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.     

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.     

Логистическая система, исходными связками которой являются эквивалентность и дизъюнкция

- Allatum est die 5 Martii 1970     

Die Rechtsansichten der Eurasier -- Rechtsordnung oder Wertordnung?

In their juridical doctrines, the members of the Evrazijstvo movement advocated the idea of a Russian special path criticizing at the same time the formalism and coldness of the western conception of law, based principally on Roman law. Their views are characterized by an evident priority accorded to justice over law, to the order of values over legal order.     

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.     

"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.     

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.     

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     

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.     

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     

On the logic of conscious belief

In this paper we are discussing a version of propositional belief logic, denoted by LB, in which so-called axioms of introspection (B BB and B B B) are added to the usual ones. LB is proved to be sound and complete with respect to Boolean algebras equipped with proper filters (Theorem 5). Interpretations in classical theories (Theorem 4) are also considered. A few modifications of LB are further dealt with, one of which turns out to be S5.     

The drive for meaning in William James' analysis of religious experience

Summary Now that we have looked at the characteristics of mystical experience, we are ready to discuss the assumption made in this paper that mystical experience can be translated into an understanding of integration or the drive for meaning which Fingarette pursues in a much more analytic fashion. Reviewing the conversion process as an integration process we have seen that for the sick-souled, beset with the meaninglessness or melancholy which paralyzes his will, his own awareness of wrong in his situation prevents him from opening up to larger views of reality. But, as James has described, at the same time as the subject is attending so strongly to his own sense of worthlessness, all the while the forces of mere organic ripening within him are going on towards their own prefigured result, and his conscious strainings are letting loose subconscious allies behind the scenes, which in their way work toward rearrangements. Yet the rearrangements can only come about by obeying the command of Chaung-Tse: Cease striving. The result is self-transformation in reconciling, unifying states. There is achieved a supersensuous meaning to the ordinary outward data of consciousness; facts already objectively before us fall into a new expressiveness and make a new connection with our active life.However, James cautions us to realize that the same incursions of the subconscious which produce such reconciling, unifying states can also produce pathological states, a diabolical mysticism, a sort of religious mysticism turned upside down. In such a state the meanings of events become dreadful and the ruling emotion is pessimism. To this possibility James applied the pragmatic test, By their fruits..., and concluded that the mystical experience which brings optimism to the individual is a genuine experience and one which brings truth. In our context then, we would say that real integration brings the subject away from the melancholy and meaninglessness he felt into the genuinely insightful resolution of which Fingarette speaks.Conversion, then, is a process in James's analysis of religious experience analogous to the process of integration and meaning-discovery while mysticism is analogous to the state in which integration or meaning-discovery is achieved. Conversion is climaxed by self-surrender; mysticism is characterized by new determination, self-transformation: two ways of describing an indivisible event. Furthermore, the four characteristics James applies to mysticism are indeed characteristic of the experience of integration.Two other points should be added here which are much in line with James's treatment of experience. In the first place, one of the basic principles of radical empiricism is that not only objects but relations between objects are the subject of experience. Such an experience of relationships, of wholeness, is exactly what characterizes integration. At the same time, the five senses are suspended, and the insight is experienced with such a strong immediacy that it is almost sensed. James refers to this quality of mystical states: The records show that even though the five senses be in abeyance in them, they are absolutely sensational in their epistemological quality, if I may be pardoned the barbarous expression, - that is, they are face to face presentations of what seems immediately to exist.I am not saying that every integration is a mystical experience. Rather I have been saying that James's discussion of religious experiences such as healthy-minded, sick-souled, melancholy, conversion, and mysticism provide analogues for better understanding the phenomenological processes and characteristics of the drive for meaning and integration which Fingarette analyzes. In fact, the very notion of religion itself for James bears not just an analogous resemblance but perhaps an identification with integration. For in his personal letters James had defined religious experience as Any moment of life that brings the reality of spiritual things more home to one. And in Varieties James defines religion as a man's total reaction upon life....; his attitude towards what he felt to be the primal truth.If we look upon this outlook of James toward religion as an exaggeration of the reality of integration, we can follow James to what he perceives as the importance of religion upon an individual's life. The man of religious feeling possesses the excitement of a higher kind of emotion, an enthusiastic temper of espousal in regions where morality strictly so called can at best but bow its head and acquiesce. So we are brought again to the area of creativity in which an individual has experienced the widening of the area of his immediate experience and is re-born in the karmic pattern, a valid pattern for both James and Fingarette. As Fingarette describes it, the converted individual creates values which the dead reality he had previously faced did not possess. The result of the achieved integration is explained by James when referring to religious experience as an excitement of the cheerful, expansive, dynamogenic order which, like any tonic, freshens our vital powers. This emotion overcomes temperamental melancholy [meaninglessness] and imparts endurances to the subject, or a zest, or a meaning, or an enchantment and glory to the common objects of life.We might sum up this discussion not by a criticism of the shortcomings of James's treatment of the religious life, such as his apparent insensitivity to the part played by institutions in the religious experience itself, but rather by underscoring the richness of the phenomenological analysis James has undertaken. James Edie acknowledges that James's studies of religious experience itself rather than of religion. ... are not only more sound phenomenologically than some of the studies which have, under the influence of Husserl, up to now explicitly invoked the phenomenological method, but they are also the first to establish any solid basis for a true phenomenology of religious experience.And John Wild has pointed out the parallel between James's concept of melancholy and Heidegger's concept of anxiety as the genesis of the process of becoming: beginning with the prospect of death and nothingness, the individual gropes toward new birth.As we have seen, then, James's analysis of the varieties of religious experience leads to a fruitful discussion of the psychological processes involved in melancholy and meaninglessness, rearrangement and integration. In all such experiences, a sense of inner unity is reached to which the following words of Fingarette would apply by analogy: The soul-racking death which leads to blissful rebirth is the death of the subjectively experienced, anxiety-generated self perception; it is the emergence into the freedom of introspective self-forgetfulness of the psychically unified self.     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

