A representation theorem for finite random scale systems

This paper investigates necessary and sufficient conditions on choice probabilities P_a,B (of picking an element a in an offered set B), for the existence of random variables U_a, satisfying the equation P_a,B = $\text{P}${U_a = max {U_b | b ∈ B}} for all nonempty finite subsets B in a fixed set A, and all a ∈ B. A complete solution to this representation problem is obtained in the case where A is finite. The proof of the representation theorem provides an algorithm to construct the random variables U_a, up to some uniqueness properties. Investigation of these uniqueness properties show that an important part of the ordinal structure of the underlying random variables can be recovered.     

A note on an alternative proof of the representation theorem for bi-semiorder

In a paper written by J. C. Falmagne and the author a representation theorem for what was called a bi-semiorder was given. A quite different proof of this theorem is given here based on Scott's linear technique. This new proof is somewhat simpler than the first one and has the advantage to be an application of a general method well known in measurement theory.     

A representation theorem for languages with generalized quantifiers through back-and-forth methods

We obtain in this paper a representation of the formulae of extensions ofL by generalized quantifiers through functors between categories of first-order structures and partial isomorphisms. The main tool in the proofs is the back-and-forth technique. As a corollary we obtain the Caicedo's version of Fraïssés theorem characterizing elementary equivalence for such languages. We also discuss informally some geometrical interpretations of our results.     

Birkhoff-like sheaf representation for varieties of lattice expansions

Given a variety we study the existence of a class such that S1 every A can be represented as a global subdirect product with factors in and S2 every non-trivial A is globally indecomposable. We show that the following varieties (and its subvarieties) have a class satisfying properties S1 and S2: p-algebras, distributive double p-algebras of a finite range, semisimple varieties of lattice expansions such that the simple members form a universal class (bounded distributive lattices, De Morgan algebras, etc) and arithmetical varieties in which the finitely subdirectly irreducible algebras form a universal class (f-rings, vector groups, Wajsberg algebras, discriminator varieties, Heyting algebras, etc). As an application we obtain results analogous to that of Nachbin saying that if every chain of prime filters of a bounded distributive lattice has at most length 1, then the lattice is Boolean.We wish to thank Lic. Alfredo Guerin and Dr. Daniel Penazzi for helping us with linguistics aspects. We are indebted to the referee for several helpful suggestions. We also wish to thank Professor Mick Adams for providing us with several reprints and useful e-mail information on the subject.Suported by CONICOR and SECyT (UNC).     

The lattice of strengthenings of a strongly finite consequence operation

First, we prove that the lattice of all structural strengthenings of a given strongly finite consequence operation is both atomic and coatomic, it has finitely many atoms and coatoms, each coatom is strongly finite but atoms are not of this kind — we settle this by constructing a suitable counterexample. Second, we deal with the notions of hereditary: algebraicness, strong finitisticity and finite approximability of a strongly finite consequence operation. Third, we formulate some conditions which tell us when the lattice of all structural strengthenings of a given strongly finite consequence operation is finite, and subsequently we give some applications of them.This paper was read at the Third Autumn School on Strongly Finite Sentential Calculi organized by the Section of Logic, Polish Academy of Sciences, Institute of Philosophy and Sociology, in Ustronie (Poland), November 1979.     

Confirmation as partial entailment: A representation theorem in inductive logic

The most prominent research program in inductive logic – here just labeled The Program, for simplicity – relies on probability theory as its main building block and aims at a proper generalization of deductive-logical relations by a theory of partial entailment. We prove a representation theorem by which a class of ordinally equivalent measures of inductive support or confirmation is singled out as providing a uniquely coherent way to work out these two major sources of inspiration of The Program.     

A comparison of regression and standard score discrepancy methods for learning disabilities identification: Effects on racial representation

Learning-disabled (LD) children are often identified for services on the basis of a discrepancy between their IQ and achievement scores. Comparisons between regression and standard score difference methods for determining IQ-achievement discrepancies have not considered the comparative effects of these methods on the racial composition of LD classes. A comparison of these methods shows that the standard score difference method produces disproportionate racial representation, whereas the regression method produces proportionate racial representation in LD classes. In addition, the regression method demonstrates advantages in measurement of discrepancies, LD program planning, and conformity with constitutional guarantees of equal protection under the law.     

A general area theorem for the same-different paradigm

According to a well-known theorem in psychophysics (Green & Swets, 1966), the area under the receiver operating characteristic (ROC) for the yes-no paradigm equals the proportion of correct responses of an unbiased observer in the two-interval, two-alternative, forced choice paradigm (2I2AFC). Here, we demonstrate a similar relationship between the ROC area in the two-interval same-different (AX or 2IAX) paradigm, and the proportion correct in the four-interval same-different (4IAX, also known as dual-pair comparison) paradigm. The theorem demonstrated here is general, in the sense that it does not require that the sensory observations have a specific distribution (e.g., Gaussian), or that they be statistically independent.     

A timid response to the consequence argument

In this paper, I challenge the Consequence Argument for Incompatibilism by arguing that the inference principle it relies upon is not well motivated. The sorts of non-question-begging instances that might be offered in support of it fall short.     

