Parameterized abstractions used for proof-planning

In order to cope with large case studies arising from the application of formal methods in an industrial setting, this paper presents new techniques to support hierarchical proof planning. Following the paradigm of difference reduction, proofs are obtained by removing syntactical differences between parts of the formula to be proven step by step. To guide this manipulation we introduce dynamic abstractions of terms. These abstractions are parameterized by the individual goals of the manipulation and are especially designed to ease the proof search based on heuristics. The hierarchical approach and thus the decomposition of the original goal into several subgoals enables the use of different abstractions or different parameters of an abstraction within the proof search. In this paper we will present one of these dynamic abstractions together with heuristics to guide the proof search in the abstract space

HDMS-A und OBSCURE in KORSO : die Funktionale Essenz von HDMS-A aus Sicht der algorithmischen Spezifikationsmethode ; Teil 2: Schablonen zur Übersetzung eines E/R-Schemas in eine OBSCURE Spezifikation

The following report is part of the central case study HDMS-A1 within the German national project KorSo2. This study is dedicated to the development of a complex information system for the support of the patient data administration in the specialized heart disease clinic DHZB3. While the developpers group PMI4 develops the real system for the clinic called HDMS, the project KorSos aim was the rigorous development of an abstracted version of HDMS by exclusive use of pure formal methods. The abstraction refers both to number of modelled documents and depth of treatment, while still considering the relevant aspects in a partly parameterized way

HDMS-A und OBSCURE in KORSO : die Funktionale Essenz von HDMS-A aus Sicht der algorithmischen Spezifikationsmethode ; Teil 2: Schablonen zur Übersetzung eines E/R-Schemas in eine OBSCURE Spezifikation

The following report is part of the central case study HDMS-A1 within the German national project KorSo2. This study is dedicated to the development of a complex information system for the support of the patient data administration in the specialized heart disease clinic DHZB3. While the developpers group PMI4 develops the real system for the clinic called HDMS, the project KorSos aim was the rigorous development of an abstracted version of HDMS by exclusive use of pure formal methods. The abstraction refers both to number of modelled documents and depth of treatment, while still considering the relevant aspects in a partly parameterized way

Computer supported mathematics with Ωmega

AbstractClassical automated theorem proving of today is based on ingenious search techniques to find a proof for a given theorem in very large search spaces—often in the range of several billion clauses. But in spite of many successful attempts to prove even open mathematical problems automatically, their use in everyday mathematical practice is still limited.The shift from search based methods to more abstract planning techniques however opened up a paradigm for mathematical reasoning on a computer and several systems of that kind now employ a mix of interactive, search based as well as proof planning techniques.The Ωmega system is at the core of several related and well-integrated research projects of the Ωmega research group, whose aim is to develop system support for a working mathematician as well as a software engineer when employing formal methods for quality assurance. In particular, Ωmega supports proof development at a human-oriented abstract level of proof granularity. It is a modular system with a central proof data structure and several supplementary subsystems including automated deduction and computer algebra systems. Ωmega has many characteristics in common with systems like NuPrL, CoQ, Hol, Pvs, and Isabelle. However, it differs from these systems with respect to its focus on proof planning and in that respect it is more similar to the proof planning systems Clam and λClam at Edinburgh

An Approach to Assertion Application via Generalised Resolution

In this paper we address assertion retrieval and application in theorem proving systems or proof planning systems for classical first-order logic. Due to Huang the notion of assertion comprises mathematical knowledge such as definitions, theorems, and axioms. We propose a distributed mediator module between a mathematical knowledge base KB and a theorem proving system TP which is independent of the particular proof representation format of TP and which applies generalised resolution in order to analyze the logical consequences of arbitrary assertions for a proof context at hand. Our approach is applicable also to the assumptions which are dynamically created during a proof search process. It therefore realises a crucial first step towards full automation of assertion level reasoning. We discuss the benefits and connection of our approach to proof planning and motivate an application in a project aiming at a tutorial dialogue system for mathematics

