Exactly What Happens After the Anscombe-Aumann Race? Representing Preferences in Vague Environments

This paper derives a representation of preferences for a choice theory with vague environments; vague in the sense that the agent does not know the precise lotteries over outcomes conditional on states. Instead, he knows only a possible set of these lotteries for each state. Thus, this paper's main departure from the standard subjective expected utility model is to relax an assumption about the environment, rather than weakening the axiomatic structure. My model is consistent with the behavior observed in the Ellsberg experiment. It can capture the same type of behavior as the multiple priors models, but can also result in behavior that is different from both the behavior implied by standard subjective expected utility models and the behavior implied by the multiple priors models.Decision Theory, Vagueness, Utility, Optimism

Vagueness, Logic and Use: Four Experimental Studies on Vagueness

Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is Bonini et al. (1999), who report empirical results on the use of vague predicates by Italian speakers, and take the results to count in favor of epistemicism. Yet several methodological difficulties mar their experiments; we outline these problems and devise revised experiments that do not show the same results. We then describe three additional empirical studies that investigate further claims in the literature on vagueness: the hypothesis that speakers confuse ‘P’ with ‘definitely P’, the relative persuasiveness of different formulations of the inductive premise of the Sorites, and the interaction of vague predicates with three different forms of negatio

On the Borders of Vagueness and the Vagueness of Borders

This article argues that resolutions to the sorites paradox offered by epistemic and supervaluation theories fail to adequately account for vagueness. After explaining the paradox, I examine the epistemic theory defended by Timothy Williamson and discuss objections to his semantic argument for vague terms having precise boundaries. I then consider Rosanna Keefe's supervaluationist approach and explain why it fails to accommodate the problem of higher-order vagueness. I conclude by discussing how fuzzy logic may hold the key to resolving the sorites paradox without positing indefensible borders to the correct application of vague terms

Evaluational adjectives

This paper demarcates a theoretically interesting class of "evaluational adjectives." This class includes predicates expressing various kinds of normative and epistemic evaluation, such as predicates of personal taste, aesthetic adjectives, moral adjectives, and epistemic adjectives, among others. Evaluational adjectives are distinguished, empirically, in exhibiting phenomena such as discourse-oriented use, felicitous embedding under the attitude verb `find', and sorites-susceptibility in the comparative form. A unified degree-based semantics is developed: What distinguishes evaluational adjectives, semantically, is that they denote context-dependent measure functions ("evaluational perspectives")—context-dependent mappings to degrees of taste, beauty, probability, etc., depending on the adjective. This perspective-sensitivity characterizing the class of evaluational adjectives cannot be assimilated to vagueness, sensitivity to an experiencer argument, or multidimensionality; and it cannot be demarcated in terms of pretheoretic notions of subjectivity, common in the literature. I propose that certain diagnostics for "subjective" expressions be analyzed instead in terms of a precisely specified kind of discourse-oriented use of context-sensitive language. I close by applying the account to `find x PRED' ascriptions

Shape matching and clustering in design

Generalising knowledge and matching patterns is a basic human trait in re-using past experiences. We often cluster (group) knowledge of similar attributes as a process of learning and or aid to manage the complexity and re-use of experiential knowledge [1, 2]. In conceptual design, an ill-defined shape may be recognised as more than one type. Resulting in shapes possibly being classified differently when different criteria are applied. This paper outlines the work being carried out to develop a new technique for shape clustering. It highlights the current methods for analysing shapes found in computer aided sketching systems, before a method is proposed that addresses shape clustering and pattern matching. Clustering for vague geometric models and multiple viewpoint support are explored