A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic

Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.     

Логистическая система, исходными связками которой являются эквивалентность и дизъюнкция

- Allatum est die 5 Martii 1970     

Aids,myth, and ethics

The present paper is a commentary on an article by Larry Churchill [1]. Churchill has argued that the negative attitudes and adverse behavior we commonly encounter in connection with (suspected) AIDS patients may be understood in terms of a dualistic myth inspiring a ritual avoidance of dirt, of dirt as something that does not belong to a clean world order. The deep-seated mythical character of attitudes and behavior here makes them less accessible to the kind of rational argument commonly employed in ethics. Churchill also proposes a remedy for the (morally outrageous) dualistic mythical-ritual behavior he has focused — a remedy that may be overly intellectualistic.Three further comments are made: on the metaphorical meaning of myth, on a reductionist tendency in Churchill's deep-looking project, and on an ethically crucial ambiguity in the meaning of the other person's otherness. These (mildly critical) comments do not, however, detract from a positive overall evaluation of Churchill's basic idea that we will understand more about adverse attitudes and behavior in connection with AIDS if we think in terms of myth, ritual, dirt, and cleanliness.     

The endorsement of irrational beliefs in a general clinical population

Burgess' Attitude and Belief Scale, a measure of Ellis' irrational beliefs, was administered to a large sample of outpatients. All 13 subscales demonstrate very adequate internal consistency. A factor analysis yielded one factor accounting for 83% of the variance, which was labeled irrationality. Clients endorsed focused items more than overgeneralized items, self-referential items more than non-self-referential items, and preferential items more than irrational items. Clients also received higher scores on the irrational process of demandingness than they did on the irrational process of awfulizing, self-worth and low frustration tolerance. The results were consistent with new formulations in Rational-Emotive theory. Suggestions were made for the construction of measures of irrational beliefs.     

Partially-Ordered (Branching) Generalized Quantifiers: A General Definition

Following Henkins discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or cardinality quantifiers, e.g., most, few, finitely many, exactly , where is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first to a general definition of monotone-increasing (M) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwises 1979 analysis of the basic case of M POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional 1st-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages.     

Third Men: The Logic of the Sophisms at Arist. SE 22, 178b36–170a10

This article aims at elucidating the logic of Arist. SE 22, 178b36–179a10 and, in particular, of the sophism labelled "Third Man" discussed in it. I suggest that neither the sophistic Walking Man argument, proposed by ancient commentators, nor the Aristotelian Third Man of the , suggested by modern interpreters, can be identified with the fallacious argument Aristotle presents and solves in the passage. I propose an alternative reconstruction of the Third Man sophism and argue that an explanation of the lines regarding the identity of Coriscus and Coriscus the musician (178b39–179a3) is indispensable for its correct understanding, since they hint at another sophism in some important aspects analogous. Finally, I show that two contradictions concerning spotted by scholars in the passage are only apparent and can be dissolved once the assumption that the anti-Platonic Third Man argument is at stake here is discarded, and once the passage is read in the light of its agonistic context.     

Cooperation,Knowledge, and Time: Alternating-time Temporal Epistemic Logic and its Applications

Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic CTL, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in CTL. Recently, CTL was generalised by Alur, Henzinger, and Kupferman in a logic known as Alternating-time Temporal Logic (ATL). The key insight in ATL is that the path quantifiers of CTL could be replaced by cooperation modalities, of the form , where is a set of agents. The intended interpretation of an ATL formula is that the agents can cooperate to ensure that holds (equivalently, that have a winning strategy for ). In this paper, we extend ATL with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with ATL, it becomes possible to express such properties as group can cooperate to bring about iff it is common knowledge in that . The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems.     

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.     

"Solar love": Nietzsche,Merleau-Ponty and the fortunes of perception

Both Nietzsche and Merleau-Ponty repudiate the mirror view of perception and embrace what Nietzsche refers to as solar love or creative perception. I argue that Merleau-Ponty thinks of this type of perception primarily in terms of convergence and Nietzsche in terms of divergence. I then show how, contrary to their own emphases, Merleau-Ponty's notion of flesh and Nietzsche's idea of chaos suggest that convergence and divergence are abstractions from an ontologically prior realm of hybrid perceptions. In this realm, each perception is shot through with the others, simultaneously inside and outside one another. The creative tension among these perceptions continually produces new perspectives or voices, that is, a realm whose very being is metamorphosis. Moreover, this realm of hybrid perceptions suggests a political principle that might prove attractive for communities in an age of diversity and cultural hybridity.     

Stuffed Cabbage in the Old New School Cafeteria

The purpose of this lecture is to celebrate the memory of Aron Gurwitsch by examining and enlarging the domain of phenomenological clarification of some elements of what Gurwitsch called the logic of reality. Chief among those elements are the nature of the taken-for-grantedness of our existential belief, the difference between presentive and non-presentive indices of reality and the ground for the self-illumination of the world of working.     

