Logic for physical space

Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones in the logical representation of space and investigate current trends. In doing so, we do not only consider classical logic, but we indulge ourselves with modal logics. These present themselves naturally by providing simple axiomatizations of different geometries, topologies, space-time causality, and vector spaces.     

Restoration: S. A. Yanovskaya's path in logic

This article presents the story of S. A. Yanovskaya's epiphany—particularly, her shift from hard-line communist orthodoxy and hostility towards ‘bourgeois minded’ Soviet-Russian mathematicians to vigorous support of mathematical logic. In light of this evidence, S. A. Yanovskaya (1896–1966) may be considered as a spiritual leader and administrative founder of modern mathematical research and education in the USSR/Russia.     

Comparing Semantics of Logics for Multi-Agent Systems

We draw parallels between several closely related logics that combine — in different proportions — elements of game theory, computation tree logics, and epistemic logics to reason about agents and their abilities. These are: the coalition game logics CL and ECL introduced by Pauly 2000, the alternating-time temporal logic ATL developed by Alur, Henzinger and Kupferman between 1997 and 2002, and the alternating-time temporal epistemic logic ATEL by van der Hoek and Wooldridge (2002). In particular, we establish some subsumption and equivalence results for their semantics, as well as interpretation of the alternating-time temporal epistemic logic into ATL. The focus in this paper is on models: alternating transition systems, multi-player game models (alias concurrent game structures) and coalition effectivity models turn out to be intimately related, while alternating epistemic transition systems share much of their philosophical and formal apparatus. Our approach is constructive: we present ways to transform between different types of models and languages.     

Measuring mindfulness—the Freiburg Mindfulness Inventory (FMI)

Mindfulness, a concept originally derived from Buddhist psychology, is essential for some well-known clinical interventions. Therefore an instrument for measuring mindfulness is useful. We report here on two studies constructing and validating the Freiburg Mindfulness Inventory (FMI) including a short form. A preliminary questionnaire was constructed through expert interviews and extensive literature analysis and tested in 115 subjects attending mindfulness meditation retreats. This psychometrically sound 30-item scale with an internal consistency of Cronbach alpha = .93 was able to significantly demonstrate the increase in mindfulness after the retreat and to discriminate between experienced and novice meditators. In a second study we broadened the scope of the concept to 86 subjects without meditation experience, 117 subjects with clinical problems, and 54 participants from retreats. Reducing the scale to a short form with 14 items resulted in a semantically robust and psychometrically stable (alpha = .86) form. Correlation with other relevant constructs (self-awareness, dissociation, global severity index, meditation experience in years) was significant in the medium to low range of correlations and lends construct validity to the scale. Principal Component Analysis suggests one common factor. This short scale is sensitive to change and can be used also with subjects without previous meditation experience.     

The Basic Algebra of Game Equivalences

We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities.En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways, game identities into modal formulae.The completeness proof is based on reduction of game terms to a certain minimal canonical form, by using only the axiomatic identities, and on showing that the equivalence of two minimal canonical terms can be established from these identities.     

Single-letter coloring and spatial cuing do not eliminate or reduce a semantic contribution to the Stroop effect

The automaticity of semantic activation in the Stroop task is still the subject of considerable debate (Augustinova & Ferrand, 2007; Manwell, Roberts, & Besner, 2004). The present experiments were designed to assess whether coloring and cuing a single letter (vs. all letters) in the Stroop task reliably eliminates semantically based Stroop interference or whether the elimination observed by Manwell et al. was due to insufficient statistical power. Experiment 1 was an exact replication of the experiment conducted by Manwell and colleagues and involved a large population. Experiment 2 replicated and extended Experiment 1 by controlling for initial fixation. In line with previous findings obtained by Augustinova and Ferrand, both experiments indicated that coloring and cuing a single letter failed to eliminate or even reduce the semantically based Stroop effect. Thus, these results add to the growing body of evidence suggesting that semantic activation in the Stroop task is automatic.     

Algorithmic correspondence and completeness in modal logic. V. Recursive extensions of SQEMA

The previously introduced algorithm SQEMA computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend SQEMA with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of modal formulae in the extension of first-order logic with monadic least fixed-points FOμ. This computation operates by transforming input formulae into locally frame equivalent ones in the pure fragment of the hybrid μ-calculus. In particular, we prove that the recursive extension of SQEMA succeeds on the class of ‘recursive formulae’. We also show that a certain version of this algorithm guarantees the canonicity of the formulae on which it succeeds.     

The beneficial effects of prosocial spending on happiness: work hard,make money,and spend it on others?

Previous research has shown that the way people spend their money is as important to happiness as how much money people earn. Specifically, it has been shown that spending money on others contributes more to an individual’s happiness than spending money on oneself. In the present study, we investigated this effect and examined the role of the money’s origin. Students were randomly assigned either to spend a small amount of money on themselves or to spend the money on others. Moreover, half of the participants received the money as a wage, whereas the other half received the money as a windfall. The results replicated previous research indicating that prosocial spenders report greater happiness than do selfish spenders. However, the happiness effect was unaffected by the source of the money (i.e. wage vs. windfall). Implications for well-being and happiness are discussed.