On the Closure Properties of the Class of Full G-models of a Deductive System

In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACS_s A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these structures with tipically logical properties of the sentential logic S. The main algebraic properties we consider are the closure of FGModS under substructures and under reduced products, and the property that for any A the lattice FACS_s A is a complete sublattice of the lattice of all algebraic closed-set systems over A. The logical properties are the existence of a fully adequate Gentzen system for S, the Local Deduction Theorem and the Deduction Theorem for S. Some of the results are established for arbitrary deductive systems, while some are found to hold only for deductive systems in more restricted classes like the protoalgebraic or the weakly algebraizable ones. The paper ends with a section on examples and counterexamples. Dedicated to the memory of Willem Johannes Blok     

Development and Evaluation of a Decision Aid About Prenatal Testing for Women of Advanced Maternal Age

Objective: To develop and evaluate a decision aid designed to prepare patients of advanced maternal age for counseling about prenatal diagnostic testing. Setting: A regional genetics center. Design: A before/after study. Interventions: Participants used an audioguided workbook to learn about options and outcomes and to clarify personal risks, values, questions, and predispositions. Subjects: 21 women of advanced maternal age and 17 spouses. Main outcome measures: Knowledge of prenatal testing alternatives, decisional conflict, level of anxiety, and acceptability of the decision aid. Results: After using the decision aid, participants had significantly reduced decisional conflict (uncertainty) and a significant increase in knowledge. There was no effect on state or trait anxiety. More than three-quarters of participants were satisfied with the length, clarity, balance, and acceptability of the decision aid. Conclusions: The decision aid shows promise as a useful aid for preparing couples for counseling.     

Proof theory and mathematical meaning of paraconsistent C-systems

A proof-theoretic analysis and new arithmetical semantics are proposed for some paraconsistent C-systems, which are a relevant sub-class of Logics of Formal Inconsistency (LFIs) introduced by W.A. Carnielli et al. (2002, 2005) [8] and [9]. The sequent versions BC, CI, CIL of the systems bC, Ci, Cil presented in Carnielli et al. (2002, 2005) [8] and [9] are introduced and examined. BC, CI, CIL admit the cut-elimination property and, in general, a weakened sub-formula property. Moreover, a formal notion of constructive paraconsistent system is given, and the constructivity of CI is proven. Further possible developments of proof theory and provability logic of CI-based arithmetical systems are sketched, and a possible weakened Hilbert?s program is discussed. As to the semantical aspects, arithmetical semantics interprets C-system formulas into Provability Logic sentences of classical Arithmetic PA (Artemov and Beklemishev (2004) [2], Japaridze and de Jongh (1998) [19], Gentilini (1999) [15], Smorynski (1991) [22]): thus, it links the notion of truth to the notion of provability inside a classical environment. It makes true infinitely many contradictions B∧¬B and falsifies many arbitrarily complex instances of non-contradiction principle ¬(A∧¬A). Moreover, arithmetical models falsify both classical logic LK and intuitionistic logic LJ, so that a kind of metalogical completeness property of LFI-paraconsistent logic w.r.t. arithmetical semantics is proven. As a work in progress, the possibility to interpret CI-based paraconsistent Arithmetic PACI into Provability Logic of classical Arithmetic PA is discussed, showing the role that PACIarithmetical models could have in establishing new meta-mathematical properties, e.g. in breaking classical equivalences between consistency statements and reflection principles.     

On the size of refutation Kripke models for some linear modal and tense logics

LetL be any modal or tense logic with the finite model property. For eachm, definer _L (m) to be the smallest numberr such that for any formulaA withm modal operators,A is provable inL if and only ifA is valid in everyL-model with at mostr worlds. Thus, the functionr _L determines the size of refutation Kripke models forL. In this paper, we will give an estimation ofr _L (m) for some linear modal and tense logicsL.     

