Cut-free tableau calculi for some propositional normal modal logics

We give sound and complete tableau and sequent calculi for the prepositional normal modal logics S4.04, K4B and G ⁰(these logics are the smallest normal modal logics containing K and the schemata A A, A A and A ( A); A A and AA; A A and ((A A) A) A resp.) with the following properties: the calculi for S4.04 and G ⁰are cut-free and have the interpolation property, the calculus for K4B contains a restricted version of the cut-rule, the so-called analytical cut-rule.In addition we show that G ⁰is not compact (and therefore not canonical), and we proof with the tableau-method that G ⁰is characterised by the class of all finite, (transitive) trees of degenerate or simple clusters of worlds; therefore G ⁰is decidable and also characterised by the class of all frames for G ⁰.Research supported by Fonds zur Förderung der wissenschaftlichen Forschung, project number P8495-PHY.Presented by W. Rautenberg     

On finite approximability of ψ-intermediate logics

The aim of this note is to show (Theorem 1.6) that in each of the cases: = {, }, or {, , }, or {, , } there are uncountably many -intermediate logics which are not finitely approximable. This result together with the results known in literature allow us to conclude (Theorem 2.2) that for each : either all -intermediate logics are finitely approximate or there are uncountably many of them which lack the property.     

Untersuchungen über Zusammenhänge zwischen drei Leistungsfaktoren und Antworten auf Fragebogenitems

Zusammenfassung 90 Oberschüler beantworteten 214 Fragebogenitems und bearbeiteten 41 Leistungsaufgaben, die zusammen drei in einer faktorenanalytischen Untersuchung von Jäger gefundene Faktoren repräsentieren. Die Zusammenhänge zwischen Fragen- und Aufgabengruppen wurden korrelations- und faktorenanalytisch untersucht. Die Leistungen in den den Faktor Anschauungsgebundenes Denken repräsentierenden Aufgaben korrelierten positiv mit durch Fragebogenitems definierten Verhaltensdimensionen Hinwendung zum Konkreten und Wohlbefinden-Emotionale Stabilität-Leistungszuversicht. Die Leistungen in Einfallsreichtum und Produktivität korrelierten positiv mit Überlegenheitsgefühl-Leistungszuversicht-Emotionale Stabilität-Wohlbefinden, sowie mit Spontaneität, Selbständigkeit und Flexibilität. Die Leistungen in einem dritten Faktor, der Tempo-Motivation bei einfach strukturierten Aufgaben benannt werden könnte, korrelierten positiv mit Soziale Zuwendung-Extraversion und scheint darüberhinaus mit einem Merkmal kompensatorischer Leistungsehrgeiz in Beziehung zu stehen. Die Ergebnisse werden diskutiert und Hypothesen zur Überprüfung und Ausweitung der Befunde formuliert.

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Summary 90 subjects answered 214 questionnaire and 41 ability test items, tbe latter representing three factors found by Jäger in an extensive factor analytic investigation. The relations between all the variables were analyzed by correlational and factor analytic methods. It was found that the ability called vision-related thinking is positively correlated with questionnaire-defined behavioral dimensions called reality orientation and well-being-emotional stability-achievement confidence. The ability fluency and productivity is positively correlated with superiority feeling-achievement confidence-emotional stability-well-being, with spontaneity, independence, and flexibility. Speed-motivation in simple tasks is positively correlated with social participation-extraversion and seems to be related to a trait called compensatory achievement orientation. The findings are discussed and hypotheses for subsequent test and extension formulated.

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Wir danken Herrn Dr. A. O. Jäger für die freundliche Erlaubnis, Aufgaben und Ergebnisse aus seiner Forschungsarbeit vor deren Veröffentlichung zu verwerten. Herrn Dipl.-Math. P. Schnell vom Deutschen Rechenzentrum in Darmstadt für die Durchführung der Berechnungen, unseren Kollegen, den Dipl.-Psychologen K. Althoff, Ch. Balzert, K. D. Stoll und P. Wolff für freundliche Mithilfe, nicht zuletzt unseren Vpn für ihren Einsatz und den Herrn Oberstudiendirektoren Jung, Hadamar, Dr. Keller, Montabaur, und Sauer, Limburg, für die Erlaubnis zur Durchführung der Untersuchungen an ihren Schulen.     

