Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial Intelligence and Symbolic Computation AISC 201

Context-adaptive learning designs by using semantic web services

IMS Learning Design (IMS-LD) is a promising technology aimed at supporting learning processes. IMS-LD packages contain the learning process metadata as well as the learning resources. However, the allocation of resources - whether data or services - within the learning design is done manually at design-time on the basis of the subjective appraisals of a learning designer. Since the actual learning context is known at runtime only, IMS-LD applications cannot adapt to a specific context or learner. Therefore, the reusability is limited and high development costs have to be taken into account to support a variety of contexts. To overcome these issues, we propose a highly dynamic approach based on Semantic Web Services (SWS) technology. Our aim is moving from the current data- and metadata-based to a context-adaptive service-orientated paradigm We introduce semantic descriptions of a learning process in terms of user objectives (learning goals) to abstract from any specific metadata standards and used learning resources. At runtime, learning goals are accomplished by automatically selecting and invoking the services that fit the actual user needs and process contexts. As a result, we obtain a dynamic adaptation to different contexts at runtime. Semantic mappings from our standard-independent process models will enable the automatic development of versatile, reusable IMS-LD applications as well as the reusability across multiple metadata standards. To illustrate our approach, we describe a prototype application based on our principles

ATP and Presentation Service for Mizar Formalizations

This paper describes the Automated Reasoning for Mizar (MizAR) service, which integrates several automated reasoning, artificial intelligence, and presentation tools with Mizar and its authoring environment. The service provides ATP assistance to Mizar authors in finding and explaining proofs, and offers generation of Mizar problems as challenges to ATP systems. The service is based on a sound translation from the Mizar language to that of first-order ATP systems, and relies on the recent progress in application of ATP systems in large theories containing tens of thousands of available facts. We present the main features of MizAR services, followed by an account of initial experiments in finding proofs with the ATP assistance. Our initial experience indicates that the tool offers substantial help in exploring the Mizar library and in preparing new Mizar articles

Change Impact Analysis based on Formalization of Trace Relations for Requirements

Evolving customer needs is one of the driving factors in software development. There is a need to analyze the impact of requirement changes in order to determine possible conflicts and design alternatives influenced by these changes. The analysis of the impact of requirement changes on related requirements can be based on requirements traceability. In this paper, we propose a requirements metamodel with well defined types of requirements relations. This metamodel represents the common concepts extracted from some prevalent requirements engineering approaches. The requirements relations in the metamodel are used to trace related requirements for change impact analysis. We formalize the relations. Based on this formalization, we define change impact rules for requirements. As a case study, we apply these rules to changes in the requirements specification for Course Management System