The Geometry of Enhancement in Multiple Regression

In linear multiple regression, “enhancement” is said to occur when R ²=b′r>r′r, where b is a p×1 vector of standardized regression coefficients and r is a p×1 vector of correlations between a criterion y and a set of standardized regressors, x. When p=1 then b≡r and enhancement cannot occur. When p=2, for all full-rank R _xx≠I, R _xx=E[xx′]=V Λ V′ (where V Λ V′ denotes the eigen decomposition of R _xx; λ ₁>λ ₂), the set B₁:={b_i:R²=b_i￠r_i=r_i￠r_i;0 < R² ￡ 1}\boldsymbol{B}_{1}:=\{\boldsymbol{b}_{i}:R^{2}=\boldsymbol{b}_{i}'\boldsymbol{r}_{i}=\boldsymbol{r}_{i}'\boldsymbol{r}_{i};0R² ￡ 1;R²l_p ￡ r_i￠r_i < R²}0p≥3 (and λ ₁>λ ₂>⋯>λ _p ), both sets contain an uncountably infinite number of vectors. Geometrical arguments demonstrate that B ₁ occurs at the intersection of two hyper-ellipsoids in ℝ ^p . Equations are provided for populating the sets B ₁ and B ₂ and for demonstrating that maximum enhancement occurs when b is collinear with the eigenvector that is associated with λ _p (the smallest eigenvalue of the predictor correlation matrix). These equations are used to illustrate the logic and the underlying geometry of enhancement in population, multiple-regression models. R code for simulating population regression models that exhibit enhancement of any degree and any number of predictors is included in Appendices A and B.     

On the Existence of Continua of Logics Between Some Intermediate Predicate Logics

A method for constructing continua of logics squeezed between some intermediate predicate logics, developed by Suzuki [8], is modified and applied to intervals of the form [L, L+ ¬¬S], where Lis a predicate logic, Sis a closed predicate formula. This solves one of the problems from Suzuki's paper.     

The existence of matrices strongly adequate for E,R and their fragments

A logic is a pair (P,Q) where P is a set of formulas of a fixed propositional language and Q is a set of rules. A formula is deducible from X in the logic (P, Q) if it is deducible from XP via Q. A matrix is strongly adequate to (P, Q) if for any , X, is deducible from X iff for every valuation in , is designated whenever all the formulas in X are. It is proved in the present paper that if Q = {modus ponens, adjunction } and P {E, R, E ⁺, R ⁺, E ^I, R ^I } then there exists a matrix strongly adequate to (P, Q).     

Significance of a Preponderance of Human Movement Responses on the Rorschach in Children Below Age Ten

Abstract

Beck, Samuel J. Rorschach's Test III. Advance in Interpretation. New York: Grune &; Stratton, 1952. Reviewed by Mortimer M. Meyer

Brower, Daniel and Abt, Lawrence Progress in Clinical Psychology. Volume I. New York: Grune &; Stratton, 1952. Reviewed by Ohmer Milton

Buhler, C., Smitter, F., and Richardson, S. Childhood Problems and the Teacher. New York: Henry Holt and Co., 1952. Pp. 372, $3.75. Reviewed by Lois Barclay Murphy

Jolles, Isaac. A Catalogue for the Qualitative Interpretation of the H-T-P. Beverly Hills: Western Psychological Services, 1952, 97 pp. Reviewed by Wilson H. Guertin

Kinget, Marian G., The Drawing-Completion Test. New York: Grune and Stratton, Inc., 1952. Reviewed by Fred Brown

Meili, Richard. Lehrbuch der Psychologischen Diagnostik. Bern: Verlag Hans Huber, 1951, 372 pp. Reviewed by Walther Joel

Szondi, L. Experimental Diagnostics of Drives (Translated by Gertrude Aull). New York: Grune and Stratton, 1952, 220 pp. Reviewed by Henry P. David     

A simplification of a completeness proof of Guaspari and Solovay

The modal completeness proofs of Guaspari and Solovay (1979) for their systems R and R ^– are improved and the relationship between R and R ^– is clarified.     

Effects of repeated collaborative retrieval on individual memory vary as a function of recall versus recognition tasks

Our research examines how prior group collaboration modulates later individual memory. We recently showed that repeated collaborative recall sessions benefit later individual recall more than a single collaborative recall session (Blumen & Rajaram, 2008). Current research compared the effects of repeated collaborative recall and repeated collaborative recognition on later individual recall and later individual recognition. A total of 192 participants studied a list of nouns and then completed three successive retrieval sessions in one of four conditions. While two collaborative recall sessions and two collaborative recognition sessions generated comparable levels of individual recall (CRecall-CRecall-I Recall ～ CRecognition-CRecognition-I Recall , Experiment 1a), two collaborative recognition sessions generated greater levels of individual recognition than two collaborative recall sessions (CRecognition-CRecognition- IRecognition > CRecall-CRecall- I Recognition , Experiment 1b). These findings are discussed in terms of two opposing mechanisms that operate during collaborative retrieval—re-exposure and retrieval disruption—and in terms of transfer-appropriate processing across collaborative and individual retrieval sessions.     

