Calendars as types: data modeling, constraint reasoning, and type checking with calendars

This thesis investigates real-life calendars, calendar and time expressions, and time and date formats. The thesis aims at the development of computer-based tools for modeling and processing such calendric data, primarily in the “World Wide Web”, in particular regarding today’s internationalization efforts and the vision of the “Semantic Web”. Applications are not only appointment scheduling problems and travel planning referring to calendar expressions like “consultation hour”, “meeting”, or “available departure times” but also mobile applications: a mobile application listing pharmacies in the surrounding of a (mobile) user will preferably only mention those that are currently open. The temporal and calendric data used in such applications is inherently heterogeneous and context-dependent, referring to cultural, professional, legal, and/or locational aspects. Today’s Web formalisms lack appropriate and specific tools for temporal and calendric data modeling and for efficiently processing such data. To realize the goal mentioned above, I have chosen a programming language approach to time and calendars that essentially differs from logic-based and algebraic approaches. The thesis underlying this work is twofold: 1. “Calendar as Type”: time and calendar expressions such as “day”, month”, “year”, “consultation hour”, and “meeting” are not modeled in a logic or an algebra but, instead, by means of data types. The user is provided with a set of language constructs (so-called type constructors). Advantages of this approach are: user-friendly modeling, increase of efficiency and consistency, program and document annotation, and abstraction. 2. “Theory Reasoning”: Problems such as appointment scheduling or travel planning are formulated in the environment of a constraint solver specific to arbitrary calendar domains (i.e. user-defined data types like “day” or “consultation hour”) rather than by axiomatization, commonly used with approaches based on ontology modeling and reasoning. The constraint solver refers to and relies on (user-defined) calendric types, it maintains the semantics of different calendric types like “day” and “consultation hour”, and it allows for efficient constraint solving with arbitrary calendric data. Concerning Computer Science, this work is related to research in the area of modeling language design and design of language constructs for programming languages based on concepts and theories from research on type systems and constraint programming. Theoretical aspects of this work are the use of data types to model time and calendar expressions