Some notes on the nature of methodological indeterminacy

This paper is an attempt to extend the meaning of the concept of indeterminacy for the human sciences. The authors do this by coining the term methodological indeterminacy and arguing that indeterminacy is better understood when linked to specific methodological techniques. Paradoxically, while specific research techniques demonstrate that the issue of indeterminacy is complex, yielding the possibility of types and degrees, it does not eliminate the problem of translation first raised by Quine. However, the authors go on to argue that, from a research perspective, indeterminacy can and must be approached in such a way that it is possible to reduce cases of it, even though never completely eliminating it in the human sciences.     

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.     

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.     

Personality organization as an aspect of back pain in a medical setting.

The MMPI profiles of 74 low back pain patients who had previously been classified as "functional,"organic," or "mixed" were sorted into six profile groups. The six profile groups were those used by Pichot, Perse, Lekous, Dureau, Perez, and Rychewaert (1972); denial, "conversion V" without defensiveness, "conversion V" with defensiveness, depressed/anxious, psychotic and normal. Results indicate that all six profile types are well represented in the low back pain group. Evidence is also presented which shows that each of the pathological MMPI profile types examined across "functional," "organic," and "mixed" classification is significantly more elevated than a normal profile group on two scales (Lb, DOR) designed to measure functional aspects of pain. Pathological MMPI profile groups did not differ significantly from each other on the "functional" pain scales. The data presented in this study point to the relationship of various forms of psychopathology with "functional pain." The findings of this study would not support a homogeneous "pain personality" for low back pain patients. However, combined "conversion V" profiles accounted for 58% of the "functional" group, 45% of the "mixed" group and 35% of the "organic" group.     

The relevance of Habermas' communicative turn

This paper points out the way in which educational and communicative action (Habermas) are to be related. It is shown that earlier attempts to put Habermas ideas to use have led to a dead end because they do not realize clearly that the new basic notion introduced by Habermas, namely communicative action, is the expression of a communicative turn. It is argued that Habermas' concept expresses a radical new attempt to grasp the intersubjective character of social action. Next implications of this communicative turn for the concept of education as a social praxis are indicated. Education can be conceived of as a praxis responding to the vulnerability of a communicative self.     

Is “some-other-time” sometimes better than “sometime” for proving partial correctness of programs?

The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or sometime-logic. We will see that the minor change in this background modal logic increases the program verifying power of Bur. The change can be described either technically as replacing the reflexive version of S5 with an irreflexive version, or intuitively as using the modality some-other-time instead of sometime. Some insights into the nature of computational induction and its variants are also obtained.This project was supported by the Hungarian National Foundation for Scientific Research, Grant No. 1810.     

On Ultrafilter Logic and Special Functions

Logics for generally were introduced for handling assertions with vague notions,such as generally, most, several, etc., by generalized quantifiers, ultrafilter logic being an interesting case. Here, we show that ultrafilter logic can be faithfully embedded into a first-order theory of certain functions, called coherent. We also use generic functions (akin to Skolem functions) to enable elimination of the generalized quantifier. These devices permit using methods for classical first-order logic to reason about consequence in ultrafilter logic.Presented by André Fuhrmann     

The relationship between perceived surface-lightness and perceived illumination

Summary An attempt was made to specify the relationship between perceived surface lightness and perceived illumination under the stimulus conditions where different combinations of albedo and illuminance gave 10 approximately equal-luminance levels of a test field (TF) on three different (black-, gray- and white-appearing) backgrounds. Two types of category judgments for TF-lightness and overall illumination were made on the total of 94 TFs by 5 Ss. The results indicated that under the condition where achromatic surface colors appear, the perceptual scission which produces two different perceptual dimensions (lightness and perceived illumination) from one sort of stimulation (luminance) was clearly observed. The relation between the two judgments was consistent with the lightness-illumination invariance hypothesis: As lightness judgments (A) changed from darker to lighter, illumination judgments (I) shifted form brighter to dimmer, the sum of A and I being kept nearly invariant for a given luminance of the TF; the psychological relationship between lightness and illumination, A+I, changed as a linear function of the photometric combination of albedo and illuminance, log A+log I. It was also found that the albedo of the background was an important factor determining the extent of perceptual scission between lightness and illumination.     

The liar: What paradox?

Most philosophers believe that the Liar Paradox is semantical in character, and arises from difficulties in the predicate true. The author argues that the paradox is pragmatic, not semantic, and arises from violations of essential conditions that define statement-making speech acts. The author shows that his solution to the paradox will not only handle the classical Liar sentences that are necessarily or intrinsically paradoxical, but also sets of Kripke-sentences that are contingently paradoxical.     

The Self Psychology of Heinz Kohut: What's It All About Theologically?

As a psychoanalytic thinker who offered by means of his self psychology a new paradigm of psychological development and functioning, Heinz Kohut was also a theologian manqué. With the help of the method of interpretation devised by Paul Tillich and David Tracy, Kohut's limit-concepts of tragic man, the self-object, and empathy, all set within his theory of narcissism, are elucidated as theological constructs. These are critiqued for adequacy from a Christian perspective. The conclusion is that Kohut's understanding of the human dilemma and of the way of salvation correlates well with Christianity, while his view of empathy as the means of salvation has created some confusion. Kohut has thus left an unfinished, profoundly important, agenda for theologians and clinicians.