Three-valued completion for abductive logic programs

In this paper, we propose a three-valued completion semantics for abductive logic programs, which solves some problems associated with the Console et al. two-valued completion semantics. The semantics is a generalization of Kunen's completion semantics for general logic programs, which is known to correspond very well to a class of effective proof procedures for general logic programs. Secondly, we propose a proof procedure for abductive logic programs, which is a generalization of a proof procedure for general logic programs based on constructive negation. This proof procedure is sound and complete with respect to the proposed semantics. By generalizing a number of results on general logic programs to the class of abductive logic programs, we present further evidence for the idea that limited forms of abduction can be added quite naturally to general logic programs.     

CONSTRAINED RESOLUTION AND ABDUCTTVE TEMPORAL REASONING

This article presents our work on the effective implementation of abduction in temporal reasoning. This works builds on some results, both in the logic programming field and in the automated reasoning area. We have defined and implemented an abductive procedure, which is well adapted for temporal reasoning because it is based on a constrained resolution principle. Constrained resolution has two advantages for temporal reasoning: First, it allows us to deal efficiently with temporal ordering and equality predicates, which are otherwise too much trouble with classical resolution; second, it allows a restricted form of abduction where hypotheses are limited to ordering relationships. From the logic programming area, our work uses results and procedures developed by others in the abductive logic programming field. The procedure we define and implement in this work is relatively independent of the temporal formalism: It has been used with some reified temporal logics and with the event calculus. More generally it can be used on any point-based temporal formalism, provided that a correct and complete algorithm is available for checking the consistency of a set of temporal ordering relationships in this language.     

Induction as Consequence Finding

This paper presents a general procedure for inverse entailment which constructs inductive hypotheses in inductive logic programming. Based on inverse entailment, not only unit clauses but also characteristic clauses are deduced from a background theory together with the negation of positive examples. Such clauses can be computed by a resolution method for consequence finding. Unlike previous work on inverse entailment, our proposed method called CF-induction is sound and complete for finding hypotheses from full clausal theories, and can be used for inducing not only definite clauses but also non-Horn clauses and integrity constraints. We also show that CF-induction can be used to compute abductive explanations, and then compare induction and abduction from the viewpoint of inverse entailment and consequence finding.     

Computing extended abduction through transaction programs

To explain observations from nonmonotonic background theories, one often needs removal of some hypotheses as well as addition of other hypotheses. Moreover, some observations should not be explained, while some are to be explained. In order to formalize these situations, extended abduction was introduced by Inoue and Sakama (1995) to generalize traditional abduction in the sense that it can compute negative explanations by removing hypotheses and anti‐explanations to unexplain negative observations. In this paper, we propose a computational mechanism for extended abduction. When a background theory is written in a normal logic program, we introduce its transaction program for computing extended abduction. A transaction program is a set of non‐deterministic production rules that declaratively specify addition and deletion of abductive hypotheses. Abductive explanations are then computed by the fixpoint of a transaction program using a bottom‐up model generation procedure. The correctness of the proposed procedure is shown for the class of acyclic covered abductive logic programs. In the context of deductive databases, a transaction program provides a declarative specification of database update. This revised version was published online in June 2006 with corrections to the Cover Date.     

Autoepistemic logic programming

An autoepistemic logic programming language is derived from a subset of a three-valued autoepistemic logic, called 3AEL. Autoepistemic programs generalize several ideas underlying logic programming: stable, supported, and well-founded models, Fitting's semantics, Kunen's semantics, and abductive frameworks can all be captured through simple autoepistemic translations; moreover, SLDNF-resolution and a generate-and-test method for stable semantics are generalized to provide sound and complete proof methods for autoepistemic programs. These methods extend existing proof methods for 3AEL. Thus autoepistemic logic programming, besides contributing to the understanding of 3AEL, can be seen as a unifying framework for the theory of logic programs. It should also be regarded as a first step toward a flexible environment where different forms of inference can be formally integrated.This paper is an extended version of [8]. I am grateful to my advisor, Giorgio Levi, to Paolo Mancarella, who read the first version of the paper, and to the anonymous referees, whose comments led to sensible improvements.     

