Classes of Terminating Logic Programs

Termination of logic programs depends critically on the selection rule, i.e. the rule that determines which atom is selected in each resolution step. In this article, we classify programs (and queries) according to the selection rules for which they terminate. This is a survey and unified view on different approaches in the literature. For each class, we present a sufficient, for most classes even necessary, criterion for determining that a program is in that class. We study six classes: a program strongly terminates if it terminates for all selection rules; a program input terminates if it terminates for selection rules which only select atoms that are sufficiently instantiated in their input positions, so that these arguments do not get instantiated any further by the unification; a program local delay terminates if it terminates for local selection rules which only select atoms that are bounded w.r.t. an appropriate level mapping; a program left-terminates if it terminates for the usual left-to-right selection rule; a program exists-terminates if there exists a selection rule for which it terminates; finally, a program has bounded nondeterminism if it only has finitely many refutations. We propose a semantics-preserving transformation from programs with bounded nondeterminism into strongly terminating programs. Moreover, by unifying different formalisms and making appropriate assumptions, we are able to establish a formal hierarchy between the different classes.Comment: 50 pages. The following mistake was corrected: In figure 5, the first clause for insert was insert([],X,[X]

Completing and Debugging Ontologies: state of the art and challenges

As semantically-enabled applications require high-quality ontologies, developing and maintaining ontologies that are as correct and complete as possible is an important although difficult task in ontology engineering. A key step is ontology debugging and completion. In general, there are two steps: detecting defects and repairing defects. In this paper we discuss the state of the art regarding the repairing step. We do this by formalizing the repairing step as an abduction problem and situating the state of the art with respect to this framework. We show that there are still many open research problems and show opportunities for further work and advancing the field.Comment: 56 page

Automatically Leveraging MapReduce Frameworks for Data-Intensive Applications

MapReduce is a popular programming paradigm for developing large-scale, data-intensive computation. Many frameworks that implement this paradigm have recently been developed. To leverage these frameworks, however, developers must become familiar with their APIs and rewrite existing code. Casper is a new tool that automatically translates sequential Java programs into the MapReduce paradigm. Casper identifies potential code fragments to rewrite and translates them in two steps: (1) Casper uses program synthesis to search for a program summary (i.e., a functional specification) of each code fragment. The summary is expressed using a high-level intermediate language resembling the MapReduce paradigm and verified to be semantically equivalent to the original using a theorem prover. (2) Casper generates executable code from the summary, using either the Hadoop, Spark, or Flink API. We evaluated Casper by automatically converting real-world, sequential Java benchmarks to MapReduce. The resulting benchmarks perform up to 48.2x faster compared to the original.Comment: 12 pages, additional 4 pages of references and appendi

A foundation for ontology modularisation

There has been great interest in realising the Semantic Web. Ontologies are used to define Semantic Web applications. Ontologies have grown to be large and complex to the point where it causes cognitive overload for humans, in understanding and maintaining, and for machines, in processing and reasoning. Furthermore, building ontologies from scratch is time-consuming and not always necessary. Prospective ontology developers could consider using existing ontologies that are of good quality. However, an entire large ontology is not always required for a particular application, but a subset of the knowledge may be relevant. Modularity deals with simplifying an ontology for a particular context or by structure into smaller ontologies, thereby preserving the contextual knowledge. There are a number of benefits in modularising an ontology including simplified maintenance and machine processing, as well as collaborative efforts whereby work can be shared among experts. Modularity has been successfully applied to a number of different ontologies to improve usability and assist with complexity. However, problems exist for modularity that have not been satisfactorily addressed. Currently, modularity tools generate large modules that do not exclusively represent the context. Partitioning tools, which ought to generate disjoint modules, sometimes create overlapping modules. These problems arise from a number of issues: different module types have not been clearly characterised, it is unclear what the properties of a 'good' module are, and it is unclear which evaluation criteria applies to specific module types. In order to successfully solve the problem, a number of theoretical aspects have to be investigated. It is important to determine which ontology module types are the most widely-used and to characterise each such type by distinguishing properties. One must identify properties that a 'good' or 'usable' module meets. In this thesis, we investigate these problems with modularity systematically. We begin by identifying dimensions for modularity to define its foundation: use-case, technique, type, property, and evaluation metric. Each dimension is populated with sub-dimensions as fine-grained values. The dimensions are used to create an empirically-based framework for modularity by classifying a set of ontologies with them, which results in dependencies among the dimensions. The formal framework can be used to guide the user in modularising an ontology and as a starting point in the modularisation process. To solve the problem with module quality, new and existing metrics were implemented into a novel tool TOMM, and an experimental evaluation with a set of modules was performed resulting in dependencies between the metrics and module types. These dependencies can be used to determine whether a module is of good quality. For the issue with existing modularity techniques, we created five new algorithms to improve the current tools and techniques and experimentally evaluate them. The algorithms of the tool, NOMSA, performs as well as other tools for most performance criteria. For NOMSA's generated modules, two of its algorithms' generated modules are good quality when compared to the expected dependencies of the framework. The remaining three algorithms' modules correspond to some of the expected values for the metrics for the ontology set in question. The success of solving the problems with modularity resulted in a formal foundation for modularity which comprises: an exhaustive set of modularity dimensions with dependencies between them, a framework for guiding the modularisation process and annotating module, a way to measure the quality of modules using the novel TOMM tool which has new and existing evaluation metrics, the SUGOI tool for module management that has been investigated for module interchangeability, and an implementation of new algorithms to fill in the gaps of insufficient tools and techniques

