An axiomatization of the modal theory of the veiled recession frame

The veiled recession frame has served several times in the literature to provide examples of modal logics failing to have certain desirable properties. Makinson [4] was the first to use it in his presentation of a modal logic without the finite model property. Thomason [5] constructed a (rather complicated) logic whose Kripke frames have an accessibility relation which is reflexive and transitive, but which is satisfied by the (non-transitive) veiled recession frame, and hence incomplete. In Van Benthem [2] the frame was an essential tool to find simple examples of incomplete logics, axiomatized by a formula in two proposition letters of degree 2, or by a formula in one proposition letter of degree 4 (the degree of a modal formula is the maximal number of nested occurrences of the necessity operator in ). In [3] we showed that the modal logic determined by the veiled recession frame is incomplete, and besides that, is an immediate predecessor of classical logic (or, more precisely, the modal logic axiomatized by the formula pp), and hence is a logic, maximal among the incomplete ones. Considering the importance of the modal logic determined by the veiled recession frame, it seems worthwhile to ask for an axiomatization, and in particular, to answer the question if it is finitely axiomatizable. In the present paper we find a finite axiomatization of the logic, and in fact, a rather simple one consisting of formulas in at most two proposition letters and of degree at most three.The paper was written with support of the Netherlands organization for the Advancement of Pure Research (Z.W.O.).     

Cross-cultural diagnostic applicability of the Pictogram Test

The aim of this study was to determine whether the Pictogram Test (PT; Vygostsky, 1960) a test of logical memory that was developed in Russia, is applicable for diagnosing and understanding thought disturbances in schizophrenia within an English-speaking population. Participants included 62 patients with schizophrenia or schizoaffective disorders and 80 community nonpatients from Russia and the United States. We used correlational analysis to organize PT variables into Concrete (CI), Attribute (AI), and Geometric (GI) indexes. Discriminant function analysis revealed that only AI and GI had significant discriminatory power. These indexes correctly classified 91% of English-speaking and 86% of Russian-speaking participants as either patients or nonpatients. Controlling for age and education, multivariate analysis revealed that patients had significantly lower AI and significantly higher GI scores relative to nonpatients, and those differences were similar across languages. These results indicate that the PT can discriminate between patients with schizophrenia or schizoaffective disorders and nonpatients, which suggests that characteristics of the PT could be used to understand the mechanism of logical thinking in patients and nonpatients.     

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.     

Pretabular varieties of modal algebras

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras.     

Non-equilibrium dynamics as an indispensable characteristic of a healthy biological system

Healthy systems in physiology and medicine are remarkable for their structural variability and dynamical complexity. The concept of fractal growth and form offers novel approaches to understanding morphogenesis and function from the level of the gene to the organism. For example, scale-invariance and long-range power-law correlations are features of non-coding DNA sequences as well as of healthy heartbeat dynamics. For cardiac regulation, perturbation of the control mechanisms by disease or aging may lead to a breakdown of these long-range correlations that normally extend over thousands of heartbeats. Quantification of such long-range scaling alterations are providing new approaches to problems ranging from molecular evolution to monitoring patients at high risk of sudden death. We briefly review recent work from our laboratory concerning the application of fractals to two apparently unrelated problems: DNA organization and beat-to-beat heart rate variability. We show how the measurement of long-range power-law correlations may provide new understanding of nucleotide organization as well as of the complex fluctuations of the heartbeat under normal and pathologic conditions.     

Assessment and validation of diagnostic interviewing skills for the mental health professions

A behavioral test was developed to assess the quality of diagnostic interviewing skills of (future) mental health professionals. Two aspects of diagnostic interviewing ability are distinguished: process skills, reflecting the interpersonal and communication skills; and content skills, referring to the information-gathering ability of the interviewer. It was found that diagnostic interviewing can be reliably measured with respect to interrater reliability. However, interviewer performance on one case proved to be a poor predictor of performance on other cases. It was concluded that a large number of cases is required to obtain reliable scores of general diagnostic interviewing ability. Validity was supported by the correlational analyses. Process skills were strongly related to patient satisfaction, whereas content skills were related to the amount of relevant information given by the patient and the accuracy of the diagnostic formulation and treatment plan.     

