Termination Proofs for Logic Programs with Tabling

Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD execution and provides a more flexible and often extremely efficient execution mechanism for logic programs. In particular, tabled execution of logic programs terminates more often than execution based on SLD-resolution. In this article, we introduce two notions of universal termination of logic programming with Tabling: quasi-termination and (the stronger notion of) LG-termination. We present sufficient conditions for these two notions of termination, namely quasi-acceptability and LG-acceptability, and we show that these conditions are also necessary in case the tabling is well-chosen. Starting from these conditions, we give modular termination proofs, i.e., proofs capable of combining termination proofs of separate programs to obtain termination proofs of combined programs. Finally, in the presence of mode information, we state sufficient conditions which form the basis for automatically proving termination in a constraint-based way.Comment: 48 pages, 6 figures, submitted to ACM Transactions on Computational Logic (TOCL

The closing operator : from partial to complete knowledge

In Proceedings of the European Conference of Artificial Intelligence, ed. H. Pradé, pp. 49-50, John Wiley and Sons, 1998status: publishe

Termination Analysis for Abductive General Logic Programs

Introduction Proving termination of programs is important in any approach to program development. In this paper, we address the termination behaviour of abductive general logic programs and queries. Abduction is a form of reasoning which, given a knowledge base and an observation Q, nds possible explanations of Q in terms of a particular set of predicates, called the abducible predicates. In the context of logic programming, abductive procedures have been used for planning, knowledge assimilation and belief revision, database updating, reasoning in the context of temporal domains with uncertainty, . . . (we refer to [7] for references to such works). In [7], Denecker and De Schreye present an abductive extension of SLDNF [1], called SLDNFA. We study termination of general logic programs executed under SLDNFA w.r.t. an arbitrary safe selection rule. We show that the termination conditions for SLDNF of Apt and Bezem [3], namely acyclicity of th

Static verification of compositionality and termination for logic programming languages

nrpages: 264 + ivstatus: publishe

Composing complete and partial knowledge

status: publishe

Identifying Mislabeled Training Examples in ILP Classification Problems

We consider the problem of noisy training examples, more precisely mislabeled training examples, in the context of ILP classification problems. We address this problem by preprocessing the training set, i.e. by identifying and removing outliers from the training set. We study a number of filtering techniques, some of which were proposed in the literature for attribute-value problems. We evaluate these techniques on a Bongard data set, which we artificially corrupt with different levels of classification noise

Composing Complete and Partial Knowledge

The representation of knowledge in the logic OLP-FOL [8], [7], is split in two parts: writing definitions for known concepts, and writing constraints, expressing partial knowledge on other concepts. This is reflected in an OLP-FOL theory T , which is a pair: T = (T d ; T c ). The definition part T d contains the definitions for known predicates in the form of a normal open logic program (OLP), whereas the first order logic (FOL) part T c is a set of FOL axioms, expressing partial knowledge on other predicates. The semantics of OLP-FOL is a generalisation of the well-founded semantics [16]. An OLP-FOL theory T = (T d ; T c ), divides the set of predicate symbols in two disjoint subsets: the defined predicates, which occur in the head of a clause of T d , and the open predicates, which occur at the most in the body of the clauses of T d . In previous work [19], the composition of two OLP-FOL theories, with non-intersecting sets of defined predicate symbols, was studied. It was argued that their composition is given by the set of common models. Here, we investigate the possibility of composing two OLP-FOL theories, which define the same predicate. Therefore, we introduce two operators on theories: the p-opening operator, which opens the definition of the predicate p in a theory completely, and the conditional p-opening operator, which maintains the definition of p in a theory if a certain condition holds, and opens p in the other cases. We show that we can compose two theories, which both have an open definition for the same predicate, or which both have a conditional open definition for the same predicate, with non-overlapping conditions

A General View on Probabilistic Logic Programming

Probabilistic logic programming oers a way of dealing with both relational and uncertain knowledge. As research in this eld has lead to numerous formalisms, originating from diverse origins, it is not always easy to get a clear picture of this domain. In this work, we present a general \framework" for looking at such formalisms. We show how several actual formalisms t into this view and how this leads to a clearer view on the relationships between them