Local reasoning and knowledge compilation for efficient temporal abduction

Generating abductive explanations is the basis of several problem solving activities such as diagnosis, planning, and interpretation. Temporal abduction means generating explanations that do not only account for the presence of observations, but also for temporal information on them, based on temporal knowledge in the domain theory. We focus on the case where such a theory contains temporal constraints that are required to be consistent with temporal information on observations. Our aim is to propose efficient algorithms for computing temporal abductive explanations. Temporal constraints in the theory and in the observations can be used actively by an abductive reasoner in order to prune inconsistent candidate explanations at an early stage during their generation. However, checking temporal constraint satisfaction frequently generates some overhead. We analyze two incremental ways of making this process efficient. First we show how, using a specific class of temporal constraints (which is expressive enough for many applications), such an overhead can be reduced significantly, yet preserving a full pruning power. In general, the approach does not affect the asymptotic complexity of the problem, but it provides significant advantages in practical cases. We also show that, for some special classes of theories, the asymptotic complexity is also reduced. We then show how, compiled knowledge based on temporal information, can be used to further improve the computation, thus, extending to the temporal framework previous results in the case of atemporal abduction. The paper provides both analytic and experimental evaluations of the computational advantages provided by our approaches.     

Generation and Selection of Abductive Explanations for Non-Omniscient Agents

Among the non-monotonic reasoning processes, abduction is one of the most important. Usually described as the process of looking for explanations, it has been recognized as one of the most commonly used in our daily activities. Still, the traditional definitions of an abductive problem and an abductive solution mention only theories and formulas, leaving agency out of the picture. Our work proposes a study of abductive reasoning from an epistemic and dynamic perspective. In the first part we explore syntactic definitions of both an abductive problem in terms of an agent’s information and an abductive solution in terms of the actions that modify the agent’s information. We look at diverse kinds of agents, including not only omniscient ones but also those whose information is not closed under logical consequence and those whose reasoning abilities are not complete. In the second part, we look at an existing logical framework whose semantic model allows us to interpret the previously stated formulas, and we define two actions that represent forms of abductive reasoning.     

Consistency-based and abductive diagnoses as generalised stable models

If realistic systems are to be successfully modelled and efficiently diagnosed using model-based techniques, a more expressive language than classical logic is required. In this paper, we present a definition of diagnosis which allows the use of a nonmonotonic construct, negation as failure, in the modelling language. This definition is based on thegeneralised stable model semantics of abduction. Furthermore, we argue that, if negation as failure is permitted in the modelling language, the distinction between abductive and consistency-based diagnosis is no longer clear. Our definition allows both forms of diagnosis to be expressed in a single framework. It also allows a single interference procedure to perform abductive or consistency-based diagnosis, as appropriate.This paper is an extended and revised version of ref. [29].     

溯因推理问题的碰集求解方法

溯因推理为归纳与演绎推理之外的另一种重要的推理形式,在人工智能等领域有着广泛的应用.通俗地讲,溯因推理是从观察(结果)去推断原因的推理过程.不同于以往的研究思路,通过使用本原蕴含式和素蕴含,证明了可以把命题逻辑和命题模态逻辑系统S5中求溯因问题的极小解释转化为求对应集合的极小碰集问题.给出了求解溯因问题的一种新方法.     

A framework for linguistic logic programming

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.     

Extending Answer Sets for Logic Programming Agents

We present systems of logic programming agents (LPAS) to model the interactions between decision-makers while evolving to a conclusion. Such a system consists of a number of agents connected by means of unidirectional communication channels. Agents communicate with each other by passing answer sets obtained by updating the information received from connected agents with their own private information. We introduce a credulous answer set semantics for logic programming agents. As an application, we show how extensive games with perfect information can be conveniently represented as logic programming agent systems, where each agent embodies the reasoning of a game player, such that the equilibria of the game correspond with the semantics agreed upon by the agents in the LPAS.     