A modal sequent calculus for a fragment of arithmetic

Global properties of canonical derivability predicates (the standard example is Pr() in Peano Arithmetic) are studied here by means of a suitable propositional modal logic GL. A whole book [1] has appeared on GL and we refer to it for more information and a bibliography on GL. Here we propose a sequent calculus for GL and, by exhibiting a good proof procedure, prove that such calculus admits the elimination of cuts. Most of standard results on GL are then easy consequences: completeness, decidability, finite model property, interpolation and the fixed point theorem.The second author holds a grant from the Consiglio Nazionale delle Ricerche, gruppo G.N.S.A.G.A.     

The countable homogeneous universal model of B 2

We give a detailed account of the Algebraically Closed and Existentially Closed members of the second Lee class B ₂ of distributive p-algebras, culminating in an explicit construction of the countable homogeneous universal model of B ₂. The axioms of Schmid [7], [8] for the AC and EC members of B ₂ are reduced to what we prove to be an irredundant set of axioms. The central tools used in this study are the strong duality of Clark and Davey [3] for B ₂ and the method of Clark [2] for constructing AC and EC algebras using a strong duality. Applied to B ₂, this method transfers the entire discussion into an equivalent dual category X ₂ of Boolean spaces which carry a pair of tightly interacting orderings. The doubly ordered spaces of X ₂ prove to be much more readily constructed and analyzed than the corresponding algebras in B ₂.     

Intermediate logics with the same disjunctionless fragment as intuitionistic logic

Given an intermediate prepositional logic L, denote by L ^–d its disjuctionless fragment. We introduce an infinite sequence {J _n}_n1 of propositional formulas, and prove:(1)For any L: L ^–d =I ^–d (I=intuitionistic logic) if and only if J _n L for every n 1.Since it turns out that L{J _{n} n}1 = Ø for any L having the disjunction property, we obtain as a corollary that L ^–d = I ^–d for every L with d.p. (cf. open problem 7.19 of [5]). Algebraic semantic is used in the proof of the if part of (1). In the last section of the paper we provide a characterization in Kripke's semantic for the logics J _n =I+ +J _n (n 1).     

A Review of Finn,Fischer, and Handler (Eds.), Collaborative/Therapeutic Assessment: A Casebook and Guide

Abstract

Oscar N. Myer The Language of Handwriting. Reviewed by Rose Wolfson

Klara Roman Handwriting: a Key to Personality. Reviewed by Rose Wolfson

Frank Victor Handwriting: A Personality Projection. Springfield, Illinois: Charles C. Thomas, 1952. American Lecture Series Monograph No. 96. Reviewed by Gerald S. Blum, Ph.D.

Robert I. Watson The Clinical Method in Psychology. New York: Harper &; Bros. 1951. $4.50. Reviewed by Walter G. Klopfer, Ph.D.     

Audience with a Healer

Up From Scapegoating: Awakening Consciousness in Groups. 1995. By Arthur D. Colman Wilmette, IL: Chiron.

The Wounded Jung. (1996). By Robert C. Smith Evanston, IL: Northwestern University Press.

The Body: An Encyclopedia for Research in Archetypal Symbolism. 1996. By George R. Elder Boston: Shambhala.

Gifts of Suffering. 1996. By Polly Young-Eisendrath New York; Addison-Wesley Co.

The Religious Function of die Psyche. 1996. By Lionel Corbett London &; New York: Routledge.

Buddhism and the Art of Psychotherapy. 1996. By Hayao Kawai College Station, TX: Texas A &; M University Press.

The Soul's Code: In Search of Character and Calling. 1996. By James Hillman New York: Random House.

Kinds of Power A Guide to Its Intelligent Uses. 1995. By James Hillman New York: Doubleday.