Given Time and the Gift of Life

Given Time and the Gift of Life explores the following nexus in Derrida's thought: the gift, the mother, and life. The first section examines life within the trajectory of the gift, the excess of gift over return in the gift of life, and the rewriting of Aristotelian generation in differantial species-being. The second section shows the quasi-transcendental nature of Derrida's thought. The conclusion sketches some of the political consequences of the gift of life thought as the quasi-transcendental gift of differantial species-being.     

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.     

Sheaves over Heyting lattices

For a complete Heyting lattice , we define a category Etale (). We show that the category Etale () is equivalent to the category of the sheaves over , Sh(), hence also with -valued sets, see [2], [1]. The category Etale() is a generalization of the category Etale (X), see [1], where X is a topological space.     

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.     

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.     

The center of gravity

In As far as possible: discovering our limits and finding ourselves (Barish and Vida, 1998), we struggled with the constraints of being two nice girls in the context of our individual professional identities as traditionally trained psychoanalysts. We were surprised to discover, through sharing with one another some painful, confusing, and even terrifying clinical experiences, how wedded we were to certain psychoanalytic conventions. It was not a pleasant discovery. What we had to face was the extent of our submissiveness to psychoanalytic theory, and of the cost to our authentic selves of that submissiveness. This daughter-paper is about our learning not to do what we were supposed to do. Its gestation has taken a form that we could not have anticipated, for, as we pursued the writing of this sequel, we seemed to get lost along the way. After working with this over a very long time, we can see now that the paper that was ultimately born, this paper, has functioned as a vehicle for us to experience ourselves in relation in an uncertain, mingling way, conscious and unconscious, trying not to be self-conscious and not defensive. This, we can also see, is how we approach the center of gravity, where our irreducible and irreconcilable tendencies are struggling to maintain a balance. And even more to the point, this paper is also a demonstration, a look at what developmental transformation is really like, the process to which we all give lip service, but hardly any of us ever pays attention to it in our real lives, and if we do, we never, never talk about it.     

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.