一个带破圈启发方法的回答集编程系统

回答集编程(answer set programming,ASP)是一种回答集语义下的逻辑编程范例,可应用于非单调推理,叙述式问题求解等领域.本文为ASP提出并实现了一种破圈启发方法与一种基部限制式前向搜索过程,所得到的系统称为LPS.实验结果显示,相对于其他经典的ASP系统,LPS能够有效地解决处于相变难区域中的逻辑程序,通常这些程序被认为是计算困难的.除此以外,通过使用被称为动态变元过滤(dynamic variable filtering,DVF)的技术,LPS可以在计算过程中极大地缩小搜索树的尺寸.     

Semantics of EqL

The formal semantics of a novel language, called EqL, are presented for first-order functional and Horn logic programming. An EqL program is a set of conditional pattern-directed rules, where the conditions are expressed as a conjunction of equations. The programming paradigm provided by this language may be called equational programming. The declarative semantics of equations is given in terms of their complete set of solutions, and the operational semantics for solving equations is an extension of reduction, called object refinement. The correctness of the operational semantics is established through the soundness and completeness theorems. Examples are given to illustrate the language and its semantics.<>     

Structures for Abstract Rewriting

When rewriting is used to generate convergent and complete rewrite systems in order to answer the validity problem for some theories, all the rewriting theories rely on a same set of notions, properties, and methods. Rewriting techniques have been used mainly to answer the validity problem of equational theories, that is, to compute congruences. Recently, however, they have been extended in order to be applied to other algebraic structures such as preorders and orders. In this paper, we investigate an abstract form of rewriting, by following the paradigm of logical-system independency. To achieve this purpose, we provide a few simple conditions (or axioms) under which rewriting (and then the set of classical properties and methods) can be modeled, understood, studied, proven, and generalized. This enables us to extend rewriting techniques to other algebraic structures than congruences and preorders such as congruences closed under monotonicity and modus ponens. We introduce convergent rewrite systems that enable one to describe deduction procedures for their corresponding theory, and we propose a Knuth-Bendix–style completion procedure in this abstract framework.     

Semantic foundations for generalized rewrite theories

Rewriting logic (RL) is a logic of actions whose models are concurrent systems. Rewrite theories involve the specification of equational theories of data and state structures together with a set of rewrite rules that model the dynamics of concurrent systems. Since its introduction, more than one decade ago, RL has attracted the interest of both theorists and practitioners, who have contributed in showing its generality as a semantic and logical framework and also as a programming paradigm. The experimentation conducted in these years has suggested that some significant extensions to the original definition of the logic would be very useful in practice. These extensions may develop along several dimensions, like the choice of the underlying equational logic, the kind of side conditions allowed in rewrite rules and operational concerns for the execution of certain rewrites. In particular, the Maude system now supports subsorting and conditional sentences in the equational logic for data, and also frozen arguments to block undesired nested rewrites; moreover, it allows equality and membership assertions in rule conditions. In this paper, we give a detailed presentation of the inference rules, model theory, and completeness of such generalized rewrite theories. Our results provide a mathematical semantics for Maude, and a foundation for formal reasoning about Maude specifications.     

Dynamically Typed Computations for Order-sorted Equational Presentations

Equational presentations with ordered sorts encompass partially defined functions and subtyping information in an algebraic framework. In this work we address the problem of computing in order-sorted algebras, with few restrictions on the allowed presentations. We adopt the G-algebra framework, where equational, membership and existence formulas can be expressed, and this provides a complete deduction calculus which incorporates the interaction between all these formulas.To practically deal with this calculus, we introduce an operational semantics for G-algebra using rewrite systems over so-called decorated terms, that has assertions concerning the sort membership of any subterm in its head node. Decorated rewrite rules perform equational replacement, decoration rewrite rules enrich the decorations and record sort information. Therefore we use the semantic sort principle, i.e. equal terms belong to equal sorts, rather than the syntactic sort principle that does not use the equational part of a presentation.In order to have a complete and decidable unification on decorated terms, we restrict to sort-inheritance theories. Then a completion procedure on decorated terms is designed to compute all interactions between equational and membership formulas. When the completion terminates, the resulting set of rewrite rules provides a way to decide equational theorems of the form (t = t′) and typing theorems of the form (t : A).The sort inheritance property is undecidable in general but we propose a test to check it for a given presentation. The test provides information on how to extend the presentation in a model conservative way, in order to obtain sort inheritance.