Distribution of the feature [+animate] in the lexicon of the child

Piaget suggests that animistic thinking is a pervasive feature of children's cognition. To test this notion, 4- to 8-year-old children were shown several inanimate objects and asked to pick those which perform activities characteristic of living organisms. These activities were typified by six verbs: eat, sleep, breathe, grow, die,, and be alive. Fifty percent of the younger children responded animistically, by misattributing life processes to inanimate objects, but only 18% of their total responses were animistic. Twenty percent of the older children responded animistically, but only 20% of their responses were animistic. In Experiment II, children were shown drawings singly and asked if the object could perform activities named by one of the six verbs. Results were similar to those of Experiment I but with somewhat less animism. Experiment III required children to spontaneously name things that are alive. There were no animistic responses. It was concluded that animistic thinking is not a genuine phenomenon but linguistic confusion elicited by novel objects and unfamiliar words.This work was supported by NSF Grant GB 23083.A portion of the data of Experiment I constituted a Bachelor Honors Thesis conducted by the first author under the direction of the second and submitted to Florida State University. These data were presented at the meeting of the Southeastern Psychological Association, New Orleans, April 1973.     

Depression and Anxiety in Persons with Parkinson's Disease With and Without “On–Off” Phenomena

On–off phenomena in Parkinson's disease (PD) are unpredictable motor fluctuations associated with long-term levodopa use. Mood fluctuations have been found to coincide with the motor fluctuations in that depression and anxiety increase while the person with PD is in the off state. What has been relatively unexplored is whether those persons with PD who have on–off phenomena differ psychologically in fundamental ways from those who do not have on–off phenomena. In the present study, depression and anxiety symptoms were assessed in 36 persons with PD (n = 14 with on–off phenomena, n = 22 without on–off phenomena). All those with on–off phenomena were assessed in their on state. Those persons with PD with on–off phenomena had significantly higher levels of anxiety than those without on–off phenomena. However, both groups, regardless of on–off status, were mildly depressed. Neurobiological interpretations of the results implicate the locus coeruleus in the pathogenesis of both on–off phenomena and anxiety, whereas psychological interpretations of the results involve the issues of learned helplessness and control over health symptoms in PD.     

Care and the dynamics of social world

The concept of social world is formulated for the purpose of deepening our understanding of the dynamics of inclusion, exclusion, and care in interpersonal interaction. World is defined as an irreducible subject-object polarity.Social world is the extremely fragile environment within which people meet, and is easily destroyed. With special attention to family and church life, the conditions for maintaining or losing this environment are examined. Three levels of social world are defined. On the highest level, mutual care, rather than shared opinion, is seen as the factor that facilitates the preservation of social world in the face of world-threatening issues.     

Nohl, Durkheim, and Mead: Three Different Types of "History of Education"

Historiography of education is not only a question of construction but also of selection. In 19th century history of education was typically a genre of great educators, mostly male and only marginally female. This construct is influential up to now, at least in popular contexts of educational reasoning. The article discusses in the introductory section problems of selection of names and meanings within history of education, and then three types of historiographical writing that are not only concerned with great educators but have larger Philosophical impact. The first type is Herman Nohls history of German progressive education, the second one is Emile Durkheims history of Higher Education in France, and the third one is George Herbert Meads Movements of Thought in 19th Century. The article compares them and discusses their implications for further development of historical writing in education.     

