A Proof-Planning Framework with explicit Abstractions based on Indexed Formulas

A major motivation of proof-planning is to bridge the gap between high-level, cognitively adequate reasoning for specific domains, and calculus-level reasoning to ensure soundness. For high reasoning levels the cognitive adequacy of representation and reasoning techniques is a major issue, while for lower reasoning levels the adequacy wrt. the modelled domain is important. Furthermore, proof construction is an engineering task and there is a need to support the design and application of proof-search engineering methods. To this end we present a framework to explicitly support different reasoning levels. To structure reasoning levels the framework allows for an explicit representation of abstractions and proof-search refinement techniques. In order to ensure soundness within a reasoning level, we use techniques developed in the context of matrix characterisation relying on the notion of indexed formulas. Furthermore, we introduce a uniform concept for contextual reasoning, and sketch basic tacticals for the definition of tactics to organise the overall proof-search inside and across different reasoning levels.     

Cooperation of categorical and behavioral learning in a practical solution to the abstraction problem

Real robots should be able to adapt autonomously to various environments in order to go on executing their tasks without breaking down. They achieve this by learning how to abstract only useful information from a huge amount of information in the environment while executing their tasks. This paper proposes a new architecture which performs categorical learning and behavioral learning in parallel with task execution. We call the architectureSituation Transition Network System (STNS). In categorical learning, it makes a flexible state representation and modifies it according to the results of behaviors. Behavioral learning is reinforcement learning on the state representation. Simulation results have shown that this architecture is able to learn efficiently and adapt to unexpected changes of the environment autonomously. Atsushi Ueno, Ph.D.: He is a research associate in the Artificial Intelligence Laboratory at the Graduate School of Information Science at the Nara Institute of Science and Technology (NAIST). He received the B.E., the M.E., and the Ph.D. degrees in aeronautics and astronautics from the University of Tokyo in 1991, 1993, and 1997 respectively. His research interest is robot learning and autonomous systems. He is a member of Japan Association for Artificial Intelligence (JSAI). Hideaki Takeda, Ph.D.: He is an associate professor in the Artificial Intelligence Laboratory at the Graduate School of Information Science at the Nara Institute of Science and Technology (NAIST). He received his Ph.D. in precision machinery engineering from the University of Tokyo in 1991. He has conducted research on a theory of intelligent computer-aided design systems, in particular experimental study and logical formalization of engineering design. He is also interested in multiagent architectures and ontologies for knowledge base systems.     

Mutation Testing in the Refinement Calculus

This article discusses mutation testing strategies in the context of refinement. Here, a novel generalisation of mutation testing techniques is presented to be applied to contracts ranging from formal specifications to programs. It is demonstrated that refinement and its dual abstraction are the key notions leading to a precise and yet simple theory of mutation testing. The refinement calculus of Back and von Wright is used to express concepts like contracts, useful mutations, test cases and test coverage.     

Reusable abstractions for modeling languages

Model-driven engineering proposes the use of models to describe the relevant aspects of the system to be built and synthesize the final application from them. Models are normally described using Domain-Specific Modeling Languages (DSMLs), which provide primitives and constructs of the domain. Still, the increasing complexity of systems has raised the need for abstraction techniques able to produce simpler versions of the models while retaining some properties of interest. The problem is that developing such abstractions for each DSML from scratch is time and resource consuming.     

Knowledge-based temporal interpolation

Temporal interpolation is the task of bridging gaps between time-oriented concepts in a context-sensitive manner. It is a subtask important for solving the temporal-abstraction task-abstraction of interval-based, higher-level concepts from time-stamped data. We present a knowledge-based approach to the temporal-interpolation task and discuss in detail the precise knowledge required by that approach, its theoretical foundations, and the implications of the approach. The temporal-interpolation computational mechanism we discuss relies, among other knowledge types, on a temporal-persistence model. The temporal-persistence model employs local temporal-persistence functions that are temporally bidirectional (i.e. extend a belief measure in a predicate both into the future and into the past) and global, maximal-gap temporal-persistence functions that bridge gaps between interval-based predicates. We investigate the quantitative and qualitative properties implied by both types of persistence functions. We have implemented our approach in the RÉSUMÉ program and evaluated it in several different medical and engineering domains. We discuss the implications of our conceptual and computational methodology for acquisition, maintenance, reuse, and sharing of temporal-abstraction knowledge.     

培养学生学习和运用数学知识的能力

本文从符号性、规范性、严密性、抽象性四个方面阐述了高等数学的特点。并针对学生学习高等数学所遇到的问题和数学自身的规律性,笔者提出了几种解决的办法:注意数学语言训练、注意运算方法的分类归纳、教学中强调数学来源于实践应用于实践。     

Abstractions of data types

The use of abstraction in the context of abstract data types, is investigated. Properties to be checked are formulas in a first order logic under Kleene's 3-valued interpretation. Abstractions are defined as pairs consisting of a congruence and a predicate interpretation. Three types of abstractions are considered,∀∀, ∀∃ and ∃^0,1∀, and for each of them corresponding property preservation results are established. An abstraction refinement property is also obtained. It shows how one can pass from an existing abstraction to a (less) finer one. Finally, equationally specified abstractions in the context of equationally specified abstract data types are discussed and exemplified.On leave from the Department of Computer Science, “Al. I. Cuza” University, Iaşi 740083, RomaniaThe research reported in this paper was partially supported by the program ECO-NET 08112WJ/2004-2005 and by the National University Research Council of Romania, grants CNCSIS 632(28)/2004 and CNCSIS 632(50)/2005.     

Abstraction paradigms for computer graphics

In computer graphics we use techniques from different areas of mathematics. Mathematical models are used to simulate real-world objects, as well as natural phenomena. In order to understand these models and pose relevant problems in each particular field of this area, it is important to create levels of abstraction. These levels encapsulate common properties of the different models and allow us to have a global, conceptual view of the methods and techniques in each field. In this paper we study a paradigm for creating abstraction levels that can also be used to characterize more general problems in computational applied mathematics. We apply this paradigm to different areas of computer graphics: modeling, animation, illumination, color theory, image processing and human-computer interface.