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 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     

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.     

Constructive Logic with Strong Negation is a Substructural Logic. I

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL _ew of the substructural logic FL _ew . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL _ew (namely, a certain variety of FL _ew -algebras) are term equivalent. This answers a longstanding question of Nelson [30]. Extensive use is made of the automated theorem-prover Prover9 in order to establish the result. The main result of this paper is exploited in Part II of this series [40] to show that the deductive systems N and NFL _ew are definitionally equivalent, and hence that constructive logic with strong negation is a substructural logic over FL _ew . Presented by Heinrich Wansing     

A Cut-Free Sequent System for the Smallest Interpretability Logic

The idea of interpretability logics arose in Visser [Vis90]. He introduced the logics as extensions of the provability logic GLwith a binary modality . The arithmetic realization of A B in a theory T will be that T plus the realization of B is interpretable in T plus the realization of A (T + A interprets T + B). More precisely, there exists a function f (the relative interpretation) on the formulas of the language of T such that T + B C implies T + A f(C).The interpretability logics were considered in several papers. An arithmetic completeness of the interpretability logic ILM, obtained by adding Montagna's axiom to the smallest interpretability logic IL, was proved in Berarducci [Ber90] and Shavrukov [Sha88] (see also Hájek and Montagna [HM90] and Hájek and Montagna [HM92]). [Vis90] proved that the interpretability logic ILP, an extension of IL, is also complete for another arithmetic interpretation. The completeness with respect to Kripke semantics due to Veltman was, for IL, ILMand ILP, proved in de Jongh and Veltman [JV90]. The fixed point theorem of GLcan be extended to ILand hence ILMand ILP(cf. de Jongh and Visser [JV91]). The unary pendant "T interprets T + A" is much less expressive and was studied in de Rijke [Rij92]. For an overview of interpretability logic, see Visser [Vis97], and Japaridze and de Jongh [JJ98].In this paper, we give a cut-free sequent system for IL. To begin with, we give a cut-free system for the sublogic IL4of IL, whose -free fragment is the modal logic K4. A cut-elimination theorem for ILis proved using the system for IK4and a property of Löb's axiom.     

Gleason's Theorem Has a Constructive Proof

Gleason's theorem for R ³ says that if f is a nonnegative function on the unit sphere with the property that f(x) + f(y) + f(z) is a fixed constant for each triple x,y,z of mutually orthogonal unit vectors, then f is a quadratic form. We examine the issues raised by discussions in this journal regarding the possibility of a constructive proof of Gleason"s theorem in light of the recent publication of such a proof.     

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).     

Trajectories of self-efficacy in persons with chronic illness: An explorative longitudinal study

Background: Self-efficacy is important for changing health behaviour in persons with chronic illness. Longer term trajectories have not been previously explored.

Objective: This study’s objective was to explore the trajectories of self-efficacy in two different groups with chronic illnesses attending a patient education course.

Design: The study design was a longitudinal, comparative cohort study with five time points during a one-year follow-up, using repeated measures analysis of variance.

Setting and participants: Persons with morbid obesity (n = 55) and persons with chronic obstructive pulmonary disease (COPD; n = 56) were recruited at the start of patient education courses in Norway and followed-up four times the following year.

Main outcome measure: The General Self-Efficacy Scale was the main outcome.

Results: Obese persons showed a linear pattern of increasing self-efficacy during the follow-up period, whereas persons with COPD had an initial increase followed by a decrease in self-efficacy. Having paid work was associated with a more positive self-efficacy trajectory.

Conclusion: The results provide support for the currently employed patient education course for morbidly obese persons. In contrast, persons with COPD may need more extensive and/or more frequent support in order to increase and maintain self-efficacy across time.     

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.     

Internet-delivered cognitive behavior therapy for anxiety and insomnia in a higher education context

Background and Objectives: Anxiety and insomnia can be treated with internet-delivered Cognitive Behavioral Therapy (iCBT). iCBT may be well-suited to students who are known to be poor help-seekers and suffer these symptoms. iCBT can offer easy access to treatment and increase service availability. The aim of this study was to evaluate the efficacy of anxiety and insomnia iCBT programs in students. Design: A randomized, controlled study. Methods: Students were randomly allocated to intervention (“Anxiety Relief”: n?=?43; “Insomnia Relief”: n?=?48; control: n?=?47). Interventions lasted six weeks. Outcome measures were the State-Trait Anxiety Inventory and the Pittsburgh Sleep Quality Index. Results: Significant within-group reductions in anxiety (t(31)?=?2.00, p?=?.03) with moderate between-groups (compared to control) effect size (d?=?.64) and increases in sleep quality (t(31)?=?3.46, p?=?.002) with a moderate between-groups effect size (d?=?.55) were found for completers of the anxiety program from pre- to post-intervention. Significant within-group increases in sleep quality were found for completers of the insomnia program from pre- to post-intervention (t(35)?=?4.28, p?>?.001) with a moderate between-groups effect size (d?=?.51). Conclusions: Findings support the use of iCBT for anxiety and insomnia in students, and indicate that further research is needed.     

