95,862 research outputs found

    A Dichotomic Analysis of the Surprise Examination Paradox

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    This paper proposes a new framework to solve the surprise examination paradox. I survey preliminary the main contributions to the literature related to the paradox. I introduce then a distinction between a monist and a dichotomic analysis of the paradox. With the help of a matrix notation, I also present a dichotomy that leads to distinguish two basically and structurally different notions of surprise, which are respectively based on a conjoint and a disjoint structure. I describe then how Quine's solution and Hall's reduction apply to the version of the paradox corresponding to the conjoint structure. Lastly, I expose a solution to the version of the paradox based on the disjoint structure

    Uncertainty behind the veil of ignorance

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    This paper argues that the decision problem in the original position should be characterized as a decision problem under uncertainty even when it is assumed that the denizens of the original position know that they have an equal chance of ending up in any given individual's place. It argues for this claim by arguing that (a) the continuity axiom of decision theory does not hold between all of the outcomes the denizens of the original position face and that (b) neither us nor the denizens of the original position can know the exact point where discontinuity sets in, because the language we employ in comparing different outcomes is ineradicably vague. It is also argued that the account underlying (b) can help proponents of superiority in value theory defend their view against arguments offered by Norcross and Griffin

    Prototype system for supporting the incremental modelling of vague geometric configurations

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    In this paper the need for Intelligent Computer Aided Design (Int.CAD) to jointly support design and learning assistance is introduced. The paper focuses on presenting and exploring the possibility of realizing learning assistance in Int.CAD by introducing a new concept called Shared Learning. Shared Learning is proposed to empower CAD tools with more useful learning capabilities than that currently available and thereby provide a stronger interaction of learning between a designer and a computer. Controlled computational learning is proposed as a means whereby the Shared Learning concept can be realized. The viability of this new concept is explored by using a system called PERSPECT. PERSPECT is a preliminary numerical design tool aimed at supporting the effective utilization of numerical experiential knowledge in design. After a detailed discussion of PERSPECT's numerical design support, the paper presents the results of an evaluation that focuses on PERSPECT's implementation of controlled computational learning and ability to support a designer's need to learn. The paper then discusses PERSPECT's potential as a tool for supporting the Shared Learning concept by explaining how a designer and PERSPECT can jointly learn. There is still much work to be done before the full potential of Shared Learning can be realized. However, the authors do believe that the concept of Shared Learning may hold the key to truly empowering learning in Int.CAD

    Multi-layered reasoning by means of conceptual fuzzy sets

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    The real world consists of a very large number of instances of events and continuous numeric values. On the other hand, people represent and process their knowledge in terms of abstracted concepts derived from generalization of these instances and numeric values. Logic based paradigms for knowledge representation use symbolic processing both for concept representation and inference. Their underlying assumption is that a concept can be defined precisely. However, as this assumption hardly holds for natural concepts, it follows that symbolic processing cannot deal with such concepts. Thus symbolic processing has essential problems from a practical point of view of applications in the real world. In contrast, fuzzy set theory can be viewed as a stronger and more practical notation than formal, logic based theories because it supports both symbolic processing and numeric processing, connecting the logic based world and the real world. In this paper, we propose multi-layered reasoning by using conceptual fuzzy sets (CFS). The general characteristics of CFS are discussed along with upper layer supervision and context dependent processing

    A unified theory of granularity, vagueness and approximation

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    Abstract: We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this theory provides a general framework within which we can understand the relation between vague terms and concepts and the corresponding crisp portions of reality. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches. Central to our approach is the idea that judgments about reality involve in every case (1) a separation of reality into foreground and background of attention and (2) the feature of granularity. On this basis we attempt to show that even vague judgments made in naturally occurring contexts are not marked by truth-value indeterminacy. We distinguish, in addition to crisp granular partitions, also vague partitions, and reference partitions, and we explain the role of the latter in the context of judgments that involve vagueness. We conclude by showing how reference partitions provide an effective means by which judging subjects are able to temper the vagueness of their judgments by means of approximations

    Typicality, graded membership, and vagueness

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    This paper addresses theoretical problems arising from the vagueness of language terms, and intuitions of the vagueness of the concepts to which they refer. It is argued that the central intuitions of prototype theory are sufficient to account for both typicality phenomena and psychological intuitions about degrees of membership in vaguely defined classes. The first section explains the importance of the relation between degrees of membership and typicality (or goodness of example) in conceptual categorization. The second and third section address arguments advanced by Osherson and Smith (1997), and Kamp and Partee (1995), that the two notions of degree of membership and typicality must relate to fundamentally different aspects of conceptual representations. A version of prototype theory—the Threshold Model—is proposed to counter these arguments and three possible solutions to the problems of logical selfcontradiction and tautology for vague categorizations are outlined. In the final section graded membership is related to the social construction of conceptual boundaries maintained through language use
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