The fallacy of fallacies

Several of the so-called fallacies in Aristotle are not in fact mistaken inference-types, but mistakes or breaches of rules in the questioning games which were practiced in the Academy and in the Lyceum. Hence the entire Aristotelian theory of fallacies ought to be studied by reference to the author's interrogative model of inquiry, based on his theory of questions and answers, rather than as a part of the theory of inference. Most of the fallacies mentioned by Aristotle can in fact be diagnosed by means of the interrogative model, including petitio principii, multiple questions, babbling, etc., and so can Aristotle's alleged anticipation of the fallacy of argumentum ad hominem. The entire Aristotelian conception of inquiry is an interrogative one. Deductive conclusions caught Aristotle's attention in the form of answers that every rational interlocutor must give, assuming only his own earlier answers. Several features of Aristotle's methodology can be understood by means of the interrogative model, including the role of endoxa in it. Theoretically, there is also considerable leeway as to whether fallacies are conceived of as mistakes in questioning or as breaches of the rules that govern questioning games.     

The elimination of de re formulas

It is shown that de re formulas are eliminable in the modal logic S5 extended with the axiom scheme x x.     

In and behind a Lenneberg paradigm

Lenneberg suggested that a chimpanzee's linguistic ability could be tested by presenting sentences containing two prepositional phrases joined by a conjunction. This would involve joining two semantic propositions, and thus represents a more complex test of chimpanzee syntactic competence than previously attempted. Jane, a five year-old language trained chimpanzee, was tested on her ability to both produce and comprehend sentences involving a preposition (in or behind) and a conjunction (and). The results from production and comprehension were substantially the same. Jane showed the ability to appropriately deploy and, behind and in, but displayed very little flexibility in their use. It is suggested that a chimpanzee may be able to learn some rules of syntax but is not able to be creative with that syntax.     

A note on syntactical and semantical functions

We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class ^–1X is also finitely axiomatizable (i.e. iff is continuous in model class topology).     

PROXY FUNCTIONS,TRUTH AND REFERENCE

Quines ontological relativity is related to Tarskis theory of truth in two ways: Quine repudiates term-by-term-correspondence, as does Tarskis rule of truth; and Quines proxy argument in support of relativity finds exact formulation in Tarskis truth definition.Unfortunately, relativity is threatened by the fact that the proxy argument doesnt comply with the rule of truth (Tarskis celebrated condition (T)). Despite Quines express allegiance to (T), use of proxy schemes does not generate all of the true sentences condition (T) requires.A possible adjustment is to drop (T), retain the satisfaction definition and proxy argument, and appeal to the theory of observation and indeterminacy of reference as grounds of relativity. But as we shall see Quines theories of assent to observation sentences and of reference-learning dont square easily with his naturalism. The first attributes intentional attitudes to observers; and the second assumes a holistic context principle and a concept of individuation which do not withstand scrutiny as empirical notions. Both appear to violate Quines behavorist canon.A saving alternative is a theory of term-reference that appears in Roots of Reference and affords a return to behaviorism, and reinstatement of the proxy argument and relativity in a way compatible with Tarskis (T).     

Test of the violation of local realism in quantum mechanics with no use of Bell's inequalities

A novel and versatile polarization-entanglement scheme is adopted to investigate the violation of the EPR local realism for a non-maximally entangled two-photon system according to the recent nonlocality proof by Lucien Hardy. In this context the adoption of a sophisticated detection method allows direct determination of any element of physical reality (viz., determined with probability equal to unity in the words of Einstein, Podolsky and Rosen) for the pair system within complete measurements that are largely insensitive to the detector quantum-efficiencies and noise.     

Spirituality in Older Adults: A Cross-Cultural and Interfaith Perspective

The definition of spirituality poses a variety of problems for the development of theory and research, as well as practical problems for persons interested in promoting the spiritual well-being of older adults. Although any definition of spirituality is problematic, a definition is proposed that comes out of the writer's clinical experience and is relevant to his understanding of the aging process in different cultural and religious contexts. Two case studies are presented to illustrate the relevance of the definition to the experience of older persons from different cultural and religious backgrounds. Reflections on the case studies suggest ways that an appropriately trained advocate might have helped the persons in these illustrations make changes in their situations that might have improved the quality of their lives. Material from the case studies is also used to clarify differences among terms such as spirituality, religion, religiosity, and piety. The paper proposes to be a contribution to a theoretical foundation for studying and working with spirituality in older adults.     

