A unified theory of granularity, vagueness and approximation

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

Disagreement dissected : vagueness as a source of ambiguity in nominal (co-)reference

Using a qualitative analysis of disagreements from a referentially annotated newspaper corpus, we show that, in coreference annotation, vague referents are prone to greater disagreement. We show how potentially problematic cases can be dealt with in a way that is practical even for larger-scale annotation, considering a real-world example from newspaper text

Multiple actualities and ontically vague identity

Gareth Evans's argument against ontically vague identity has been picked over on many occasions. But extant proposals for blocking the argument do not meet well-motivated general constraints on a successful solution. Moreover, the pivotal position that defending ontically vague identity occupies vis a vis ontic vagueness more generally has not yet been fully appreciated. This paper advocates a way of resisting the Evans argument meeting all the mentioned constraints: if we can find referential indeterminacy in virtue of ontic vagueness, we can get out of the Evans argument while still preserving genuinely ontically vague identity. To show how this approach can vindicate particular cases of ontically vague identity, I develop a framework for describing ontic vagueness in general in terms of multiple actualities. The effect, overall, is to provide a principled and attractive approach to ontically vague identity that is immune from Evansian worries

Vagueness and referential ambiguity in a large-scale annotated corpus

In this paper, we argue that difficulties in the definition of coreference itself contribute to lower inter-annotator agreement in certain cases. Data from a large referentially annotated corpus serves to corroborate this point, using a quantitative investigation to assess which effects or problems are likely to be the most prominent. Several examples where such problems occur are discussed in more detail, and we then propose a generalisation of Poesio, Reyle and Stevenson’s Justified Sloppiness Hypothesis to provide a unified model for these cases of disagreement and argue that a deeper understanding of the phenomena involved allows to tackle problematic cases in a more principled fashion than would be possible using only pre-theoretic intuitions

The interactional work of configuring a mathematical object in a technology-enabled embodied learning environment

We present a detailed account of interactional mechanisms that support participation in STEM disciplinary practices as an adult and a child explore a technology-enabled embodied learning environment for mathematics. Drawing on ethnomethodological studies of technologyrich workplaces, we trace the process of transforming a vague reference into a mutually available mathematical object: a covariant variable. Our analysis reveals that this mathematical object is an interactional achievement, configured via a reciprocal process of instructing one another's attention. In particular, we demonstrate how participants' explicit responsiveness to indexical and multimodal resources achieves this object

Imperfect identity

Questions of identity over time are often hard to answer. A long tradition has it that such questions are somehow soft: they have no unique, determinate answer, and disagreements about them are merely verbal. I argue that this claim is not the truism it is taken to be. Depending on how it is understood, it turns out either to be false or to presuppose a highly contentious metaphysical claim

Rough Set Theory for Real Estate Appraisal: An Application to Directional District of Naples

This paper proposes an application of Rough Set Theory (RST) to the real estate field, in order to highlight its operational potentialities for mass appraisal purposes. RST allows one to solve the appraisal of real estate units regardless of the deterministic relationship between characteristics that contribute to the formation of the property market price and the same real estate prices. RST was applied to a real estate sample (office units located in Directional District of Naples) and was also integrated with a functional extension so-called Valued Tolerance Relation (VTR) in order to improve its flexibility. A multiple regression analysis (MRA) was developed on the same real estate sample with the aim to compare RST and MRA results. The case study is followed by a brief discussion on basic theoretical connotations of this methodology