Large-scale Reasoning with Nonmonotonic and Imperfect Knowledge Through Mass Parallelization

Due to the recent explosion of available data coming from the Web, sensor readings, social media, government authorities and scientific databases, both academia and industry have increased their interest in utilizing this knowledge. Processing huge amounts of data introduces several scientific and technological challenges, and creates new opportunities. Existing works on large-scale reasoning through mass parallelization (namely parallelization based on utilizing a large number of processing units) concentrated on monotonic reasoning, which can process only consistent datasets. The question arises whether and how mass parallelization can be applied to reasoning with huge amounts of imperfect (e.g. inconsistent, incomplete) information. Potential scenarios involving such imperfect data and knowledge include ontology evolution, ontology repair and smart city applications combining a variety of heterogeneous data sources. In this thesis, we overcome the limitations of monotonic reasoning, by studying several nonmonotonic logics that have the ability to handle imperfect knowledge, and it is shown that large-scale reasoning is indeed achievable for such complex knowledge structures. This work is mainly focused on adapting existing methods, thus ensuring that the proposed solutions are parallel and scalable. Initially, preliminaries and literature review are presented in order to introduce the reader to basic background and the state-of-the-art considering large-scale reasoning. Subsequently, each chapter presents an approach for large-scale reasoning over a given logic. Large-scale reasoning over defeasible logic is supported allowing conflict resolution by prioritizing the superiority among rules in the rule set. A solution for stratified semantics is presented where rules may contain both positive and negative subgoals, thus allowing reasoning over missing information in a given dataset. The approach for stratified semantics is generalized in order to fully support the well-founded semantics, where recursion through negation is allowed. Finally, conclusion includes observations from a preliminary investigation on a restricted form of answer set programming, a generic evaluation framework for large-scale reasoning, a discussion of the main findings of this work, and opportunities for future work

Large-scale Parallel Stratified Defeasible Reasoning

We are recently experiencing an unprecedented explosion of available data from the Web, sensors readings, scientific databases, government authorities and more. Such datasets could benefit from the introduction of rule sets encoding commonly accepted rules or facts, application- or domain-specific rules, commonsense knowledge etc. This raises the question of whether, how, and to what extent knowledge representation methods are capable of handling huge amounts of data for these applications. In this paper, we consider inconsistency-tolerant reasoning in the form of defeasible logic, and analyze how parallelization, using the MapReduce framework, can be used to reason with defeasible rules over huge datasets. We extend previous work by dealing with predicates of arbitrary arity, under the assumption of stratification. Moving from unary to multi-arity predicates is a decisive step towards practical applications, e.g. reasoning with linked open (RDF) data. Our experimental results demonstrate that defeasible reasoning with millions of data is performant, and has the potential to scale to billions of facts

Representing time and space for the semantic web

Representation of temporal and spatial information for the Semantic Web often involves qualitative defined information (i.e., information described using natural language terms such as "before" or "overlaps") since precise dates or coordinates are not always available. This work proposes several temporal representations for time points and intervals and spatial topological representations in ontologies by means of OWL properties and reasoning rules in SWRL. All representations are fully compliant with existing Semantic Web standards and W3C recommendations. Although qualitative representations for temporal interval and point relations and spatial topological relations exist, this is the first work proposing representations combining qualitative and quantitative information for the Semantic Web. In addition to this, several existing and proposed approaches are compared using different reasoners and experimental results are presented in detail. The proposed approach is applied to topological relations (RCC5 and RCC8) supporting both qualitative and quantitative (i.e., using coordinates) spatial relations. Experimental results illustrate that reasoning performance differs greatly between different representations and reasoners. To the best of our knowledge, this is the first such experimental evaluation of both qualitative and quantitative Semantic Web temporal and spatial representations. In addition to the above, querying performance using SPARQL is evaluated. Evaluation results demonstrate that extracting qualitative relations from quantitative representations using reasoning rules and querying qualitative relations instead of directly querying quantitative representations increases performance at query time

Exploiting Parallelism for Hard Problems in Abstract Argumentation

Abstract argumentation framework (AF) is a unifying framework able to encompass a variety of nonmonotonic reasoning approaches, logic programming and computational argumentation. Yet, efficient approaches for most of the decision and enumeration problems associated to AF s are missing, thus potentially limiting the efficacy of argumentation-based approaches in real domains. In this paper, we present an algorithm for enumerating the preferred extensions of abstract argumentation frameworks which exploits parallel computation. To this purpose, the SCC-recursive semantics definition schema is adopted, where extensions are defined at the level of specific sub-frameworks. The algorithm shows significant performance improvements in large frameworks, in terms of number of solutions found and speedup

