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.     

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.     

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.     

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.     

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).     

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.     

Adult self-image and well-being after testicular cancer: The role of agency and meaning

Objective: Cancer during young adulthood can limit the extent to which one adopts an adult self-image. However, the relationship of adult self-image to cancer-related adjustment remains unexplored. The current study examines relationships of adult self-image and social/emotional well-being and job-related problems in young testicular cancer survivors. Factors thought to facilitate future-oriented goals (i.e. agency and meaning) are examined as intermediary processes.

Design: Testicular cancer survivors (N = 171) between the ages of 18 and 29 completed questionnaire measures of adult self-image, agency, sense of meaning and indicators of adjustment.

Main Outcome Measures: Social and emotional well-being were measured by the Functional Assessment of Cancer Therapy-General. Job problems were assessed using the EORTC’s testicular cancer supplement (EORTC QLQ-TC26).

Results: Path model results revealed direct associations of survivors’ adult self-image with social (β = .20, p < .05), but not emotional well-being (β = .14, p < .01). Both agency and meaning mediated the relationship of adult self-image and well-being indicators. Finally, the relationship between adult self-image and job problems was only significant for those who were employed or in school (β = ?.19, p < .05).

Outcomes: Assessment of adult self-image might be useful in identifying risk for poor adjustment. Interventions that target agency and meaning might facilitate developmental goals.     

An interview with emily and john visher

Abstract

Making an Issue of Child Abuse: Political Agenda Setting for Social Problems, by Barbara J. Nelson. Chicago: University of Chicago Press, 1984, 269 pages, $27.50.

Child Abuse: A Community Concern, edited by Kim Oates. New York: Brunner/Mazel, 1984, 336 pages, $25.00.

Death and Grief in the Family, edited by Thomas T. Frantz. Rockville, MD: Aspen Systems Corporation, 1984, 122 pages, $18.00.

A Child Dies: A Portrait of Family Grief, by loan Hagan Arnold &; Penelope Buschman Gernuna. Rockville, MD: Aspen Systems Corporation, 1983, 162 pages (price unknown).

The Single Child Family, edited by Toni Falbo. New York: Guilford Press, 1984, 304 pages, $27.50.

Adolescent Crises: Family Counseling Approaches, by Eva Leveton. New York: Springer Publishing, 1984, 285 pages, $24.95.

The Narcissistic and Borderline Disorders: An Integrated Developmental Approach, by J. F. Masterson. New York: Brunner/Mazel, 1982, 256 pages, $20.00.

The Battered Woman Syndrome, by Lenore E. Walker. New York: Springer, 1984, 272 pages, $21.95.

Human Sexuality: Contemporary Controversies, edited by Harold Feldman 6 Andrea Parrot. Beverly Hills, CA: Sage Publications, 1984, 333 pages.

Family Relationships in Later Life, edited by Timothy Brubaker. Beverly Hills, CA: Sage Publications, 1983, 272 pages, $25.00, paperback $12.50.

Overcrowding in the Household, An Analysis of Determinants and Effects, by Walter R. Gove &; Michael Hughes. New York: Academic Press, 1983, 326 pages, $39.00.

Origins and Evolution of Behavior Disorders, by Stella Chess &; Alexander Thomas. New York: Brunner/Mazel, 1984, 320 pages, $30.00.

Psychotherapy with Psychotherapists, edited by Florence W. Kaslow. New York: Haworth Press, 1984, 202 pages, $22.95.

Innovations in Clinical Practice: A Source Book, Volume 3, edited by Peter A. Keller &; Lawrence G. Ritt. Sarasota, FL: Professional Resource Exchange, 1984, 482 pages, hardbound $39.95; looseleaf binder, $44.95.

Guiding the Family: Practical Counseling Techniques, by B. B. Grunwald &; H. V. McAbee. Muncie, IN: Accelerated Development, 1985, 346 pages, $17.95.

Applying Family Therapy: A Practical Guide for Social Workers, by Helen C. Masson &; Patrick O'Byrne. Oxford, England: Pergamon Press, 1984, 148 pages, hardbound $20.00; paperback $13.00.

Parent Training, edited by Richard F. Dungel &; Richard A. Polster. New York: Guilford, 1984, 576 pages, $35.00.

New Developments in Behavior Therapy, edited by Cyril M. Franks. New York: The Hawthorne Press, 1984, 589 pages, $45.00 hardbound, $24.95 softbound.

Symptom Reduction Through Clinical Biofeedback, by Ivan Wentworth-Rohr, New York: Human Sciences Press, 1984, 273 pages.

American Family Law in Transition, by Walter O. Weyrauch &; Sandord N. Katz. Washington, DC: The Bureau of National Affairs, 1983, 629 pages, $35.00.

The Denial of Stress, edited by Sholomo Breznitz. New York: International Universities Press, 1983, 316 pages, $25.00.

Stress Reduction and Prevention, edited by Donald Meichenbaum 6 Matt Jaremko. New York: Plenum, 1983, 512 pages, $32.50.

Life-Span Developmental Psychology: Nonnormative Life Events, edited by Edward J. Callahan &; Kathleen A. McCluskey. New York: Academic Press, 1983, 314 pages, $29.50.     

