Normal Modal Substructural Logics with Strong Negation

We introduce modal propositional substructural logics with strong negation, and prove the completeness theorems (with respect to Kripke models) for these logics.     

Manifest Rationality Reconsidered: Reply to my Fellow Symposiasts

In this paper, I respond to papers on my Manifest Rationality (2000) by Leo Groarke, Hans Hansen, David Hitchcock, and Christopher Tindale presented at the meetings of the Ontario Philosophical Society, October 2000. From the many useful challenges they have directed at my position, I have chosen to focus on two. The dominant issue raised by their papers concerns my definition of argument, and particularly problems with the idea of a dialectical tier. I have selected that as the first strand. Second, several have raised questions that deal with the relationship between logic, rhetoric and dialectic. That is the second strand.     

Modal Logic,Truth, and the Master Modality

In the paper (Braüner, 2001) we gave a minimal condition for the existence of a homophonic theory of truth for a modal or tense logic. In the present paper we generalise this result to arbitrary modal logics and we also show that a modal logic permits the existence of a homophonic theory of truth if and only if it permits the definition of a so-called master modality. Moreover, we explore a connection between the master modality and hybrid logic: We show that if attention is restricted to bidirectional frames, then the expressive power of the master modality is exactly what is needed to translate the bounded fragment of first-order logic into hybrid logic in a truth preserving way. We believe that this throws new light on Arthur Prior's fourth grade tense logic.     

Computing with Cylindric Modal Logics and Arrow Logics,Lower Bounds

The complexity of the satisfiability problems of various arrow logics and cylindric modal logics is determined. As is well known, relativising these logics makes them decidable. There are several parameters that can be set in such a relativisation. We focus on the following three: the number of variables involved, the similarity type and the kind of relativised models considered. The complexity analysis shows the importance and relevance of these parameters.     

An Elementary Construction for a Non-elementary Procedure

We consider the problem of the product finite model property for binary products of modal logics. First we give a new proof for the product finite model property of the logic of products of Kripke frames, a result due to Shehtman. Then we modify the proof to obtain the same result for logics of products of Kripke frames satisfying any combination of seriality, reflexivity and symmetry. We do not consider the transitivity condition in isolation because it leads to infinity axioms when taking products.     

A Predicate Logical Extension of a Subintuitionistic Propositional Logic

We develop a predicate logical extension of a subintuitionistic propositional logic. Therefore a Hilbert type calculus and a Kripke type model are given. The propositional logic is formulated to axiomatize the idea of strategic weakening of Kripke's semantic for intuitionistic logic: dropping the semantical condition of heredity or persistence leads to a nonmonotonic model. On the syntactic side this leads to a certain restriction imposed on the deduction theorem. By means of a Henkin argument strong completeness is proved making use of predicate logical principles, which are only classically acceptable.     

Posttraumatic Stress Disorder and executive dysfunction among children and adolescents: A Latent Profile Analysis

Background/ObjectiveThe current study aimed to examine the relationship between Posttraumatic Stress Disorder (PTSD) symptoms and executive dysfunction in children and adolescents after psychological trauma.MethodParticipants were 13,438 of children and adolescents aged 6 to 18 years exposed to the 2008 Wenchuan earthquake. PTSD and dysexecutive symptoms were assessed using the UCLA PTSD Reaction Index for Children and the Self-Report Dysexecutive Questionnaire. Latent Profile Analysis (LPA) was conducted using Mplus version 7.4. Subgroup differences in trauma exposure and quality of life were calculated using ANCOVA.ResultsA 4-class parallel model was found to best describe latent PTSD symptom profiles and executive dysfunction. Individuals in higher symptom groups showed more trauma exposure and lower quality of life.ConclusionsThis LPA study shed light on the relationship between PTSD and executive dysfunction symptoms in children and adolescents. The correlation between PTSD and executive dysfunction was maintained after individual differences were taken into consideration. Our findings provide a new view on how PTSD relates to executive dysfunction and several suggestions for treating child and adolescent PTSD patients.     

Can a before-school physical activity program decrease bullying victimization in disadvantaged children? The Active-Start Study

Background/ObjectiveTo test the effectiveness of an 8-week before-school physical activity program to reduce bullying victimization among a group of socially disadvantaged children in the Active-Start study.MethodA non-blinded randomized controlled trial was conducted in three public schools classified as highly vulnerable and located in a deprived area of Santiago (Chile). A total of 5 classes participated, totaling 170 fourth grade children. The intervention was delivered before starting the first school-class (8:00–8:30 a.m.). The program lasted for 8 weeks. Primary outcome measurement on bullying victimization was assessed by the CUBE questionnaire at baseline and post-intervention.ResultsThere was a statistically significant reduction in the probability of suffering physical bullying (OR= 0.18, 95% CI, 0.04-0.82; p= .027) and verbal bullying (OR=0.13, 95% CI, 0.02-0.97; p= .046) after the 8-week program.ConclusionsParticipation in an 8-week before-school physical activity intervention implemented in schools located in a disadvantaged district in Santiago (Chile) resulted in lower levels of bullying victimization among study participants. The Active-Start program may be a feasible and potentially scalable intervention option to improve the climate and pro-sociality environment at schools.     

ALTERNATIVE AXIOMATICS AND COMPLEXITY OF DELIBERATIVE STIT THEORIES

We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and Chellas’s STIT.     

An Approach to Glivenko’s Theorem in Algebraizable Logics

In a classical paper [15] V. Glivenko showed that a proposition is classically demonstrable if and only if its double negation is intuitionistically demonstrable. This result has an algebraic formulation: the double negation is a homomorphism from each Heyting algebra onto the Boolean algebra of its regular elements. Versions of both the logical and algebraic formulations of Glivenko’s theorem, adapted to other systems of logics and to algebras not necessarily related to logic can be found in the literature (see [2, 9, 8, 14] and [13, 7, 14]). The aim of this paper is to offer a general frame for studying both logical and algebraic generalizations of Glivenko’s theorem. We give abstract formulations for quasivarieties of algebras and for equivalential and algebraizable deductive systems and both formulations are compared when the quasivariety and the deductive system are related. We also analyse Glivenko’s theorem for compatible expansions of both cases. Presented by Jacek Malinowski