Towards Merging PlatΩ and PGIP

AbstractThe PGIP protocol is a standard, abstract interface protocol to connect theorem provers with user interfaces. Interaction in PGIP is based on ASCII-text input and a single focus point-of-control, which indicates a linear position in the input that has been checked thus far. This fits many interactive theorem provers whose interaction model stems from command-line interpreters. PlatΩ, on the other hand, is a system with a new protocol tailored to transparently integrate theorem provers into text editors like that support semi-structured XML input files and multiple foci of attention. In this paper we extend the PGIP protocol and middleware broker to support the functionalities provided by PlatΩ and beyond. More specifically, we extend PGIP (i) to support multiple foci in provers; (ii) to display semi-structured documents; (iii) to combine prover updates with user edits; (iv) to support context-sensitive service menus, and (v) to allow multiple displays. As well as supporting , the extended PGIP protocol in principle can support other editors such as OpenOffice, Word 2007 and graph viewers; we hope it will also provide guidance for extending provers to handle multiple foci

Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

Course generation as a hierarchical task network planning problem

This thesis presents course generation based on Hierarchical Task Network planning (HTN planning). This course generation framework enables the formalization and application of complex and realistic pedagogical knowledge. Compared to previous course generation, this approach generates structured courses that are adapted to a variety of different learning goals and to the learners\u27; competencies. The thesis describes basic techniques for course generation, which are used to formalize seven different types of courses (for instance introducing the learner to previously unknown concepts and supporting him during rehearsal) and several elementary learning goals (e. g., selecting an appropriate example or exercise). The course generator developed in this thesis is service-oriented thus allowing the integration of learning supporting services into the generated course in a generic and pedagogically sensible way. Furthermore, learning environments can access the functionality of the course generator using a Web-service interface. Repositories are treated as services that can register at the course generator and make their content available for course generation. The registration is based on an ontology of instructional objects. Its classes allow categorizing learning objects according to their pedagogical purpose in a more precise way than existing metadata specifications; hence it can be used for intelligent pedagogical functionalities other than course generation. Course generation based on HTN planning is implemented in Paigos and was evaluated by technical, formative and summative evaluations. The technical evaluation primarily investigated the performance to Paigos; the formative and summative evaluations targeted the users\u27; acceptance of Paigos and of the generated courses.Diese Arbeit stellt Kursgenerierung vor, die auf Hierarchical Task Network Planung (HTN Planung) basiert. Der gewählte Rahmen erlaubt die Formalisierung von komplexem und realistischem pädagogischem Wissen und ermöglicht im Vergleich zu bisherigen Techniken die Generierung von strukturierten Kursen, die an eine Vielzahl von Lernzielen angepasst sind. Aufbauend auf allgemeinen Techniken zur Kursgenerierung wird das pädagogische Wissen für sieben verschiedene Kurstypen und für eine Reihe von elementaren Lernzielen formalisiert. Die in dieser Arbeit vorgestellte Kursgenerierung ist service-orientiert. Dadurch steht ein generischer Rahmen zu Verfügung, in dem externe Lernsysteme in die generierten Kurse eingebunden werden und dem Lernenden zur Verfügung gestellt werden können, wenn es pädagogisch sinnvoll ist. Weiterhin können andere Lernsysteme über eine Web-Service Schnittstelle auf die Funktionalitäten des Kursgenerators zugreifen: Datenbanken werden als Services betrachtet, die an dem Kursgenerator registriert werden können, und auf die während der Kurserstellung zugegriffen wird. Die Registrierung verwendet eine Ontologie, die verschiedene instruktionale Typen von Lernobjekten repräsentiert und es erlaubt, Lernobjekte nach ihrem pädagogischen Verwendungszweck zu klassifizieren. Sie geht dabei über existierende Metadatenspezifikationen hinaus und ermöglicht pädagogische komplexe Funktionalitäten, so wie beispielsweise Kursgenerierung und weitere. Die vorgestellte Kursgenerierung ist implementiert in Paigos und wurde durch technische, formative und summative Evaluationen untersucht. Die technische Evaluation analysierte in erster Linie die Performanz von Paigos; die formative und summative Evaluationen widmeten sich der Frage der Akzeptanz und Verständlichkeit der von Paigos erzeugten Kurse aus Benutzersicht