. The different formalisations are here presented in a general framework that gathers the basic notions, concepts and constructions underlying default logic. Our view is to interpret defaults as special rules that impose a restriction on the juxtaposition of monotonic Hubert-style proofs of a given logicL. We propose to describe default logic as a logic where the juxtaposition of default proofs is subordinate to a restriction condition . Hence a default logic is a pair (L, ) where properties of the logic , like compactness, can be interpreted through the restriction condition . Different default systems are then given a common characterization through a specific condition on the logicL. We also prove cumulativity for any default logic (L, ) by slightly modifying the notion of default proof. We extend, in fact, the language ofL in a way close to that followed by Brewka in the formulation of his cumulative default system. Finally we show the existence of infinitely many intermediary default logics, depending on and called linear logics, which lie between Reiter's and ukaszewicz' versions of default logic.Work carried out in the framework of the agreement between Italian PT Administration and FUBLaforia, Université Paris VI Pierre et Marie Curie, 4 Place Jussieu,Tour 46, 75252 Paris, France     

A framework for building knowledge-bases under uncertainty

Managing uncertainty during the knowledge engineering process from elicitation to validation and verification requires a flexible, intuitive, and semantically sound knowledge representation. This is especially important since this process is typically highly interactive with the human user to add, update, and maintain knowledge. In this paper, we present a model of knowledge representation called Bayesian Knowledge-Bases (BKBs). It unifies a ‘if-then’ style rules with probability theory. We also consider the computational efficiency of reasoning over BKBs. We can show that through careful construction of the knowledge-base, reasoning is computationally tractable and can in fact be polynomial-time. BKBs are currently fielded in the PESKI intelligent system development environment.     

An improved representation for evolving programs

A representation has been developed that addresses some of the issues with other Genetic Program representations while maintaining their advantages. This combines the easy reproduction of the linear representation with the inheritable characteristics of the tree representation by using fixed-length blocks of genes representing single program statements. This means that each block of genes will always map to the same statement in the parent and child unless it is mutated, irrespective of changes to the surrounding blocks. This method is compared to the variable length gene blocks used by other representations with a clear improvement in the similarity between parent and child. In addition, a set of list evaluation and manipulation functions was evolved as an application of the new Genetic Program components. These functions have the common feature that they all need to be 100% correct to be useful. Traditional Genetic Programming problems have mainly been optimization or approximation problems. The list results are good but do highlight the problem of scalability in that more complex functions lead to a dramatic increase in the required evolution time.