Ghost Gestures: Phenomenological Investigations of Bodily Micromovements and Their Intercorporeal Implications

This paper thematizes the operative kinaesthetic style of world-experiencing life by turning to the ongoing how of our habitual bodily comportment: to our deeply sedimented way(s) of making a body; to schematic inner vectors or tendencies toward movement that persist as bodily ghost gestures even if one is not making the larger, visible gestures they imply; and to inadvertent isometrics, i.e., persisting patterns of trying, bracing, freezing, etc. All such micromovements witness to our sociality insofar as they are not only socially shaped, but perpetuate certain styles of intercorporeal interaction and sustain certain modes of responsivity. Reactivating the sediment -- retrieving the tacit choreography of everyday life from its anonymity and sensing our ongoing ways of living out the legacy of our communal body -- not only allows one's individual bodily style to shift, but can open new possibilities for healthy interkinaesthetic comportment. Such work can thus contribute to an embodied ethics in both theory and practice.     

Yes,Virginia, Lemons are Yellow

This paper discusses a number of themes and arguments in The Quest for Reality: Stroud's distinction between philosophical and ordinary questions about reality; the similarity he finds between the view that coloris unreal and the view that it is subjective; his argument against thesecondary quality theory; his argument against the error theory; and the disappointing conclusion of the book.     

Relevant analytic tableaux

Tableau formulations are given for the relevance logics E (Entailment), R (Relevant implication) and RM (Mingle). Proofs of equivalence to modus-ponens-based formulations are vialeft-handed Gentzen sequenzen-kalküle. The tableau formulations depend on a detailed analysis of the structure of tableau rules, leading to certain global requirements. Relevance is caught by the requirement that each node must be used; modality is caught by the requirement that only certain rules can cross a barrier. Open problems are discussed.     

No-common-cause EPR-like Funny Business in Branching Space-times

There is no EPR-like funny business if (contrary to apparent fact)our world is as indeterministic as you wish, but is free from theEPR-like quantum mechanical phenomena such as is sometimes described interms of superluminal causation or correlation between distant events.The theory of branching space-times can be used to sharpen thetheoretical dichotomy between EPR-like funny business and noEPR-like funny business. Belnap (2002) offered two analyses of thedichotomy, and proved them equivalent. This essay adds two more, bothconnected with Reichenbachs principle of the common cause, theprinciple that sends us hunting for a common-causal explanation ofdistant correlations. The two previous ideas of funny business and thetwo ideas introduced in this essay are proved to be all equivalent,which increases ones confidence in the stability of (and helpfulnessof) the BST analysis of the dichotomy between EPR-like funny businessand its absence.     

On superintuitionistic logics as fragments of proof logic extensions

Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI set up correspondingly by the calculiFor any calculus we denote by the set of all formulae of the calculus and by the lattice of all logics that are the extensions of the logic of the calculus, i.e. sets of formulae containing the axioms of and closed with respect to its rules of inference. In the logiclG the sign is decoded as follows: A = (A & A). The result of placing in the formulaA before each of its subformula is denoted byTrA. The maps are defined (in the definitions of x and the decoding of is meant), by virtue of which the diagram is constructedIn this diagram the maps, x and are isomorphisms, thereforex ^–1 = ; and the maps and are the semilattice epimorphisms that are not commutative with lattice operation +. Besides, the given diagram is commutative, and the next equalities take place: ^–1 = ^–1 and = ^–1 x. The latter implies in particular that any superintuitionistic logic is a superintuitionistic fragment of some proof logic extension.