A compactness theorem for linear equations

It is proved that a system of linear equations over an arbitrary field has a solution if every finite subsystem has a solution provided that the set of variables can be well ordered.Presented by J. Zygmunt     

A neuronal model for syllable representation

A speculative neuronal template, equivalent to canonical syllable forms and independent of segmental representations, is offered to help account for (1) the inviolate nature of phonotactic constraints in aphasic speech output, and (2) left hemisphere specialization for speech sound access and output. The model, which attempts to relate plausible neuronal systems to linguistic function, is based on cell assemblies that are thought to develop by way of genetic predisposition and ontogenetic language experience, into configurations that can represent canonical slot positions for the consonants and vowel comprising a syllable. The syllable is assumed to be the basic organizational rhythmic unit for serial concatenation of sublexical segments. A scheme for neurological differentiation of vowels and consonants is offered. Phonotactic constraints can become "hard-wired" to help create the automaticity underlying phonological sound organization. Testable predictions are offered to substantiate the claims of the model.     

A depictive neural model for the representation of motion verbs

In this paper, we present a depictive neural model for the representation of motion verb semantics in neural models of visual awareness. The problem of modelling motion verb representation is shown to be one of function application, mapping a set of given input variables defining the moving object and the path of motion to a defined output outcome in the motion recognition context. The particular function-applicative implementation and consequent recognition model design presented are seen as arising from a noun-adjective recognition model enabling the recognition of colour adjectives as applied to a set of shapes representing objects to be recognised. The presence of such a function application scheme and a separately implemented position identification and path labelling scheme are accordingly shown to be the primitives required to enable the design and construction of a composite depictive motion verb recognition scheme. Extensions to the presented design to enable the representation of transitive verbs are also discussed.     

A metacompleteness theorem for contraction-free relevant logics

I note that the logics of the relevant group most closely tied to the research programme in paraconsistency are those without the contraction postulate(A.AB).AB and its close relatives. As a move towards gaining control of the contraction-free systems I show that they are prime (that wheneverA B is a theorem so is eitherA orB). The proof is an extension of the metavaluational techniques standardly used for analogous results about intuitionist logic or the relevant positive logics.The main results of this paper were presented at the Paraconsistent Logic conference in Canberra in 1980. The author wishes to thank the participants in that conference for comments and suggestions made at the time.     

A characterization theorem for random utility variables

In this note we investigate the condition that the distribution of the maximum of a set of random variables does not depend on which variable attains the maximum. This problem arises in random utility theory. When the random variables are independent, the property implies that all the marginal distributions must be Double Exponential (with distribution function exp(?e^?x) in standard form). When dependence is allowed the property characrerizes a much broader class consisting of arbitrary functions of arbitrary homogeneous functions of the variables e^?xi, a result stated without proof in D. J. Strauss (Journal of Mathematical Psychology, 1979, 20, 35–52). These are the distributions such that the maximum has the same distribution (apart from a location shift) as the marginals, provided the marginals are the same.     

A fixed point theorem for the Weak Kleene valuation scheme

Journal of Philosophical Logic -     

Logical consequence: A defense of Tarski

In his classic 1936 essay “On the Concept of Logical Consequence”, Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. Many of his criticisms are meant to apply to the model-theoretic account as well. In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of the logical properties:

1. Tarski's account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right.
2. Tarski's account cannot be brought into line with the model-theoretic account, because the two are fundamentally incompatible.
3. There are simple counterexamples (enumerated by Etchemendy) which show that Tarski's account is wrong.
4. Tarski committed a modal fallacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account.
5. Tarski's account depends on there being a distinction between the “logical terms” and the “non-logical terms” of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made. Etchemendy's critique raises historical and philosophical questions about important foundational work. However, Etchemendy is mistaken about each of these central criticisms. In the course of justifying that claim, I give a sustained explication and defense of Tarski's account. Moreover, since I will argue that Tarski's account and the model-theoretic account really do come to the same thing, my subsequent defense of Tarski's account against Etchemendy's other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties.

     

A graphical representation of the mediated effect

Mediation analysis is widely used in the social sciences. Despite the popularity of mediation models, few researchers have used graphical methods, other than structural path diagrams, to represent their models. Plots of the mediated effect can help a researcher better understand the results of the analysis and convey these results to others. This article presents a method for creating and interpreting plots of the mediated effect for a variety of mediation models, including models with (1) a dichotomous independent variable, (2) a continuous independent variable, and (3) an interaction between an independent variable and the mediating variable. An empirical example is then presented to illustrate these plots. Sample code for creating plots of the mediated effect in R and SAS is also included, and may be downloaded from www.psychonomic.org/archive.     

Attentional selection: A salience-based competition for representation

The role of salience in localized attentional interference (LAI) was examined. In two experiments, target discrimination performance was measured as a function of the spatial separation between the target and a salient distractor item. In Experiment 1, both the salience of the distractor and that of a target were manipulated. Distractor salience was manipulated via size changes to the distractor, and target salience was manipulated by using unmasked or onset targets. When the target was of low salience, the magnitude of interference from the distractor increased with distractor salience. However, when the target had an abrupt onset, the distractor had no impact on target performance. In Experiment 2, the attentional salience of the distractor was manipulated using a probability manipulation. Displays contained both a target and a color singleton distractor. The color singleton produced LAI when it was predictive of the target location but not when it was unpredictive of the target location. The results of both experiments are consistent with models of competition-based attentional selection.