Investigating Reliabilities of Intraindividual Variability Indicators

Reliabilities of the two most widely used intraindividual variability indicators, ISD ² and ISD, are derived analytically. Both are functions of the sizes of the first and second moments of true intraindividual variability, the size of the measurement error variance, and the number of assessments within a burst. For comparison, the reliability of the intraindividual mean, , is also derived. Simulations are conducted to confirm accuracy of the derived functions. The influences of different factors on the reliabilities of these indicators are also studied. Results show that the reliabilities of ISD ² and ISD are lower than the reliability of in all studied conditions and the reliability of ISD is lower than that of ISD ² in most studied conditions. The derived functions are applied to calculate the reliabilities of intraindividual variability indicators of negative affect measured over 56 days and perceptual-motor performance measured over five assessments. Implications for measurement-burst study designs are discussed.     

Inferential Intensionality

The paper is a study of properties of quasi-consequence operation which is a key notion of the so-called inferential approach in the theory of sentential calculi established in [5]. The principal motivation behind the quasi-consequence, q-consequence for short, stems from the mathematical practice which treats some auxiliary assumptions as mere hypotheses rather than axioms and their further occurrence in place of conclusions may be justified or not. The main semantic feature of the q-consequence reflecting the idea is that its rules lead from the non-rejected assumptions to the accepted conclusions.First, we focus on the syntactic features of the framework and present the q-consequence as related to the notion of proof. Such a presentation uncovers the reasons for which the adjective inferential is used to characterize the approach and, possibly, the term inference operation replaces q-consequence. It also shows that the inferential approach is a generalisation of the Tarski setting and, therefore, it may potentially absorb several concepts from the theory of sentential calculi, cf. [10]. However, as some concrete applications show, see e.g.[4], the new approach opens perspectives for further exploration.The main part of the paper is devoted to some notions absent, in Tarski approach. We show that for a given q-consequence operation W instead of one W-equivalence established by the properties of W we may consider two congruence relations. For one of them the current name is kept preserved and for the other the term W-equality is adopted. While the two relations coincide for any W which is a consequence operation, for an arbitrary W the inferential equality and the inferential equivalence may differ. Further to this we introduce the concepts of inferential extensionality and intensionality for q-consequence operations and connectives. Some general results obtained in Section 2 sufficiently confirm the importance of these notions. To complete a view, in Section 4 we apply the new intensionality-extensionality distinction to inferential extensions of a version of the ukasiewicz four valued modal logic.     

Completeness and Decidability Results for Some Propositional Modal Logics Containing “Actually” Operators

The addition of actually operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing actually operators has concentrated entirely upon extensions of KT5 and has employed a particular model-theoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing actually operators, the weakest of which are conservative extensions of K, using a novel generalisation of the standard semantics.     

Remarks on Gregory's “Actually” Operator

In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing actually operators, Journal of Philosophical Logic 30(1): 57–78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an actually operator with the work of Arthur Prior now known under the name of hybrid logic. This analysis relates the actually axioms to standard hybrid axioms, yields the decidability results in [8], and provides a number of complexity results. Finally, we use a bisimulation argument to show that the hybrid language is strictly more expressive than Gregory's language.     

Bounded contraction and Gentzen-style formulation of Łukasiewicz logics

In this paper, we consider multiplicative-additive fragments of affine propositional classical linear logic extended with n-contraction. To be specific, n-contraction (n 2) is a version of the contraction rule where (n+ 1) occurrences of a formula may be contracted to n occurrences. We show that expansions of the linear models for (n + 1)- valued ukasiewicz logic are models for the multiplicative-additive classical linear logic, its affine version and their extensions with n-contraction. We prove the finite axiomatizability for the classes of finite models, as well as for the class of infinite linear models based on the set of rational numbers in the interval [0, 1]. The axiomatizations obtained in a Gentzen-style formulation are equivalent to finite and infinite-valued ukasiewicz logics.Presented by Jan Zygmunt     

Free Łukasiewicz and Hoop Residuation Algebras

Hoop residuation algebras are the {, 1}-subreducts of hoops; they include Hilbert algebras and the {, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated free algebras in varieties of k-potent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown that the free algebra on n generators in any of these varieties can be represented as a union of n subalgebras, each of which is a copy of the {, 1}-reduct of the same finite MV-algebra, i.e., of the same finite product of linearly ordered (simple) algebras. The cardinality of the product can be determined in principle, and an inclusion-exclusion type argument yields the cardinality of the free algebra. The methods are illustrated by applying them to various cases, both known (varieties generated by a finite linearly ordered Hilbert algebra) and new (residuation reducts of MV-algebras and of hoops).     

Choice and Logic

There is a little known paradox the solution to which is a guide to a much more thoroughgoing solution to a whole range of classic paradoxes. This is shown in this paper with respect to Berrys Paradox, Heterologicality, Russells Paradox, and the Paradox of Predication, also the Liar and the Strengthened Liar, using primarily the epsilon calculus. The solutions, however, show not only that the first-order predicate calculus derived from Frege is inadequate as a basis for a clear science, and should be replaced with Hilbert and Bernays conservative extension. Standard second-order logic, and quantified propositional logic also must be substantially modified, to incorporate, in the first place, nominalizations of predicates, and whole sentences. And further modifications must be made, so as to insist that predicates are parts of sentences rather than forms of them, and that truth is a property of propositions rather than their sentential expressions. In all, a thorough reworking of what has been called logic in recent years must be undertaken, to make it more fit for use.Portions of this paper have previously been published in Logical Studies, vol. 9, http://www.logic.ru/LogStud/09/No9-06.html, and the Australasian Journal of Logic, vol. 2, http://www.philosophy.unimelb.edu.au/ajl/2004/2004_4.pdf.     

Treating the “Wise Baby”

In a previous examination of Ferenczis concept of the Wise Baby (1996), I had noted both its applications and its limitations in the analytic treatment of an unusually intelligent adult. Ferenczis concepts of the origin of intellect in trauma and of the wise baby have often left the indistinct impression of being interrelated phenomena. In this paper, I regard as arguable the notion that very high intelligence is pathological when it is precocious. This return visit to the territory of the wise baby extends Ferenczis ideas about the origin and use of the intellect to include a consideration of what may constitute effective treatment for those who suffer from giftedness.Judith E. Vida, M.D. edits On the Arts for this journal. She is a Founding Member and Faculty of the Institute of Contemporary Psychoanalysis in Los Angeles, CA, a member of both American and International Psychoanalytic Associations, and of the Sándor Ferenczi Society of Budapest. Her private practice is in Pasadena, CA.Address correspondence to Judith E. Vida, 301 S. Fair Oaks Ave., Suite 406A, Pasadena, CA 91105, USA; e-mail: jvida@spence.net