This paper firstly provides a re-appraisal of the development of techniques for inverting deduction, secondly introduces Mode-Directed Inverse Entailment (MDIE) as a generalisation and enhancement of previous approaches and thirdly describes an implementation of MDIE in the Progol system. Progol is implemented in C and available by anonymous ftp. The re-assessment of previous techniques in terms of inverse entailment leads to new results for learning from positive data and inverting implication between pairs of clauses.

The purpose of this paper is to study the fundamental mechanism humans use in argumentation and its role in different major approaches to commonsense reasoning in AI and logic programming. We present three novel results: We develop a theory for argumentation in which the acceptability of arguments is precisely defined. We show that logic programming and nonmonotonic reasoning in AI are different forms of argumentation. We show that argumentation can be viewed as a special form of logic programming with negation as failure. This result introduces a general method for generating metainterpreters for argumentation systems. 1.

In many cases, a logic program can be divided into two parts, so that one of them, the \bottom " part, does not refer to the predicates de ned in the \top " part. The \bottom " rules can be used then for the evaluation of the predicates that they de ne, and the computed values can be used to simplify the \top " de nitions. We discuss this idea of splitting a program in the context of the answer set semantics. The main theorem shows how computing the answer sets for a program can be simpli ed when the program is split into parts. The programs covered by the theorem may use both negation as failure and classical negation, and their rules may have disjunctive heads. The usefulness of the concept of splitting for the investigation of answer sets is illustrated by several applications. First, we show that a conservative extension theorem by Gelfond and Przymusinska and a theorem on the closed world assumption by Gelfond and Lifschitz are easy consequences of the splitting theorem. Second, (locally) strati ed programs are shown to have a simple characterization in terms of splitting. The existence and uniqueness of an answer set for such a program can be easily derived from this characterization. Third, we relate the idea of splitting to the notion of order-consistency. 1

In this chapter, we summarize the research on querying inconsistent databases we have been conducting over the last five years. The formal framework we have used is based on two concepts: repair and consistent query answer. We describe different approaches to the issue of computing consistent query answers: query transformation, logic programming, inference in annotated logics, and specialized algorithms. We also characterize the computational complexity of this problem. Finally, we discuss related research in artificial intelligence, databases, and logic programming.

We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the proof-theoretic and model-theoretic issues and the relationships between them.

In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten- sions of the language of definite logic programs by classical (strong) negation, disjunc- tion, and some modal operators and show how each of the added features extends the representational power of the language.

The Context Interchange strategy presents a novel perspective for mediated data access in which semantic conflicts among heterogeneous systems are not identified a priori, but are detected and reconciled by a context mediator through comparison of contexts axioms corresponding to the systems engaged in data exchange. In this article, we show that queries formulated on shared views, export schema, and shared “ontologies ” can be mediated in the same way using the Context Interchange framework. The proposed framework provides a logic-based object-oriented formalism for representing and reasoning about data semantics in disparate systems, and has been validated in a prototype implementation providing mediated data access to both traditional and web-based information sources. Categories and Subject Descriptors: H.2.4 [Database Management]: Systems—Query processing; H.2.5 [Database Management]: Heterogeneous Databases—Data translation

We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, non-monotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions. An assumption can be defeated (or "attacked") if its "contrary" can be proved, possibly with the aid of other conflicting assumptions. We show that, given such a framework, the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions, as an extension of a given theory, if and only if the set of assumptions is conflict-free (in the sense that it does not attack itself) and it attacks every assumption not in the set. We propose a more liberal, argumentation-theoretic semantics, based upon the notion of admissible extension in logic pro...

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions. In DeLP an argumentation formalism will be used for deciding between contradictory goals. Queries will be supported by arguments that could be defeated by other arguments. A query q will succeed when there is an argument A for q that is warranted, i. e. the argument A that supports q is found undefeated by a warrant procedure that implements a dialectical analysis. The defeasible argumentation basis of DeLP allows to build applications that deal with incomplete and contradictory information in dynamic domains. Thus, the resulting approach is suitable for representing agent’s knowledge and for providing an argumentation based reasoning mechanism to agents.

We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. de nite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, thatrunsfora class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have beendeveloped independently in each research eld. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can signi cantly outperform the Inside-Outside algorithm. 1.