Calendars as Types Data Modeling, Constraint Reasoning, and Type Checking with Calendars Stephanie Spranger Munchen¨ 2005 Calendars as Types Data Modeling, Constraint Reasoning, and Type Checking with Calendars Stephanie Spranger Dissertation an der Fakult¨at fur¨ Mathematik, Informatik und Statistik der Ludwig–Maximilians–Universit¨at Munchen¨ vorgelegt von Stephanie Spranger aus Preetz Munchen,¨ 10. Oktober 2005 Erstgutachter: Prof. Dr. Fran¸cois Bry Zweitgutachter: Prof. Dr. Nachum Dershowitz (Tel Aviv University, Israel) Tag der mundlichen¨ Prufung:¨ 22. November 2005 Acknowledgments This work has been developed during my three-year scholarship from the PhD program “Logics in Computer Science” (GKLI) at the University of Munich, funded by the Ger- man Research Society (DFG). Special thanks are due to Helmut Schwichtenberg who has launched this PhD program. Above all, I thank my supervisor Fran¸coisBry, the head of the research unit “Programming and Modeling Languages” (PMS) at the Institute for Informatics at the University of Munich. Without his confidence in my skills and perseverance on the one hand side and his numerous valuable ideas on the other hand side, surely, this work wouldn’t have been realized. Nachum Dershowitz, many thanks to you for examining this thesis and for supporting me during my work. Your interest in calendars, and in particular, your book on calendric calculations has inspired me for this work. I have to thank the team from PMS for a pleasant working atmosphere. Many colleagues from the research unit PMS, from the PhD program GKLI as well as from the REWERSE project (funded by the European Commission and by the Swiss Federal Office for Educa- tion and Science) gave me a lot of ideas. Thanks in particular to Hans J¨urgen Ohlbach, Bernhard Lorenz, Klaus Schulz, Martin Hofmann, and Emmanuel Coquery. And I have to thank Fran¸coisFages who gave me a hint to easily show completeness of the constraint solver, introduced in this thesis. I thank Arnaud Lallouet for good ideas and an encouraging teamwork in Munich and Orl´eans and Matthias Wagner for his invitation to present this work at DoCoMo Research Labs Europe and the resulting interesting comments and remarks. Furthermore, I thank Jutta Haußer from Japanese studies (“Japan Zentrum”) of the Uni- versity of Munich for an interesting interdisciplinary cooperation; I have learned several things about Japanese time and calendar culture. I have to exceptionally thank the student Frank-Andr´eRieß who has worked with me on this project for a long and fruitful period of time. I want to thank several colleagues from media research (“Institut f¨urKommunikationswis- senschaften”) of the University of Munich for good “lunch-times”. Finally, I thank my family and my friends who have sympathized with me for this work. Munich, 10th October 2005 Stephanie Spranger ii “Le temps passe, et progressivement tout devient vrai ce qu’on a eu de mensonger.” (Marcel Proust, 1871 – 1922, A la recherche du temps perdu, La fugitive) Abstract 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”. Ap- plications 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 surround- ing 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. To- day’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 con- structs (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. Theo- retical aspects of this work are the use of data types to model time and calendar expressions iv Abstract with type checking approaches and constraint solving over different domains referring to such calendric types. Practical aspects of this work are user-friendly language constructs for modeling calendars and calendric data and constraints which can be efficiently pro- cessed. Such specialized language constructs and processing tools for data that refer to a specific domain such as calendars and time are (or will be) important for several Semantic Web applications. Due to use of data types and type checking approaches to temporal and calendric data, the proposed tools can be integrated into any Web language. The thesis shows perspectives for future research on using data types and specific inference algorithms (e.g. constraint solving) for modeling and reasoning on specific theories (e.g. topologies and locational data). Zusammenfassung Untersuchungsgegenstand der Dissertation sind Kalender, Kalender- und Zeitbegriffe und Uhrzeit- und Datumsangaben des t¨aglichen Lebens. Ziel ist die Entwicklung von compu- tergestutzten¨ Werkzeugen zur Modellierung und Verarbeitung solcher Begriffe und Daten, die vor allem im World Wide Web” und insbesondere im Zuge der Internationalisierungs- ” bestrebungen und der Vision des sogenannten Semantic Web” an Bedeutung gewinnen. ” Anwendungsbeispiele sind nicht nur Terminabsprachesysteme und Reisebuchungs- und Pla- nungssysteme in denen Zeitbegriffe wie Sprechstunde”, Konferenz” und verfugbare¨ Ab- ” ” ” flugtermine” auftauchen k¨onnen, sondern auch mobile System – beispielsweise wenn eine Person eine offene Apotheke in ihrer N¨ahe sucht. Wesentliche Eigenschaften, der in sol- chen Anwendungen verwendeten Zeitbegriffe und Uhrzeit- und Datumsangaben, sind He- terogenit¨at und Kontextabh¨angigkeit, wobei sich der Kontext auf kulturelle, berufliche, gesetzliche und/oder ortsgebundene Aspekte beziehen kann. Insbesondere gegenw¨artigen Webformalismen fehlen umfangreiche und geeignete Zeit- und Kalendermodelle und Stra- tegien zur Modellierung und Verarbeitung solcher Begriffe und Daten. Zur Realisierung des in dieser Arbeit formulierten Zieles ist ein programmiersprachen- basierter Ansatz gew¨ahlt worden, der sich wesentlich von bisherigen logikbasierten und algebraischen Ans¨atzen zur Beschreibung und Verarbeitung von Kalender- und Zeitbegrif- fen unterscheidet. Die beiden nachfolgenden Thesen formulieren die Kernidee, die dieser Arbeit zugrundeliegt. 1. Calendar as Type”: Kalenderbegriffe, insbesondere Zeiteinheiten, wie zum Beispiel ” Tag”, Monat” und Jahr” und Zeitbegriffe wie zum Beispiel Sprechstunde” und ” ” ” ” Konferenz” werden nicht logisch oder algebraisch sondern mittels Datentypen mo- ” delliert. Dazu werden dem Benutzer von der entwickelten Sprache deklarative Sprach- konstrukte (sog. Typkonstruktoren) zur Verfugung¨ gestellt. Vorteil dieses Ansatzes sind: benutzerfreundliche Modellierung, Erh¨ohung von Effizienz und Konsistenz, An- notation von Dokumenten und Programmen und Datenabstraktion. 2. Theory Reasoning”: Anfragen wie zum Beispiel Terminabsprachen oder eine Reise- ” planung werden als Constraintproblem formuliert und mittels speziell fur¨ Kalender- und Zeitbegriffe geeignetem Constraintl¨osen uber¨ beliebigen endlichen Kalenderberei- chen (also benutzerdefinierte Datentypen wie Tag” oder Sprechstunde”) beantwor- ” ” tet und nicht wie bei webbasierten ontologischen Ans¨atzen ublich¨ mittels Axiomen. Der Constraintl¨oser bezieht sich dabei auf (benutzerdefinierte) Kalenderdatentypen vi Zusammenfassung wodurch sowohl die Sematik von Kalenderbegriffen wie Tag” oder Sprechstunde” ” ” erhalten als auch die Effizienz des Constraintl¨osers verbessert wird. In der Informatik ist die Arbeit im Bereich des Entwurfs von Modellierungssprachen und Sprachkonstrukten fur¨ Programmiersprachen unter Verwendung von Konzepten und Theorien der Entwicklung von Typsystemen und Constraintprogrammierung einzuordnen. Theoretische Aspekte der Arbeit sind die Verwendung von Datentypen