Living Without Beth and Craig: Definitions and Interpolants in Description Logics with Nominals and Role Inclusions

The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The projective Beth definability property (PBDP) states that an explicit definition exists iff a formula stating implicit definability is valid. Thus, the CIP and PBDP transform potentially hard existence problems into deduction problems in the underlying logic. Description Logics with nominals and/or role inclusions do not enjoy the CIP nor PBDP, but interpolants and explicit definitions have many potential applications in ontology engineering and ontology-based data management. In this article we show the following: even without Craig and Beth, the existence of interpolants and explicit definitions is decidable in description logics with nominals and/or role inclusions such as ALCO, ALCH and ALCHIO. However, living without Craig and Beth makes this problem harder than deduction: we prove that the existence problems become 2ExpTime-complete, thus one exponential harder than validity. The existence of explicit definitions is 2ExpTime-hard even if one asks for a definition of a nominal using any symbol distinct from that nominal, but it becomes ExpTime-complete if one asks for a definition of a concept name using any symbol distinct from that concept name.Comment: We have added results on description logics with role inclusions and an ExpTime-completeness result for the explicit definability of concept names. The title has been modified by adding role inclusions. This paper has been accepted for AAAA 202

On the Utility of Adding An Abstract Domain and Attribute Paths to SQL

Albeit its popularity today, RDBMS and the relational model still have many limitations. For example, one needs to pay premature attention to naming issues in the schema designing phase; and the syntax for conjunctive queries is verbose and redundant, especially for multi-table joins and composite primary/foreign keys. In this thesis, we introduce and explain the method to handle and resolve these issues that is proposed by Borgida, Toman, and Weddell: the conceptual schema that supports abstract relations and attributes, and an extended query language SQLpath built on top of standard SQL that supports the usage of attribute paths and abstract attributes in queries. We demonstrate a systematic approach to map a database schema expressed in the relational model to the abstract relational model and illustrate how to write SQLpath queries with attribute paths to solve query problems involving complex table joins. This thesis can serve as both an introduction and tutorial to abstract database modelling and the SQLpath query language. Additionally, we performed an empirical experiment to evaluate the performance of SQLpath when solving real database query problems by employing students with prior experience with SQL to read and write SQLpath queries and recorded their accuracy and time consumption against usage of regular SQL. The result of this experiment is presented in this thesis, including a statistical analysis of the results. In short, we uncover evidence that SQLpath is more efficient to use for both reading and writing conjunctive and alike queries, especially for non-trivial cases where multiple constraints were required. However, while SQLpath can hide explicit table joins when writing queries spanning multiple intermediate tables, whether this benefit can make users produce more accurate results still remains unclear as we were not able to draw any conclusion from collected data due to lack of statistical significance