In Praise of Impredicativity: A Contribution to the Formalization of Meta-Programming

Processing programs as data is one of the successes of functional and logic programming. Higher-order functions, as program-processing programs are called in functional programming, and meta-programs, as they are called in logic programming, are widespread declarative programming techniques. In logic programming, there is a gap between the meta-programming practice and its theory: The formalizations of meta-programming do not explicitly address its impredicativity and are not fully adequate. This article aims at overcoming this unsatisfactory situation by discussing the relevance of impredicativity to meta-programming, by revisiting former formalizations of meta-programming, and by defining Reflective Predicate Logic, a conservative extension of first-order logic, which provides a simple formalization of meta-programming

Bottom-up evaluation of HiLog in the context of deductive database systems

Bibliography: leaves 127-130.HiLog is a logic-based language which boasts the expressiveness of a higher-order syntax while retaining the simplicity of a first-order semantics. This work examines the suitability of Horn-clause HiLog as a query language for deductive databases by investigating the feasibility of adapting well-established Datalog evaluation algorithms for the evaluation of HiLog programs. Each of the evaluation algorithms examined in the work is formally described and verified in terms of completeness and correctness. Furthermore, a practical HiLog evaluator based on each algorithm verifies the feasibility of its implementation in a real-world context. It is demonstrated that the Datalog evaluation algorithms do indeed have realistic HiLog analogs. The work also compares the performance of these analogs

Design and foundations of ontologies with meta-modelling.

Ontologies are broadly used and proved modelling artifacts to conceptualize a domain. In particular the W3C standard ontology language OWL, based on description logics, allows the ontology engineer to formally represent a domain as a set of assertions about concepts, individuals and roles. Nowadays, complex applications leads to combine autonomously built ontologies into ontology networks by relating them through di erent kind of relations. Some relations, such as the mapping of two concepts from di erent ontologies, can be expressed by the standard ontology language OWL, i.e. by the description logics behind it. However, there are other kind of relations that are not soundly represented by OWL, such as the meta-modelling relation. The meta-modelling relation has to do with the modelling of the same real object with di erent abstraction levels, e.g. as a concept in one ontology and as an individual in another ontology. Even though there are a set of approaches that extend description logics to deal with meta-modelling, they do not solve relevant requirements of some real scenarios. The present thesis work introduces an extension to the description logic SHIQ which provides a exible syntax and a strong semantics, and moreover ensures the well-foundedness of the interpretation domain. This approach is di erent from existing meta-modelling approaches either in the syntax or in the semantics (or both), and moreover ensures the well-foundedness of the domain which is an original contribution from the theoretical point of view. The meta-modelling extension of SHIQ introduced in the present work is justi ed by a detailed description of a set of real case studies, with an analysis of the bene ts of the new approach to solve some relevant requirements. Finally, the present work addresses the methodological issue by introducing a design pattern to help the ontology engineer in the use of the proposed meta-modelling approach