CBR and MBR techniques: review for an application in the emergencies domain

The purpose of this document is to provide an in-depth analysis of current reasoning engine practice and the integration strategies of Case Based Reasoning and Model Based Reasoning that will be used in the design and development of the RIMSAT system. RIMSAT (Remote Intelligent Management Support and Training) is a European Commission funded project designed to: a.. Provide an innovative, 'intelligent', knowledge based solution aimed at improving the quality of critical decisions b.. Enhance the competencies and responsiveness of individuals and organisations involved in highly complex, safety critical incidents - irrespective of their location. In other words, RIMSAT aims to design and implement a decision support system that using Case Base Reasoning as well as Model Base Reasoning technology is applied in the management of emergency situations. This document is part of a deliverable for RIMSAT project, and although it has been done in close contact with the requirements of the project, it provides an overview wide enough for providing a state of the art in integration strategies between CBR and MBR technologies.Postprint (published version

Tools for Tutoring Theoretical Computer Science Topics

This thesis introduces COMPLEXITY TUTOR, a tutoring system to assist in learning abstract proof-based topics, which has been specifically targeted towards the population of computer science students studying theoretical computer science. Existing literature has shown tremendous educational benefits produced by active learning techniques, student-centered pedagogy, gamification and intelligent tutoring systems. However, previously, there had been almost no research on adapting these ideas to the domain of theoretical computer science. As a population, computer science students receive immediate feedback from compilers and debuggers, but receive no similar level of guidance for theoretical coursework. One hypothesis of this thesis is that immediate feedback while working on theoretical problems would be particularly well-received by students, and this hypothesis has been supported by the feedback of students who used the system. This thesis makes several contributions to the field. It provides assistance for teaching proof construction in theoretical computer science. A second contribution is a framework that can be readily adapted to many other domains with abstract mathematical content. Exercises can be constructed in natural language and instructors with limited programming knowledge can quickly develop new subject material for COMPLEXITY TUTOR. A third contribution is a platform for writing algorithms in Python code that has been integrated into this framework, for constructive proofs in computer science. A fourth contribution is development of an interactive environment that uses a novel graphical puzzle-like platform and gamification ideas to teach proof concepts. The learning curve for students is reduced, in comparison to other systems that use a formal language or complex interface. A multi-semester evaluation of 101 computer science students using COMPLEXITY TUTOR was conducted. An additional 98 students participated in the study as part of control groups. COMPLEXITY TUTOR was used to help students learn the topics of NP-completeness in algorithms classes and prepositional logic proofs in discrete math classes. Since this is the first significant study of using a computerized tutoring system in theoretical computer science, results from the study not only provide evidence to support the suitability of using tutoring systems in theoretical computer science, but also provide insights for future research directions

Efficient Loop Detection in Forwarding Networks and Representing Atoms in a Field of Sets

The problem of detecting loops in a forwarding network is known to be NP-complete when general rules such as wildcard expressions are used. Yet, network analyzer tools such as Netplumber (Kazemian et al., NSDI'13) or Veriflow (Khurshid et al., NSDI'13) efficiently solve this problem in networks with thousands of forwarding rules. In this paper, we complement such experimental validation of practical heuristics with the first provably efficient algorithm in the context of general rules. Our main tool is a canonical representation of the atoms (i.e. the minimal non-empty sets) of the field of sets generated by a collection of sets. This tool is particularly suited when the intersection of two sets can be efficiently computed and represented. In the case of forwarding networks, each forwarding rule is associated with the set of packet headers it matches. The atoms then correspond to classes of headers with same behavior in the network. We propose an algorithm for atom computation and provide the first polynomial time algorithm for loop detection in terms of number of classes (which can be exponential in general). This contrasts with previous methods that can be exponential, even in simple cases with linear number of classes. Second, we introduce a notion of network dimension captured by the overlapping degree of forwarding rules. The values of this measure appear to be very low in practice and constant overlapping degree ensures polynomial number of header classes. Forwarding loop detection is thus polynomial in forwarding networks with constant overlapping degree