Solving Smullyan Puzzles with Formal Systems

Solving numeric, logic and language puzzles and paradoxes is common within a wide community of high school and university students, fact witnessed by the increasing number of books published by mathematicians such as Martin Gardner (popular books as old as Gardner in Aha! insight. W. H. Freeman & Co., London, ass="CitationRef">1978, Wheels, life and other mathematical amusements. W H Freeman & Co., London, ass="CitationRef">1985), Douglas Hofstadter [in one of the best popular science books on paradoxes (Hofstadter in Godel, escher, bach: an eternal golden braid, Penguin, London, ass="CitationRef">2000)], inspired by Gödel’s incompleteness theorems), Patrick Hughes and George Brecht (see Hughes and Brecht in Vicious circles and infinity, an anthology of paradoxes. Penguin Books, London, ass="CitationRef">1993) and Raymond M. Smullyan (the most well known being Smullyan in Forever undecided, puzzle guide to godel. Oxford Paperbacks, Oxford ass="CitationRef">1988, To Mock a Mockingbird and other logic puzzles. Oxford Paperbacks, Oxford ass="CitationRef">2000, The lady or the tiger? And other logic puzzles. Dover Publications Inc., Mineola ass="CitationRef">2009), inter alia. Books by Smullyan (such as Smullyan ass="CitationRef">1988, ass="CitationRef">2000) are, however, much more involved, since ass="EmphasisTypeItalic ">they introduce learning trajectories and strategies across several subjects of mathematical logic, as difficult as combinatorial logic (see, e.g., Smullyan ass="CitationRef">2000), computability theory (see Smullyan ass="CitationRef">1988), and proof theory (see Smullyan ass="CitationRef">1988, ass="CitationRef">2009). These books provide solutions to their suggested exercises. Both statements and their solutions are written in the natural language, introducing some informal algorithms. As an exercise in Mathematics we wonder if an easy proof system could be devised to solve the amusing equations proposed by Smullyan in his books. Moreover, university students of logic could well train themselves in constructing deductive systems to solve puzzles instead of a non-uniform treatment one by one. In this paper, addressing students, we introduce one such formal systems, a tableaux approach able to provide the solutions to the puzzles involving either propositional logic, first order logic, or aspect logic. Let the reader amuse herself or himself!     

The specificity of age-related decline in interpretation of emotion cues from prosody

Older adults are not as good as younger adults at decoding prosodic emotions. We sought to determine the specificity of this finding. Performance of older and younger adults was compared on a prosodic emotion task, a "pure" prosodic emotion task, a linguistic prosody task, and a "pure" linguistic prosody task. Older adults were less accurate at interpreting prosodic emotion cues and nonemotional contours, concurrent semantic processing worsened interpretation, and performance was further degraded when identifying negative emotions and questions. Older adults display a pervasive problem interpreting prosodic cues, but further study is required to clarify the stage at which performance declines.     

Reduced habituation to angry faces: increased attentional capture as to override inhibition of return

The aim of this paper was to study whether real angry faces do capture attention to the extent of overcoming the inhibition of return (IOR) effect and whether the anxiety level of participants modulates this effect by stressing biases toward threatening stimuli. With this purpose, participants categorized the emotional valence of face targets in a standard spatial cueing procedure suitable to measure IOR. In Experiment 1, participants were selected according to their high vs. low-trait anxiety, whereas in Experiment 2 participants were induced a positive vs. anxiety mood state. The typical IOR effect was observed with neutral and happy face targets, which disappeared with angry face targets. Similar results were observed for all anxiety groups and in both experiments. The results indicate that IOR is overridden when the target is a biologically relevant angry face, as highly relevant targets should suffer less from habituation to attentional capture regardless of anxiety. We suggest that these data show that attentional capture is less likely to habituate for threatening information, so that no cost is measured in detecting new threatening information appearing at recently cued locations.     

Legacies of Srebrenica: The Dutch Factor in EU‐Serbian Relations

Having been traumatized by the actions of the Bosnian Serb army and its primary supporter Serbia in Srebrenica, the Netherlands insisted on applying strict EU conditionality criteria for Belgrade's candidacy. The Dutch determination to repeatedly stall the process of EU‐Serbian negotiations and to snub the preferences of the rest of the EU members cannot be adequately explained without taking into account the role of self‐conscious affect. The article not only provides a fresh perspective of the enlargement process, but it also offers revisions to the habituated‐deliberative choice hypothesis, which to date has not taken into account the role of self‐conscious affect.     

The owl and the pussycat: Gaze cues and visuospatial orienting

Recent research has shown that nonpredictive gaze cues trigger reflexive shifts in attention toward the looked-at location. But just how generalizable is this spatial cuing effect? In particular, are people especially tuned to gaze cues provided by conspecifics, or can comparable shifts in visual attention be triggered by other cue providers and directional cues? To investigate these issues, we used a standard cuing paradigm to compare the attentional orienting produced by different cue providers (i.e., animate vs. inanimate) and directional cues (i.e., eyes vs. arrows). The results of three experiments revealed that attentional orienting was insensitive to both the identity of the cue provider and the nature of the triggering cue. However, compared with arrows, gaze cues prompted a general enhancement in the efficiency of processing operations. We consider the implications of these findings for accounts of reflexive visual orienting.     

Interpretation mistakes in statistical methods: their importance and some recommendations

Interpretation mistakes in statistical methods: Their importance and some recommendations. Prior research has identified some of the most common misconceptions on how researchers interpret the results of significance tests. In this study, we examine the scope of these misconceptions in a sample of university professors and researchers from Spain on the basis of a short questionnaire. The obtained results provide important information: i) to prevent wrong interpretation from the data, ii) to correct the wrong use of statistical testing, iii) to suggest new ways of examining the data, and iv) to propose some modifications on the editorial criteria to publish scientific work.     

Quality service in supermarkets: a proposal of measurement

This assignment has the aim of going deeply into the study of service quality perception in supermarkets. The research tries to find the criterion used when rating the services received in a supermarket and also to elaborate an instrument to measure the service quality in this context. From the review of the existing bibliography, four theoretical factors and a thirteen items scale have been composed. These four factors are: price, product, service and image and fresh product. In order to check the psychometrical properties of the questionnaire we carried out a computer assisted telephone interviewing (CATI) with a sample of 300 interviews. The results obtained allow us to show a scale with a factorial structure of 4 dimensions that throws up optimal indexes of reliability and validity. At the same time we conclude that the variable called establishment global rate is an important variable in the perceptive structure of the consumers.     

How Robert M. MacIver was forgotten: Columbia and American sociology in a new light, 1929-1950

It is necessary to reevaluate the role of the Department of Sociology at Columbia University in the years 1929-1950. The impact of Robert M. MacIver, who played a significant role in the exchange between European and American thinkers, is examined, as well as his marginalization. It is argued that in the 1930s it was characteristic that the sociologists in the centers in Chicago and Columbia exchanged their disciplinary functions. It was MacIver's Columbia that took on the role of advocate of humanistic sociology and Mead's and Cooley's heritage.