A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming

Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly in the spatial and temporal domains, with several practical applications such as naval traffic monitoring, warehouse process optimisation and robot manipulation. Even if a number of specialised qualitative reasoning tools have been developed so far, an important barrier to the wider adoption of these tools is that only qualitative reasoning is supported natively, when real-world problems most often require a combination of qualitative and other forms of reasoning. In this work, we propose to overcome this barrier by using ASP as a unifying formalism to tackle problems that require qualitative reasoning in addition to non-qualitative reasoning. A family of ASP encodings is proposed which can handle any qualitative calculus with binary relations. These encodings are experimentally evaluated using a real-world dataset based on a case study of determining optimal coverage of telecommunication antennas, and compared with the performance of two well-known dedicated reasoners. Experimental results show that the proposed encodings outperform one of the two reasoners, but fall behind the other, an acceptable trade-off given the added benefits of handling any type of reasoning as well as the interpretability of logic programs. This paper is under consideration for acceptance in TPLP.Comment: Paper presented at the 36th International Conference on Logic Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September 2020, 18 pages, 3 figure

Design and Evaluation of Small-Large Outer Joins in Cloud Computing Environments

Large-scale analytics is a key application area for data processing and parallel computing research. One of the most common (and challenging) operations in this domain is the join. Though inner join approaches have been extensively evaluated in parallel and distributed systems, there is little published work providing analysis of outer joins, especially in the extremely popular cloud computing environments. A common type of outer join is the small-large outer join, where one relation is relatively small and the other is large. Conventional implementations on this condition, such as one based on hash redistribution, often incur significant network communication, while the duplication-based approaches are complex and inefficient. In this work, we present a new method called DDR (duplication and direct redistribution), which aims to enable efficient small-large outer joins in cloud computing environments while being easy to implement using existing predicates in data processing frameworks. We present the detailed implementation of our approach and evaluate its performance through extensive experiments over the widely used MapReduce and Spark platforms. We show that the proposed method is scalable and can achieve significant performance improvements over the conventional approaches. Compared to the state-of-art method, the DDR algorithm is shown to be easier to implement and can achieve very similar or better performance under different outer join workloads, and thus, can be considered as a new option for current data analysis applications. Moreover, our detailed experimental results also have provided insights of current small-large outer join implementations, thereby allowing system developers to make a more informed choice for their data analysis applications

A Trajectory Calculus for Qualitative Spatial Reasoning Using Answer Set Programming

Spatial information is often expressed using qualitative terms such as natural language expressions instead of coordinates; reasoning over such terms has several practical applications, such as bus routes planning. Representing and reasoning on trajectories is a specific case of qualitative spatial reasoning that focuses on moving objects and their paths. In this work, we propose two versions of a trajectory calculus based on the allowed properties over trajectories, where trajectories are defined as a sequence of non-overlapping regions of a partitioned map. More specifically, if a given trajectory is allowed to start and finish at the same region, 6 base relations are defined (TC-6). If a given trajectory should have different start and finish regions but cycles are allowed within, 10 base relations are defined (TC-10). Both versions of the calculus are implemented as ASP programs; we propose several different encodings, including a generalised program capable of encoding any qualitative calculus in ASP. All proposed encodings are experimentally evaluated using a real-world dataset. Experiment results show that the best performing implementation can scale up to an input of 250 trajectories for TC-6 and 150 trajectories for TC-10 for the problem of discovering a consistent configuration, a significant improvement compared to previous ASP implementations for similar qualitative spatial and temporal calculi. This manuscript is under consideration for acceptance in TPLP.Comment: Paper presented at the 34th International Conference on Logic Programming (ICLP 2018), Oxford, UK, July 14 to July 17, 2018, 20 pages, LaTeX, 16 figure

A survey of large-scale reasoning on the Web of data

As more and more data is being generated by sensor networks, social media and organizations, the Webinterlinking this wealth of information becomes more complex. This is particularly true for the so-calledWeb of Data, in which data is semantically enriched and interlinked using ontologies. In this large anduncoordinated environment, reasoning can be used to check the consistency of the data and of asso-ciated ontologies, or to infer logical consequences which, in turn, can be used to obtain new insightsfrom the data. However, reasoning approaches need to be scalable in order to enable reasoning over theentire Web of Data. To address this problem, several high-performance reasoning systems, whichmainly implement distributed or parallel algorithms, have been proposed in the last few years. Thesesystems differ significantly; for instance in terms of reasoning expressivity, computational propertiessuch as completeness, or reasoning objectives. In order to provide afirst complete overview of thefield,this paper reports a systematic review of such scalable reasoning approaches over various ontologicallanguages, reporting details about the methods and over the conducted experiments. We highlight theshortcomings of these approaches and discuss some of the open problems related to performing scalablereasoning