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.     

Modal logic with names

We investigate an enrichment of the propositional modal language with a universal modality having semanticsx iff y(y ), and a countable set of names — a special kind of propositional variables ranging over singleton sets of worlds. The obtained language _c proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment () of, where is an additional modality with the semanticsx iff y(y x y ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in _c. Strong completeness of the normal _c-logics is proved with respect to models in which all worlds are named. Every _c-logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from to _c are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched.     

Analityczne komponenty definicji arbitralnych

Tre: Wstp. I. Definicje arbitralne. II. Syntetyczne konsekwencje definicji arbitralnych III. Analityczne i rzeczowe komponenty definicji arbitralnych. IV. Zdania analityczne.Artyku ten w nieznacznym tylko stopniu róni si od pracy doktorskiej, któr przedstawiem w 1962 r. Jak najuprzejmiej dzikuj Prof. Dr M. Kokoszyskiej-Lutman, Prof. Dr J. Supeckiemu oraz Doc. Dr M. Przeckiemu za szereg uwag i wskazówek, z których tak wiele skorzystaem przygotowujc ostateczn redakcj pracy.     

Логистическая система, исходными связками которой являются эквивалентность и дизъюнкция

- Allatum est die 5 Martii 1970     

"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.     

Variations in use of the term “or”

Two studies showed that adults' responses to questions involving the term or varied markedly depending upon the type of question presented. When presented with various objects (A's and B's) and asked to circle all things which are A or B subjects tended to circle A's as well as B's, whereas when asked to circle all the A's or B's subjects showed a relatively stronger tendency to circle one or the other. Moreover the nature of the sets of objects (As and Bs) influenced behavior as well. There was also evidence that the effects due to question wording or set type transferred.     

Moral Philosophy and the Ontology of Relations

The essay undertakes to explore the possibilities of mutually fruitful dialogue between moral philosophy and ontology, in particular, the ontology of relations. The latter copes with the question of how relations relate, whereas moral philosophy often ignores the ontological implications of such crucial relations as love and interpersonality. The paper proceeds as follows. First, the ontology of relations is discussed. Second, various examples are analysed. From this, a conception of relation instantiation emerges, according to which to determine which relation actually obtains, one has to take into account (a) the context, (b) the specific content or meaning of the relation, and (c) some action or decision or mode of existence of the relata. This conception suggests that relation instantiation cannot be explained by a single formula. By the help of this conception, Hume's thesis of the identity of killing relations between human and nonhuman beings is questioned. Then, the relation of love is analysed. It is shown that love as a moral relation is perfectly explicable in terms of ontology. Moreover, its essence is best captured by the interrelation of the particulars, the relation of love as a universal, and by the relating action of the particulars. Finally, the alleged relation of universal fraternity (interpersonality as such), linking up each human being to all other human beings, is discussed.     

Независимость одной системы аксиом и правила вывода пропозиционального исчисления

- Allatum est die 5 Martii 1970     

Children's understanding of some temporal terms denoting order,duration, and simultaneity

This study examined the comprehension by children of the concepts of order, duration, and simultaneity as reflected in certain linguistic structures. The children in the study were 3, 5, and 7 years old. Temporal order was examined through children's comprehension of two-clause sentences containing the conjunctions after, before, since, and until. Temporal duration was examined through children's understanding of one-clause sentences containing the progressive aspect and two-clause sentences containing the conjunctions since and until. These two conjunctions signal duration in the main clause when they conjoin two clauses. Simultaneity was studied through children's comprehension of two-clause sentences containing while. The results revealed that the order sentence structures (before and after) were generally comprehended by the children before the duration or simultaneous sentence structures, although at 7 years of age children were still not performing above chance on the order relation in since and until sentences. The duration sentence structures were comprehended by the children before the simultaneous sentence structures. The results support the literature in cognitive psychology and in philosophy which argues that order is simpler than duration is simpler than simultaneity.This report is based on a dissertation submitted to the University of Michigan in partial fulfillment of the requirement for the Ph.D.     

