Equivalents of Mingle and Positive Paradox

Relevant logic is a proper subset of classical logic. It does not include among its theorems any ofpositive paradox A (B A)mingle A (A A)linear order (A B) (B A)unrelated extremes (A ) (B B¯)This article shows that those four formulas have different effects when added to relevant logic, and then lists many formulas that have the same effect as positive paradox or mingle.     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

Axiomatization of the De Morgan type rules

In Section 1 we show that the De Morgan type rules (= sequential rules in L(, ) which remain correct if and are interchanged) are finitely based. Section 2 contains a similar result for L(). These results are essentially based on special properties of some equational theories.     

Intuitionistic uniformity principles for propositions and some applications

This note deals with the prepositional uniformity principlep-UP: p x N A (p, x) x N p A (p, x) ( species of all propositions) in intuitionistic mathematics.p-UP is implied by WC and KS. But there are interestingp-UP-cases which require weak KS resp. WC only. UP for number species follows fromp-UP by extended bar-induction (ranging over propositions) and suitable weak continuity. As corollaries we have the disjunction property and the existential definability w.r.t. concrete objects. Other consequences are: there is no non-trivial countable partition of;id is the only injective function from to; there are no many-place injective prepositional functions; card () is incomparable with the cardinality of all metric spaces containing at least three elements.     

A modification of kendall's tau for measuring association in contingency tables

A coefficient of association is described for a contingency table containing data classified into two sets of ordered categories. Within each of the two sets the number of categories or the number of cases in each category need not be the same.=+1 for perfect positive association and has an expectation of 0 for chance association. In many cases also has –1 as a lower limit. The limitations of Kendall's _a and _b and Stuart's _c are discussed, as is the identity of these coefficients to' under certain conditions. Computational procedure for is given.     

The Deep Structure of Group Life: Unconscious Dimensions

There is a reconsideration and renaissance of interest in expanded conceptions of unconscious processes as they affect individuals and groups (Grotstein, 1999). Recent focus on social unconscious (Hopper, 1996) and cultural unconscious processes (Henderson, 1988) and the nature of intersubjectivity (Harwood and Pines, 1998) raise questions about the location of group analysis. This paper considers the deep structure of group life by examining four functions of the unconscious: repressive, conservative, creative, and mythopoetic (Ellenberger, 1970). On an individual level of analysis, these functions are equated respectively with formative ideas about the: personal–subjective, social–political, intersubjective–cultural and collective–objective unconscious. Group level analogs, as they develop and affect groups and their members, are explored as synthetic, shared, symbolicy and synchronous unconscious processes.     

Interpretations of the first-order theory of diagonalizable algebras in peano arithmetic

For every sequence |p _n } _n of formulas of Peano ArithmeticPA with, every formulaA of the first-order theory diagonalizable algebras, we associate a formula ⁰ A, called the value ofA inPA with respect to the interpretation. We show that, ifA is true in every diagonalizable algebra, then, for every, ⁰ A is a theorem ofPA.     

On finite approximability of ψ-intermediate logics

The aim of this note is to show (Theorem 1.6) that in each of the cases: = {, }, or {, , }, or {, , } there are uncountably many -intermediate logics which are not finitely approximable. This result together with the results known in literature allow us to conclude (Theorem 2.2) that for each : either all -intermediate logics are finitely approximate or there are uncountably many of them which lack the property.     

A group ministry in the inner city

Conclusion The Group Ministry approach is an attempt at one way of facing the need for renewal of the Church in its understanding of the means of Christian commitment and witness in the world. There are many dangers in a Group Ministry. It runs the risk of becoming apower block or separation of men and women from their primary responsibility in the local church; of facingemotional strain on those who must work closely together in a group of sinners; of developing apsychic dependence on each other rather than looking to Christ as the primary source of support and unity; of becomingless efficient when more workers are placed in one small area; oflacking a sense of direction because one leader is not given responsibility and authority.Yet the Group Ministry approach takes these risks in the knowledge that the Church must work to fashion patterns by which it may again express itself with power in places where the word is scarce.For further information about the East Harlem Protestant Parish, readers may write directly to 2050 Second Avenue, New York 29, N. Y.     

Michael Balint's Group Approach: The Boston Balint Group

Michael Balint was a physician/psychoanalyst who trained in Hungary and emigrated to England in 1939 when Nazi Germany began to dominate Europe. At the Tavistock Clinic, he and his wife met with social workers and physicians around case discussion seminars. With his strong interest in medicine and his curiosity about the patient-physician relationship, he initiated research/training groups with interested physicians, which ultimately led to publication of the now-classic The Doctor, His Patient, and the Illness, a rich text that has become a virtual staple of family practice residencies, along with Balint Groups for training. Balint refrained from considering his groups psychotherapy in order to minimize resistance of his physician-students. But because the groups lasted sometimes for years and explored transference and countertransference in patient-physician relationships, he acknowledged that the result was personal growth of the participants. His techniques are described and an example of a Balint Group (Boston Group) are presented here.     

A reduction rule for Peirce formula

A reduction rule is introduced as a transformation of proof figures in implicational classical logic. Proof figures are represented as typed terms in a -calculus with a new constant P ⁽⁽⁾⁾. It is shown that all terms with the same type are equivalent with respect to -reduction augmented by this P-reduction rule. Hence all the proofs of the same implicational formula are equivalent. It is also shown that strong normalization fails for P-reduction. Weak normalization is shown for P-reduction with another reduction rule which simplifies of (( ) ) into an atomic type.This work was partially supported by a Grant-in-Aid for General Scientific Research No. 05680276 of the Ministry of Education, Science and Culture, Japan and by Japan Society for the Promotion of Science. Hiroakira Ono     

Computer content analysis of sex differences in the language of children

This study presents empirical procedures for the collection and content analysis of the oral language of kindergarten children. The analysis technique used material and machines available to most researchers. The results of the analysis of language samples of 144 randomly selected children from the entire kindergarten class of the Ithaca, New York, school system showed that boys produced significantly more language than did the girls as well as significantly more references to aggression, self, time, space, quantity, fears, good, act of oral communication, negation, and affirmation, and asked more questions of the examiner than did the girls. The girls made significantly more female references than did the boys. Implications for future research are discussed.     

