Much has been written about theory and practice in the law, and the tension between practitioners and theorists. Judges do not cite theoretical articles often; they rarely "apply" theories to particular cases. These arguments are not revisited. Instead the Essay explores the working and interaction of theory and practice, practitioners and theorists. The Essay starts with a story about solving a legal issue using our intellectual tools - theory, practice, and their progenies: experience and "gut." Next the Essay elaborates on the nature of theory, practice, experience and "gut." The third part of the Essay discusses theories that are helpful to practitioners and those that are less helpful. The Essay concludes that practitioners theorize, and theorists practice. They use these intellectual tools differently because the goals and orientations of theorists and practitioners, and the constraints under which they act, differ. Theory, practice, experience and "gut" help us think, remember, decide and create. They complement each other like the two sides of the same coin: distinct but inseparable.

Of Theory and Practice

The recently introduced series of description logics under the common moniker 'DL-Lite' has attracted attention of the description logic and semantic web communities due to the low computational complexity of inference, on the one hand, and the ability to represent conceptual modeling formalisms, on the other. The main aim of this article is to carry out a thorough and systematic investigation of inference in extensions of the original DL-Lite logics along five axes: by (i) adding the Boolean connectives and (ii) number restrictions to concept constructs, (iii) allowing role hierarchies, (iv) allowing role disjointness, symmetry, asymmetry, reflexivity, irreflexivity and transitivity constraints, and (v) adopting or dropping the unique name assumption. We analyze the combined complexity of satisfiability for the resulting logics, as well as the data complexity of instance checking and answering positive existential queries. Our approach is based on embedding DL-Lite logics in suitable fragments of the one-variable first-order logic, which provides useful insights into their properties and, in particular, computational behavior.

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The DL-lite family and relations

Combining answer set programming with description logics for the Semantic Web

This introduction presents the main motivations for the development of Description Logics (DLs) as a formalism for representing knowledge, as well as some important basic notions underlying all systems that have been created in the DL tradition. In addition, we provide the reader with an overview of the entire book and some guidelines for reading it.We first address the relationship between Description Logics and earlier semantic network and frame systems, which represent the original heritage of the field. We delve into some of the key problems encountered with the older efforts. Subsequently, we introduce the basic features of DL languages and related reasoning techniques.DL languages are then viewed as the core of knowledge representation systems. considering both the structure of a DL knowledge base and its associated reasoning services. The development of some implemented knowledge representation systems based on Description Logics and the first applications built with such systems are then reviewed.Finally, we address the relationship of Description Logics to other fields of Computer Science. We also discuss some extensions of the basic representation language machinery; these include features proposed for incorporation in the formalism that originally arose in implemented systems, and features proposed to cope with the needs of certain application domains.

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An Introduction to Description Logic

In this paper we study data complexity of answering conjunctive queries over Description Logic knowledge bases constituted by an ABox and a TBox. In particular, we are interested in characterizing the FOL-reducibility and the polynomial tractability boundaries of conjunctive query answering, depending on the expressive power of the Description Logic used to specify the knowledge base. FOL-reducibility means that query answering can be reduced to evaluating queries over the database corresponding to the ABox. Since first-order queries can be expressed in SQL, the importance of FOL-reducibility is that, when query answering enjoys this property, we can take advantage of Data Base Management System (DBMS) techniques for both representing data, i.e., ABox assertions, and answering queries via reformulation into SQL. What emerges from our complexity analysis is that the Description Logics of the DL-Lite family are the maximal logics allowing conjunctive query answering through standard database technology. In this sense, they are the first Description Logics specifically tailored for effective query answering over very large ABoxes.

Data complexity of query answering in description logics

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, it was an open problem whether conjunctive query answering over DL knowledge bases is decidable if transitive roles are admitted in the query. In this paper, we consider conjunctive queries over knowledge bases formulated in the popular DL SHIQ and allow transitive roles in both the query and the knowledge base. We show that query answering is decidable and establish the following complexity bounds: regarding combined complexity, we devise a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query. Regarding data complexity, we prove co-NP-completeness.

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Conjunctive query answering for the description logic SHIQ

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP.

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While exam-style questions are a fundamental educational tool serving a variety of purposes, manual construction of questions is a complex process that requires training, experience, and resources. This, in turn, hinders and slows down the use of educational activities (e.g. providing practice questions) and new advances (e.g. adaptive testing) that require a large pool of questions. To reduce the expenses associated with manual construction of questions and to satisfy the need for a continuous supply of new questions, automatic question generation (AQG) techniques were introduced. This review extends a previous review on AQG literature that has been published up to late 2014. It includes 93 papers that were between 2015 and early 2019 and tackle the automatic generation of questions for educational purposes. The aims of this review are to: provide an overview of the AQG community and its activities, summarise the current trends and advances in AQG, highlight the changes that the area has undergone in the recent years, and suggest areas for improvement and future opportunities for AQG. Similar to what was found previously, there is little focus in the current literature on generating questions of controlled difficulty, enriching question forms and structures, automating template construction, improving presentation, and generating feedback. Our findings also suggest the need to further improve experimental reporting, harmonise evaluation metrics, and investigate other evaluation methods that are more feasible.

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A Systematic Review of Automatic Question Generation for Educational Purposes

Extracting a subset of a given ontology that captures all the ontology's knowledge about a specified set of terms is a well-understood task. This task can be based, for instance, on locality-based modules. However, a single module does not allow us to understand neither topicality, connectedness, structure, or superfluous parts of an ontology, nor agreement between actual and intended modeling.

The strong logical properties of locality-based modules suggest that the family of all such modules of an ontology can support comprehension of the ontology as a whole. However, extracting that family is not feasible, since the number of locality-based modules of an ontology can be exponential w.r.t. its size.

In this paper we report on a new approach that enables us to efficiently extract a polynomial representation of the family of all locality-based modules of an ontology. We also describe the fundamental algorithm to pursue this task, and report on experiments carried out and results obtained.

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The modular structure of an ontology: atomic decomposition

Ontologies with potential educational value are available in di↵erent domains. However, it is still unclear how such ontologies can be exploited to generate useful instructional content, e.g., assessment questions. In this paper, we present an approach to automatically generate multiple-choice questions from OWL ontologies. We describe a psychologically-plausible theory to control the di culty of questions. Our contributions include designing a protocol to evaluate the characteristics of the generated questions, in particular, question di culty. We report on our experience on generating questions from ontologies and present promising results of evaluating our di culty-control theory.

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Uli Sattler

Papers

Conjunctive query answering for the description logic SHIQ

Conjunctive query answering for the description logic SHIQ

A Systematic Review of Automatic Question Generation for Educational Purposes

The modular structure of an ontology: atomic decomposition

Generating multiple choice questions from ontologies: Lessons learnt