Review of “Clinical Psychology and Psychotherapy as a Science: An Iconoclastic Perspective,” by Luciano L'Abate

Abstract

adult children of divorce speak out, by claire berman. new york: simon&;schuster, 1991, 285 pages, $18.95

adolescents and their families: paths of ego development, by stuart t. hauser with sally i. powers and gil g. noam, new york: free press, 1991, 318 pages, $29.95

alcohol and the addictive brain: new hope for alcoholics from biogenetic research, by kenneth blum, in collaboration with james e. payne. new york: free press, 1991, 320 pages, $24.95     

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.     

Generic generalized Rosser fixed points

To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical (Solovay-type) completeness theorem with respect to PA is obtained for LR. This paper supersedes: Franco Montagna, Extremely undecidable sentences and generic generalized Rosser's fixed points, Rapporto Matematico, No. 95, Siena, 1983.     

Completeness and conservative extension results for some boolean relevant logics

This paper presents completeness and conservative extension results for the boolean extensions of the relevant logic T of Ticket Entailment, and for the contractionless relevant logics TW and RW. Some surprising results are shown for adding the sentential constant t to these boolean relevant logics; specifically, the boolean extensions with t are conservative of the boolean extensions without t, but not of the original logics with t. The special treatment required for the semantic normality of T is also shown along the way.     

Predicting physical activity in adolescents: The role of compensatory health beliefs within the Health Action Process Approach

Objective: Compensatory health beliefs (CHBs), defined as beliefs that healthy behaviours can compensate for unhealthy behaviours, may be one possible factor hindering people in adopting a healthier lifestyle. This study examined the contribution of CHBs to the prediction of adolescents’ physical activity within the theoretical framework of the Health Action Process Approach (HAPA).

Design: The study followed a prospective survey design with assessments at baseline (T1) and two weeks later (T2).

Method: Questionnaire data on physical activity, HAPA variables and CHBs were obtained twice from 430 adolescents of four different Swiss schools. Multilevel modelling was applied.

Results: CHBs added significantly to the prediction of intentions and change in intentions, in that higher CHBs were associated with lower intentions to be physically active at T2 and a reduction in intentions from T1 to T2. No effect of CHBs emerged for the prediction of self-reported levels of physical activity at T2 and change in physical activity from T1 to T2.

Conclusion: Findings emphasise the relevance of examining CHBs in the context of an established health behaviour change model and suggest that CHBs are of particular importance in the process of intention formation.     

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.     

Book reviews

Abstract

Eldercare by James Kenny&;Stephen Spicer. Buffalo, NY: Prometheus Books, 1988, 152 pages, $11.95 paper

Lonely All the Time: Recognizing, Understanding and Overcoming Sex Addiction, for Addicts and Co-dependents by Ralph Earle&;Gregory Crow with Kevin Osborn. New York: Pocket Books, 1989, 337 pages, $19.95

The Imperfect Therapist: Learning from Failure in Therapeutic Practice by Jeffrey A. Kotter&;Diane S. Blau. San Francisco: Jossey-Bass, 1989, 188 pages, $19.95

Families with a Difference: Varieties of Surrogate Parenthood by Michael Humphreys&;Heather Humphreys. New York: Routledge, 1988, 177 pages, $45.00

Between Husbands and Wives: Communication in Marriage by Mary Anne Fitzpatrick. Newbury Park, CA: Sage Publications, 1988, 283 pages, $35.00 hardbound, $16.50 paperback     

Social cognitions measured in 4 to 6 year olds are predictive of objectively measured physical activity

Objective: This study tested whether social cognitions from the reasoned action approach (RAA) can be reliably measured in a sample of primary school children (aged 4–6 years) and whether these RAA measures are predictive of physical activity.

Design: Longitudinal observational study with repeated measures over six months.

Measures: RAA variables were measured using a novel choice paradigm between physically active and sedentary pastimes. Relative reinforcing value, covariates (sex, age, deprivation and BMI) and physical activity by accelerometry (primary outcome) were also measured.

Results: RAA cognitions could be measured with acceptable retest reliability and discriminant validity and social norms regarding parents and teachers (but not friends) were correlated with physical activity and change in physical activity when relative reinforcing value and other covariates were controlled for.

Conclusions: RAA cognitions can be reliably measured in primary school children aged 4–6 and RRA measures appear useful in understanding children’s activity choices and may potentially inform future interventions.