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     

Eye Movements and Fixations during Initial Viewing of Rorschach Cards

Abstract

Blum, Lucille H., Davidson, Helen H., and Fieldsteel, Nina D. A Rorschach Workbook. International Universities Press, New York, 1954, $2.00. Pp. 168. Reviewed by Leonard B. Olinger

Endara, Julio Psicodiagnóstico de Rorschach. Técnica General. Aplicaciones Clínicas. Investigations de Clínica Psicológica. (Rorschach Psychodiagnostics. General Technique. Clinical Applications. Clinical Psychological Investigations.) Quito, Ecuador: Casa de la Cultura Ecuatoriana, 1954. 326pp. Reviewed by Marvin Spiegelman

Holsopple, James Quinter and Miale, Florence R. Sentence Completion: A Projective Method for the Study of Personality. Thomas, 1954, $5.50. Pp. xiii + 177. Reviewed by Leonard B. Olinger

Lowenfeld, Margaret The Lowenfeld Mosaic Test. London: Newman Neame Limited, 1954, 349 pp. plus 144 colored plates in separate container. Reviewed by Barbara Bowen

Schafer, Roy Psychoanalytic Interpretation in Rorschach Testing. New York: Grune and Stratton, 1954, 446 pp. + xiv. Reviewed by Mortimer M. Meyer     

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     

Examining the effects of perceived social support on momentary mood and symptom reports in asthma and arthritis patients

Objective: Social support has been linked to beneficial effects on health directly (main effect) and as a buffer to stress. Most research, however, has examined these relationships using global and retrospective assessments of health and stress, which may be subject to recall biases. This study used ambulatory ecological momentary assessment (EMA) methods to test the main and stress-buffering effects of social support on the daily health and well-being of asthma and rheumatoid arthritis (RA) patients.

Design: Community volunteers with asthma (n?=?97) or RA (n?=?31) responded to EMA prompts five times daily for one week.

Main outcomes: Baseline perceived social support was obtained, and then, participants reported mood, stress and symptoms using EMA. Multilevel mixed-modelling examined whether social support predicted mood and symptoms directly or via stress-reducing effects.

Results: Supporting a main effect, more perceived social support predicted decreased negative mood and stress severity. Supporting a stress-buffering effect, more perceived social support resulted in fewer reported symptoms when stress was present.

Conclusion: Results suggest perceived social support directly relates to better ambulatory status and dynamically buffers individuals against the negative effects of stressors, and highlight the importance of studying social support across different temporal and contextual levels.     

Undecidability and intuitionistic incompleteness

Let S be a deductive system such that S-derivability (s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and s, it follows constructively that the K-completeness of s implies MP(S), a form of Markov's Principle. If s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when s is many-one complete, MP(S) implies the usual Markov's Principle MP.An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implics MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP.These results give extensions of the theorem of Gödel and Kreisel (in [4]) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Gödel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article.     

Axiomatization and completeness of uncountably valued approximation logic

A first order uncountably valued logicL _Q(0,1) for management of uncertainty is considered. It is obtained from approximation logicsL _T of any poset type (T, ) (see Rasiowa [17], [18], [19]) by assuming (T, )=(Q(0, 1), ) — whereQ(0, 1) is the set of all rational numbersq such that 0<q<1 and is the arithmetic ordering — by eliminating modal connectives and adopting a semantics based onLT-fuzzy sets (see Rasiowa and Cat Ho [20], [21]). LogicL _Q(0,1) can be treated as an important case ofLT-fuzzy logics (introduced in Rasiowa and Cat Ho [21]) for (T, )=(Q(0, 1), ), i.e. asLQ(0, 1)-fuzzy logic announced in [21] but first examined in this paper.L _Q(0,1) deals with vague concepts represented by predicate formulas and applies approximate truth-values being certain subsets ofQ(0, 1). The set of all approximate truth-values consists of the empty set ø and all non-empty subsetss ofQ(0, 1) such that ifqs andqq, thenqs. The setLQ(0, 1) of all approximate truth-values is uncountable and covers up to monomorphism the closed interval [0, 1] of the real line.LQ(0, 1) is a complete set lattice and therefore a pseudo-Boolean (Heyting) algebra. Equipped with some additional operations it is a basic plain semi-Post algebra of typeQ(0, 1) (see Rasiowa and Cat Ho [20]) and is taken as a truth-table forL _Q(0,1) logic.L _Q(0,1) can be considered as a modification of Zadeh's fuzzy logic (see Bellman and Zadeh [2] and Zadeh and Kacprzyk, eds. [29]). The aim of this paper is an axiomatization of logicL _Q(0,1) and proofs of the completeness theorem and of the theorem on the existence ofLQ(0, 1)-models (i.e. models under the semantics introduced) for consistent theories based on any denumerable set of specific axioms. Proofs apply the theory of plain semi-Post algebras investigated in Cat Ho and Rasiowa [4].Presented byCecylia Rauszer     

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     

Negative life events and symptoms of depression and anxiety: stress causation and/or stress generation

Background and Objectives: Stressful life events are known to contribute to development of depression; however, it is possible this link is bidirectional. The present study examined whether such stress generation effects are greater than the effects of stressful life events on depression, and whether stress generation is also evident with anxiety. Design: Participants were two large age cohorts (N = 732 aged 44 years; N = 705 aged 63 years) from the West of Scotland Twenty-07 study. Methods: Stressful life events, depression, and anxiety symptoms were measured twice five years apart. Cross-lagged panel analysis examined the mutual influences of stressful life events on depression and on anxiety over time. Results: Life events predicted later depressive symptomatology (p = .01), but the depression predicting life events relationship was less strong (p = .06), whereas earlier anxiety predicted life events five years later (p = .001). There was evidence of sex differences in the extent to which life events predicted later anxiety. Conclusions: This study provides evidence of stress causation for depression and weaker evidence for stress generation. In contrast, there was strong evidence of stress generation for anxiety but weaker evidence for stress causation, and that differed for men and women.     

A Comparison of Rorschach Responses Between Negro and White College Students

Abstract

David, Henry P. and Brengelmann, J.C., (eds.). Perspectives In Personality Research. New York: Springer, Inc., 1960. 370 pp. $7.50. Reviewed by Kenneth R. Wurtz

Gottsegen, Monroe G. and Gottsegen, Gloria B. Professional School Psychology. New York: Grune &; Stratton, 1960, Pp. 292, $7.75. Reviewed by Henry L. Levy

Klopfer, Walter G. The Psychological Report: Use and Communication of Psychological Findings. New York: Grune &; Stratton, 1960. Pp. ix and 146. Reviewed by Dale S. Higbee     

Parallel processing of whole words and morphemes in visual word recognition

Models of morphological processing make different predictions about whether morphologically complex written words are initially decomposed and recognized on the basis of their morphemic subunits or whether they can directly be accessed as whole words and at what point semantics begin to influence morphological processing. In this study, we used unprimed and masked primed lexical decision to compare truly suffixed (darkest) and pseudosuffixed words (glossary) with within-boundary (d ra kest/g ol ssary) to across-boundary (dar ek st/glos as ry) letter transpositions. Significant transposed-letter similarity effects were found independently of the morphological position of the letter transposition, demonstrating that, in English, morphologically complex whole-word representations can be directly accessed at initial word processing stages. In a third masked primed lexical decision experiment, the same materials were used in the context of stem target priming, and it was found that truly suffixed primes facilitate the recognition of their stem-target (darkest–DARK) to the same extent as pseudosuffixed primes (glossary–GLOSS), which is consistent with theories of early morpho-orthographic decomposition. Taken together, our findings provide evidence for both whole-word access and morphological decomposition at initial stages of visual word recognition and are discussed in the context of a hybrid account.     

Prospective associations between unforgiveness and physical health and positive mediating mechanisms in a nationally representative sample of older adults

Objective: This study examined the prospective association between unforgiveness and self-reported physical health and potential positive psychological mediators of this association.

Design: Participants were a national sample of 1024 USA’s adults of ages 66 years and older. Data were collected at two time points separated by three years.

Main Outcome Measures: Measures of trait unforgiveness, self-rated physical health, socio-demographics, health behaviours and positive psychological traits (e.g. life satisfaction, self-esteem) were included in a comprehensive survey known as the ‘Religion, Aging, and Health Survey.’

Results: The results indicated that unforgiveness was prospectively associated with declines in self-reported physical health three years later, and poor initial self-reported health status did not predict increases in unforgiveness across time. Furthermore, the prospective association of unforgiveness with self-reported health was mediated by a latent positive psychological traits variable.

Conclusion: These results confirm cross-sectional findings suggesting that unforgiveness is related to health. The present study also suggests that unforgiveness has a prospective, but not reciprocal, association with self-reported physical health. Unforgiveness may have its association with self-reported physical health through its interruption of other positive traits that typically confer health benefits.     

Mediation analysis of decisional balance,sun avoidance and sunscreen use in the precontemplation and preparation stages for sun protection

Objective: Mediation analyses of sun protection were conducted testing structural equation models using longitudinal data with three waves. An effect was said to be mediated if the standardised path between processes of change, decisional balance and sun protection outcomes was significant.

Design: Longitudinal models of sun protection using data from individuals in the precontemplation (N = 964) and preparation (N = 463) stages who participated of an expert system intervention.

Main outcome measures: Nine processes of change for sun protection, decisional balance constructs of sun protection (pros and cons), sun avoidance behaviour and sunscreen use.

Results: With the exception of two processes in the preparation stage, processes of change predicted the pros (r = .126–.614), and the pros predicted the outcomes (r = .181–.272). Three models with the cons as mediator in the preparation stage, and none in the precontemplation stage, showed a mediated relationship between processes and outcomes.

Conclusion: In general, mediation analyses found both the process of change-to-pros and pros-to-behaviour paths significant for both precontemplation and preparation stages, and for both sun avoidance and sunscreen use outcomes. Findings provide support for the importance of assessing the role of underlying risk cognitions in improving sun protection adherence.