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.     

“God as Friend”: Metaphoric Theology in Pastoral Care

Because of postmodernity's claim of deconstruction, the naming of God has become a crucial issue for a hermeneutics of pastoral care. Inadequate and inappropriate perceptions of God, because of specific experiences of faith, create unhelpful images of God which eventually lead to a pathology of faith. Taking into consideration the figurative means of symbolic language and its rootedness in culture, this article explores the possibility of the metaphor, God as Friend, in order to move beyond the paradigm of the suffering God (theopaschitic theology) to the paradigm of the faithful God—God as our Soul Friend.     

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.     

Development of Gender Differences in Children's Responses to Animated Entertainment

This study examined gender differences in children's responses to animated scenes from an action adventure versus a sad film, and to animated previews of a prototypical male versus female movie. Females were more likely than males to express sadness in response to the sad scene, and gender differences in intensities of sadness increased with age. Children were much more likely to stereotype the male preview as most liked by other boys, whereas the majority of children perceived the female preview as liked by either gender equally. In terms of enjoyment of the male and female previews, gender differences in enjoyment of the male preview were apparent only among children who perceived the film as more appealing to boys, and gender differences in enjoyment of the female preview were apparent only among children who perceived the film as more appealing to girls. Implications for children's programming are discussed.     

Formalization of the basic concepts of animal ecology

Summary Formal definitions of the following concepts of animal ecology are given: environment, niche, locality, local population, natural population, community, ecosystem. Five primitive (undefined) notions are used including animal, offspring and habitat, the latter in the sense of Charles Elton. The defining equations for the environment of one animal are first given, then niche (in the Elton sense) is formally defined in terms of the environment. The fifth primitve notion habitat is then introduced in order to define the remaining concepts.     

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.     

Six-year-old children's understanding of sentences adjoined with time adverbs

The adjoining of clauses with temporal links is the basis for many sentences that convey sequence of events. The present study attempts to delineate 6-year-old children's (N=30) understanding of the meaning sequences imparted by sentences adjoined with after, before, and until. Their performance of the meaning sequence for each of 24 carefully constructed sentences is compared to an adult model. Analysis of the results (using a Wilcoxon Matched Pairs Signed Rank Test) indicated that: (1)Ss understood sentences adjoined with after according to an adult model more frequently than before adjoined sentences (P<0.01); (b) Until adjoined sentences with a negative marker in the main clause were understood according to an adult model more often than until adjoined sentences with no such negative element, but the difference was not significant at a=0.01; (3)Ss understood before adjoined sentences according to an adult model more often than until adjoined sentences, but the difference was not significant at a=0.01. In general, the results indicated that 6-year-olds have not yet completed development of an adult grammar with respect to adjoining clauses with temporal links, after, before, and until.     

The responsive order: A new empiricism

The uniqueness of logic is upheld and contrasted with twenty roles of a wider responsive order that includes us and our procedures. Empirical responses are precise, but different in different approaches. Procedures and findings are independent of (not separable from) their concepts. Two-way feedback obviates a top-down derivation of findings from assumptions, hypotheses, history, or language. The postmodern problems of interpretation, conditions of appearances and relativism involve the ancient error of making perception the model-instance of experience. Instead, bodily interaction functions in language and precedes perception and interpretation. Logic, space time locations and individuated referents involve positional relations derived from comparing. Beyond Kuhn, Feyerabend, Newton and Einstein, if we can give interaction priority over comparing, the responsive objectivity of both can be upheld. A new empiricism, neither naive nor constructivist, uses the words order, explication, truth, and exactly to build on Wittgenstein and on Dilthey's hermeneutic. Natural language is metaphor-like, originally crossed. Logic must ignore its assumptions. It must render everything as a machine and drop humans and animals out. A new discipline is proposed, to move between the logical and the responsive orders, to deal with the machine/human interface and the social uses of science such as bioengineering.     

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.     

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.