Non-Termination Inference of Logic Programs

We present a static analysis technique for non-termination inference of logic programs. Our framework relies on an extension of the subsumption test, where some specific argument positions can be instantiated while others are generalized. We give syntactic criteria to statically identify such argument positions from the text of a program. Atomic left looping queries are generated bottom-up from selected subsets of the binary unfoldings of the program of interest. We propose a set of correct algorithms for automating the approach. Then, non-termination inference is tailored to attempt proofs of optimality of left termination conditions computed by a termination inference tool. An experimental evaluation is reported. When termination and non-termination analysis produce complementary results for a logic procedure, then with respect to the leftmost selection rule and the language used to describe sets of atomic queries, each analysis is optimal and together, they induce a characterization of the operational behavior of the logic procedure.Comment: Long version (algorithms and proofs included) of a paper submitted to TOPLA

Inference of termination conditions for numerical loops in Prolog

We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these difficulties. Our approach is based on transforming a program in a way that allows integrating and extending techniques originally developed for analysis of numerical computations in the framework of query-mapping pairs with the well-known framework of acceptability. Such an integration not only contributes to the understanding of termination behaviour of numerical computations, but also allows us to perform a correct analysis of such computations automatically, by extending previous work on a constraint-based approach to termination. Finally, we discuss possible extensions of the technique, including incorporating general term orderings.Comment: To appear in Theory and Practice of Logic Programming. To appear in Theory and Practice of Logic Programmin

Logic, parallelism and semantic networks : the binary predicate execution model

This thesis develops the Binary Predicate Execution Model; a distributed, massively-parallel system for semantic networks and knowledge bases that is built on a subset of first-order predicate logic. The use of logic gives the model an easily-understood programming paradigm and a well-defined semantics of execution. When expressed in binary predicates, a simple graphical interpretation can be used. All program facts are represented in an assertion graph. Each vertex is associated with a term appearing in a fact and the edges are labeled with the predicate names. Similar graphs are also associated with each rule body and the query. Finding all possible solutions corresponds to finding all possible matches between the query graph and the assertion graph. Invoking a rule corresponds to substituting the graph of its body constrained by the dependencies between its arguments. This can be implemented in a parallel, message-passing fashion where the assertion graph vertices are active processing elements which asynchronously exchange messages identifying different parts of the query that remain to be matched and containing any binding information from previous matching required to accomplish this. The model is data-driven since every message can be immediately processed without the need for any centralized control or centralized memory. By restricting how functional terms can occur, distributed data structures and remote data look-ups for unification are eliminated. Thus, the model's performance on increasingly larger problems scales-up given increasingly larger machines in most cases. Architectural support for the model is investigated and simulation results of a relatively simple software implementation are reported. This suggests performance on the order of 10^5 logical inferences per second for 256 processing elements in an n-cube configuration. Further research directions, including that of increasing efficiency, are discussed

Proceedings of Sixth International Workshop on Unification

Swiss National Science Foundation; Austrian Federal Ministry of Science and Research; Deutsche Forschungsgemeinschaft (SFB 314); Christ Church, Oxford; Oxford University Computing Laborator

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas