Prior distributions on symmetric groups

Fully and partially ranked data arise in a variety of contexts. From a Bayesian perspective, attention has focused on distance-based models; in particular, the Mallows model and extensions thereof. In this paper, a class of prior distributions, the Binary Tree, is developed on the symmetric group. The attractive features of the class are: it provides a closed-form solution to the posterior distribution; and a simple way to interpret the parameters of the prior distribution. The advantages of the proposed method are illustrated by comparing it to metric-based models using data analyzed by other researchers in this context.This revised article was published online in August 2005 with the PDF paginated correctly.     

Combining speed and accuracy to assess error-free cognitive processes

Both the speed and accuracy of responding are important measures of performance. A well-known interpretive difficulty is that participants may differ in their strategy, trading speed for accuracy, with no change in underlying competence. Another difficulty arises when participants respond slowly and inaccurately (rather than quickly but inaccurately), e.g., due to a lapse of attention. We introduce an approach that combines response time and accuracy information and addresses both situations. The modeling framework assumes two latent competing processes. The first, the error-free process, always produces correct responses. The second, the guessing process, results in all observed errors and some of the correct responses (but does so via non-specific processes, e.g., guessing in compliance with instructions to respond on each trial). Inferential summaries of the speed of the error-free process provide a principled assessment of cognitive performance reducing the influences of both fast and slow guesses. Likelihood analysis is discussed for the basic model and extensions. The approach is applied to a data set on response times in a working memory test. The authors wish to thank Roger Ratcliff, Christopher Chabris, and three anonymous referees for their helpful comments, and Aureliu Lavric for providing the data analyzed in this paper.     

On the Exclusivity Implicature of ‘Or’ or on the Meaning of Eating Strawberries

This paper is a contribution to the program of constructing formal representations of pragmatic aspects of human reasoning. We propose a formalization within the framework of Adaptive Logics of the exclusivity implicature governing the connective ‘or’.Keywords: exclusivity implicature, Adaptive Logics.     

On Finite Models of the Lambek Calculus

We study a class of finite models for the Lambek Calculus with additive conjunction and with and without empty antecedents. The class of models enables us to prove the finite model property for each of the above systems, and for some axiomatic extensions of them. This work strengthens the results of [3] where only product-free fragments of these systems are considered. A characteristic feature of this approach is that we do not rely on cut elimination in opposition to e.g. [5], [9].     

Frames and MV-algebras

We describe a class of MV-algebras which is a natural generalization of the class of “algebras of continuous functions”. More specifically, we're interested in the algebra of frame maps Hom (Ω(A), K) in the category T of frames, where A is a topological MV-algebra, Ω(A) the lattice of open sets of A, and K an arbitrary frame. Given a topological space X and a topological MV-algebra A, we have the algebra C (X, A) of continuous functions from X to A. We can look at this from a frame point of view. Among others we have the result: if K is spatial, then C(pt(K), A), pt(K) the points of K, embeds into Hom (Ω(A), K) analogous to the case of C (X, A) embedding into Hom (Ω(A), Ω (X)). 1991 Mathematics Subject Classification: 06F20, 06F25, 06D30 Presented by Ewa Orlowska     

Under Carnap’s Lamp: Flat Pre-semantics

“Flat pre-semantics” lets each parameter of truth (etc.) be considered sepa-rately and equally, and without worrying about grammatical complications. This allows one to become a little clearer on a variety of philosophical-logical points, such as the use fulness of Carnapian tolerance and the deep relativity of truth. A more definite result of thinking in terms of flat pre-semantics lies in the articulation of some instructive ways of categorizing operations on meanings in purely logical terms in relation to various parame- ters of truth (etc.); namely, closing vs. leaving open, local vs. translocal, and anchored vs. unanchored. Basic relations among these categories are established.     

Shared Being,Old Promises,and the Just Necessity of Affirmative Action

Although the residues of official segregation are widespread, affirmative action continues to meet resistance in both official and everyday life, even in such recent Supreme Court decisions as Grutter v Bollinger (539 U.S. 306). This is due in part to a governing ontology that draws the line between individual and collective. But there are other possibilities for conceiving the social, and I offer one here in a theory of affirmative action that is developed through close examination of sharing and promising as elemental qualities of equitable communal life. The nature and value of these actions are demonstrated in narrative formulations of fairness as exemplified in triage and the situation at the end of slavery; of the difference between equality and equity and how justice depends on their conjunction; and finally of theorizing how these may come together in the permutable, opaque, yet resilient interdependence of person and community that represents most deeply the Greek idea of two in one, that is, of one two, not two ones. In these respects the paper is successful insofar as it discloses the kinds of reasoning that underlie both resistance and commitment to affirmative action.     

Power,Freedom, and Individuality: Foucault and Sexual Difference

This paper offers a detailed account of Foucaults ethical and political notion of individuality as presented in his late work, and discusses its relationship to the feminist project of the theory of sexual difference. I argue that Foucaults elaboration of the classical ethos of care for the self opens the way for regarding the I-woman as an ethical, political and aesthetic self-creation. However, it has significant limitations that cannot be ignored. I elaborate on two aspects of Foucaults avoidance of sexual difference as a relevant category for an account of political and ethical individuality, which thus implicitly associates individual agency with men. I argue that Foucault implicitly assumes the existence of an ontological desire to become engaged in political self-creation. However, the ethical position of self-knowledge and desire should be understood as a contingent option that depends on material and historical conditions for its realization. Hence, I argue that a feminist reworking of Foucaults notion of political individuality should add a substantial ethical condition to the imperative of self-knowledge and self-creation – making possible the desiring woman subject.