Fragments of R-Mingle

The logic RM and its basic fragments (always with implication) are considered here as entire consequence relations, rather than as sets of theorems. A new observation made here is that the disjunction of RM is definable in terms of its other positive propositional connectives, unlike that of R. The basic fragments of RM therefore fall naturally into two classes, according to whether disjunction is or is not definable. In the equivalent quasivariety semantics of these fragments, which consist of subreducts of Sugihara algebras, this corresponds to a distinction between strong and weak congruence properties. The distinction is explored here. A result of Avron is used to provide a local deduction-detachment theorem for the fragments without disjunction. Together with results of Sobociski, Parks and Meyer (which concern theorems only), this leads to axiomatizations of these entire fragments — not merely their theorems. These axiomatizations then form the basis of a proof that all of the basic fragments of RM with implication are finitely axiomatized consequence relations.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

Influence of chronic corticosterone and glucocorticoid receptor antagonism in the amygdala on fear conditioning

Glucocorticoid receptor activation within the basolateral amygdala (BLA) during fear conditioning may mediate enhancement in rats chronically exposed to stress levels of corticosterone. Male Sprague-Dawley rats received corticosterone (400 microg/ml) in their drinking water (days 1-21), a manipulation that was previously shown to cause hippocampal CA3 dendritic retraction. Subsequently, rats were adapted to the fear conditioning chamber (day 22), then trained (day 23), and tested for conditioned fear to context and tone (day 25). Training consisted of two tone (20s) and footshock (500 ms, 0.25 mA) pairings. In Experiment 1, muscimol (4.4 nmol/0.5 microl/side), a GABAergic agonist, was microinfused to temporarily inactivate the BLA during training. Rats given chronic corticosterone showed enhanced freezing to context, but not tone, compared to vehicle-supplemented rats. Moreover, BLA inactivation impaired contextual and tone conditioning, regardless of corticosterone treatment. In Experiment 2, RU486 (0, 0.3, and 3.0 ng/0.2 microl/side) was infused on training day to antagonize glucocorticoid receptors in the BLA. Corticosterone treatment enhanced fear conditioning to context and tone when analyzed together, but not separately. Moreover, RU486 (3.0 ng/side) selectively exacerbated freezing to context in chronic corticosterone-exposed rats only, but failed to alter tone conditioning. Serum corticosterone levels were negatively correlated with contextual, not tone, conditioning. Altogether, these suggest that chronic corticosterone influences fear conditioning differently than chronic stress as shown previously. Moreover, chronic exposure to corticosteroids alters BLA functioning in a non-linear fashion and that contextual conditioning is influenced more than tone conditioning by chronic corticosterone and BLA glucocorticoid receptor stimulation.     

Interpretation of pronouns in VP-ellipsis constructions in Dutch Broca's and Wernicke's aphasia

In this paper, we investigate the ability of Dutch agrammatic Broca's and Wernicke's aphasics to assign reference to possessive pronouns in elided VP constructions. The assumption is that the comprehension problems in these two populations have different sources that are revealed in distinct patterns of responses. The focus is primarily on the performance of the agrammatic group whose errors in comprehension are not viewed as a consequence of a breakdown of grammatical knowledge but as a result of limited processing resources (for an overview see Grodzinsky, 2000). The results of the present study provide evidence for the psycholinguistic reality of the economy hierarchy as proposed in the Primitives of Binding (Reuland, 2001). According to the economy hierarchy proposed for the non-brain-damaged, the more economical semantic dependencies are preferred over the costlier discourse dependencies. This hierarchy is reflected in agrammatic aphasia where the semantic dependencies are available on time and preferred over the discourse dependences that are not available on time as a result of the lack of processing resources with consequences for comprehension.