Psychotherapy as a Mutual Process. 1996. By J. Marvin Spiegelman Tempe, AZ: New Falcon Publications.

Soul Cards. By Deborah Koff-Chapin 1995. Langley, WA: The Center for Touch Drawing.     

A Comparison of Clinical Manifestations of Hostility with Rorschach and MAPS Test Performances

Abstract

De Martino, Manfred F., (Ed.) Dreams and personality dynamics. Springfield, III.: Charles C. Thomas. 1959, pp. 377, $10.00. Reviewed by Sohan Lal Sharma

Ledwith, Nettie H. A Rorschach Study of Child Development. Pittsburgh, Pa: Univ. of Pittsburgh Press 1960 pp. lx-336. Reviewed by Mortimer M. Meyer

Nel, B. F., and Pelser, A. J. K. The South African Picture Analysis Test (SAPAT). Amsterdam: Swets &; Zeitlinger, 1960; pp. 74. Paper bound. Price with plates ca. $6.50. Reviewed by Wilson H. Guertin

Orr, Miriam Le Test De Rorschach et L'Imago Maternelle. (The Rorschach and maternal imago.) Paris: Groupement Francais du Rorschach, 1958, pp. 104, paper bound, 500 fr. Reviewed by Mary Engel

Zulliger, H. The Behn-Rorschach Test. Hans Huber, Bern: 1956, 200 pp. Reviewed by Murray Levine     

Book Reviews

Abstract

Beteendeterapi inom Psykiatrin L.G. Öst (Red). (1987). Stockholm: Natur &; Kultur. Pris: 330 sv kr. Reviewed by Arnold Torstenson.

“Till de Bildade bland dess Föraktare” Reviewed by Car-Erik Brattemo.

Beteendeterapi inom Psykiatrin Reviewed by Solveig og Carl Erik Grenness.

Schizofrenibehandling — Psykiatri på Liv och Död S. Belin (1987) Stockholm: Natur &; Kultur, 170 sidor. Pris: 205 SEK. Reviewed by Staffan Sohlberg.

Symtom — Diagnos G. Birke (1988) Stockholm: Almqvist &; Wiksell, 616 sidor Reviewed by Birgitta och Roberg Forsberg.     

A weak intuitionistic propositional logic with purely constructive implication

We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripke-type model theory for WM is given.This work was partially supported by NSF Grant DCR85-13417     

Experimenter Modeling Effects as Determinants of Subject's Responses

Abstract

Ames, Louise Bates, Metraux, Ruth W., Walker, Richard N. Adolescent Rorschach Responses. New York: Paul B. Hoeber, 1959, xi plus 313. $8.50. Reviewed by Mortimer M. Meyer

Bass, B. F. and Berg, I. A. Objective Approaches to Personality Assessment. New York: D. Van Nostrand, 1959, pp. x-233. $4.95. Reviewed by Wilson H. Guertin

Bellak, L. (Ed.), Ostow, M., Pumpian-Mindlin, E., Stanton, A. H., and Szasz, T. S. Conceptual and methodological problems in psychoanalysis. New York: Annals of the N. Y. Academy of Sciences, 1959, p. 973–1134. Reviewed by A. I. Rabin

Buros, Oscar K. (Ed.) The fifth mental measurements yearbook. Highland Park, N.J.: Gryphon Press, 1959. Reviewed by Bertram R. Forer

Caligor, Leopold. A New Approach to Figure Drawing. Springfield, III.: Charles Thomas, Publisher, 1957, pp. 148, $4.50. Reviewed by Emanuel F. Hammer, Ph.D.

Hallower, Molly. Personality Change and Development. New York and London: Grune &; Stratton. 1958. 383 pp. $10.00. Reviewed by Theodore H. Blau

Ledwith, Nettie H. Rorschach responses of elementary school children. Pittsburgh: Univ. Pittsburgh Press, 1959. Reviewed by Mortimer M. Meyer

Tomkins, Silvan S. and Miner, John B. PAT Interpretation. Springer Publishing Company, Inc., New York, 1959. 184 pp. Reviewed by Leonard P. Ullmann     

On the lattice of quasivarieties of Sugihara algebras

Let S denote the variety of Sugihara algebras. We prove that the lattice (K) of subquasivarieties of a given quasivariety K S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice (S) is not modular.