Confirmation holism and semantic holism

Fodor and Lepore, in their recent book Holism, maintain that if an inference from semantic anatomism to semantic holism is allowed, certain fairly deleterious consequences follow. In Section 1 Fodor and Lepore's terminology is construed and amended where necessary with the result that the aforementioned deleterious consequences are neither so apparent nor straightforward as they had suggested. In Section 2 their Argument A is considered in some detail. In Section 3 their argument attributed to Quine is examined at length and a shorter and more perspicacious argument suggested which avoids their charge that the Quinean argument is guilty of an equivocation on the word statement.     

Gentzen-type formulation of the prepositional logic LQ

We give a Gentzen-type formulation GQ for the intermediate logic LQ and prove the cut-elimination theorem on it, where LQ is the propositional logic obtained from the intuitionistic propositional logic LI by adding the axioms of the form AV A.     

New lower and upper bounds for communality in factor analysis

We derive several relationships between communalities and the eigenvalues for ap ×p correlation matrix under the usual factor analysis model. For suitable choices ofj, _j (), where _j () is thej-th largest eigenvalue of , provides either a lower or an upper bound to the communalities for some of the variables. We show that for at least one variable, 1 - _p () improves on the use of squared mulitiple correlation coefficient as a lower bound.This research was done while the second author was at Tokyo Institute of Technology.     

A further note on freeman's measure of association

This note extends and elaborates Hubert's attempt to provide an interpretation of Freeman's measure of association,. The measure is used in a a contingency table when observations are ordered on one variable and unordered on the other. No attempt is made explore the distribution of.     

Sheaves over Heyting lattices

For a complete Heyting lattice , we define a category Etale (). We show that the category Etale () is equivalent to the category of the sheaves over , Sh(), hence also with -valued sets, see [2], [1]. The category Etale() is a generalization of the category Etale (X), see [1], where X is a topological space.     

An Exploration of Johnson's Sense of ‘Argument’

This essay attempts to give definitions and identity conditions for the two predominant senses of Argument currently in use, the one involving reasons for a conclusion and the other denoting an expressed disagreement with ensuing verbal behaviour by two parties. I see Johnson's new concept of Argument, as developed in his book Manifest Rationality, as a hybrid of the two common senses of Argument, and, accordingly, I try to define and give the identity conditions of Johnson-arguments. Finally, I disagree with Johnson on the nature of the definition he thinks he has proposed, and I conclude with observations suggesting that his logical perspective has dialectical and rhetorical components.     

Signal Detection Analysis of Choice Behavior and Aging

The primary research question was whether older adults respond to the contingencies of reinforcement such that they allocate their behavior as predicted by the reinforcement contingencies and discriminative stimuli programmed by the experimenters. Six subjects, ranging in age from 62 to 74 years, participated in 15 experimental sessions. Subjects were instructed to press the F1 key when they saw a white circle, and to press the F12 key when they saw a red letter A. Responses on the F1 key were reinforced on a variable interval (VI) 30-s schedule (i.e., a VI schedule of reinforcement with 11 arithmetically spaced intervals with a mean of 30 s); F12 key responses were reinforced on a VI 60-s schedule (i.e., a VI schedule of reinforcement with 11 arithmetically spaced intervals with a mean of 60 s). Reinforcers included monetary units (10 cents) and verbal praise. Results indicated positive effects of stimulus control of behavior. Collective false alarms and miss rates represented only 0.05% of the total responses. Also, two thirds of the subjects allocated behavior consistent with the second hypothesis that a denser reinforcement schedule (i.e., the VI 30-s) would cause subjects to respond more quickly to this condition. Implications of the present results for clinical studies of Alzheimer's Disease and dementia, as well as behavior modification strategies with aging individuals, are discussed.     

Algebraic aspects of deduction theorems

The first known statements of the deduction theorems for the first-order predicate calculus and the classical sentential logic are due to Herbrand [8] and Tarski [14], respectively. The present paper contains an analysis of closure spaces associated with those sentential logics which admit various deduction theorems. For purely algebraic reasons it is convenient to view deduction theorems in a more general form: given a sentential logic C (identified with a structural consequence operation) in a sentential language I, a quite arbitrary set P of formulas of I built up with at most two distinct sentential variables p and q is called a uniform deduction theorem scheme for C if it satisfies the following condition: for every set X of formulas of I and for any formulas and , C(X{{a}}) iff P(, ) AC(X). [P(, ) denotes the set of formulas which result by the simultaneous substitution of for p and for q in all formulas in P]. The above definition encompasses many particular formulations of theorems considered in the literature to be deduction theorems. Theorem 1.3 gives necessary and sufficient conditions for a logic to have a uniform deduction theorem scheme. Then, given a sentential logic C with a uniform deduction theorem scheme, the lattices of deductive filters on the algebras A similar to the language of C are investigated. It is shown that the join-semilattice of finitely generated (= compact) deductive filters on each algebra A is dually Brouwerian.A part of this paper was presented in abstracted form in Bulletin of the Section of Logic, Vol. 12, No. 3 (1983), pp. 111–116, and in The Journal of Symbolic Logic.