Matrices,primitive satisfaction and finitely based logics

We examine the notion of primitive satisfaction in logical matrices. Theorem II. 1, being the matrix counterpart of Baker's well-known result for congruently distributive varieties of algebras (cf [1], Thm. 1.5), links the notions of primitive and standard satisfaction. As a corollary we give the matrix version of Jónsson's Lemma, proved earlier in [4]. Then we investigate propositional logics with disjunction. The main result, Theorem III. 2, states a necessary and sufficient condition for such logics to be finitely based.     

Logical matrices and the amalgamation property

The main result of the present paper — Theorem 3 — establishes the equivalence of the interpolation and amalgamation properties for a large family of logics and their associated classes of matrices.     

Towards a topological philosophy

This article examines the use of mathematical concepts in philosophy, focusing on topology, which may be viewed as a modern supplement to geometry. We show that Plato and Parmenides were already employing geometric ideas in their research, and discuss three examples of the application of topology to philosophical problems: the first concerns the analysis of the Cartesian distinction between res extensa and res cogitans, the second the ontology of possible worlds of Wittgenstein's Tractatus, and the third Leibniz's monadology. We also consider the role of topology in mathematical explanations of the sort found in science, arguing that it can perform a role in philosophy that is of comparable importance.     

Prevalence and correlates of depressive symptoms following traumatic brain injuries in children.

The prevalence and correlates of depressive symptoms following childhood traumatic brain injuries (TBI) were examined using data drawn from a prospective longitudinal study. Participants included 38 children with severe TBI, 51 with moderate TBI, and 55 with orthopedic injuries (OI). Assessments occurred shortly after injury (baseline) and at 6- and 12-month follow-ups. Children completed the Child Depression Inventory (CDI). Parents rated depressive symptoms using the Child Behavior Checklist (CBC), with baseline ratings reflecting premorbid status. Assessments also included measures of children's neurocognitive functioning and the family environment. The three groups did not differ overall in self-reported symptoms on the CDI, but did display different trends over time. The three groups did not differ on parent ratings of premorbid depressive symptoms on the CBC, but parents reported more depressive symptoms in the TBI groups than in the OI group at 6- and 12-month follow-ups. Child and parent reports were correlated for children in the TBI groups, but not for those in the OI group. Depressive symptoms were related to socioeconomic status in all groups. Socioeconomic status also was a significant moderator of group differences, such that the effects of TBI were exacerbated in children from more disadvantaged homes. Although self-reports of depressive symptoms were related inconsistently to children's verbal memory, parent reports of depressive symptoms were unrelated to IQ or verbal memory. The findings suggest that TBI increases the risk of depressive symptoms, especially among more socially disadvantaged children, and that depressive symptoms are not strongly related to post-injury neurocognitive deficits.     

The ADH gene cluster SNP rs1789891 and temperamental dimensions in patients with alcohol dependence and affective disorders

This study had three objectives: (1) to assess the relationship between the single nucleotide polymorphism (SNP) rs1789891 in the alcohol dehydrogenase gene cluster and alcohol dependence and affective disorders; (2) to assess the differences in the Regulative Theory of Temperament (RTT) traits between an alcohol dependent group, an affective disorders group, and a healthy group; and (3) to assess the relationship between rs1789891 and temperament traits in a healthy group, taking into account the interaction of genotype and sex. The SNP rs1789891 was genotyped in a group of 194 alcohol dependent men, aged 21 to 71 years; 137 patients with affective disorders, including 51 males and 86 females, aged 19 to 85 years; and a group of 207 healthy individuals, including 89 males and 118 females, aged 18 to 71 years. Temperament traits (briskness, perseveration, sensory sensitivity, emotional reactivity, endurance, and activity) were assessed in all groups using the Formal Characteristics of Behaviour‐Temperament Inventory. The comparative analysis of genotypic frequencies showed no significant differences between patients with alcoholism or affective disorders and those in the control group. Alcohol dependent men and the affective disorder group were characterised by higher levels of emotional reactivity (p‐value 1.4e‐5 and 9.84e‐7, respectively) and lower levels of briskness, sensory sensitivity, endurance, and activity (p‐value from 3.76e‐8 to 0.012) when compared to the healthy group. The rs1789891 polymorphism was associated with briskness (p = 0.02), sensory sensitivity (p = 0.036), and activity (p = 0.049). None of the results were statistically significant after Bonferroni correction.