On quasivarieties and varieties as categories

Finitary quasivarieties are characterized categorically by the existence of colimits and of an abstractly finite, regularly projective regular generator G. Analogously, infinitary quasivarieties are characterized: one drops the assumption that G be abstractly finite. For (finitary) varieties the characterization is similar: the regular generator is assumed to be exactly projective, i.e., hom(G, –) is an exact functor. These results sharpen the classical characterization theorems of Lawvere, Isbell and other authors.Supported by the Czech Grant Agency (Project 201/02/0148).Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

On the structure of lattices of subquasivarieties of congruence-noetherian quasivarieties

We study the structure of algebraic -closed subsets of an algebraic lattice L, where is some Browerian binary relation on L, in the special case when the lattice of such subsets is an atomistic lattice. This gives an approach to investigate the atomistic lattices of congruence-Noetherian quasivarieties.V. A. Gorbunov has died in January 1999Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, W. Dziobiak, and A. V. Kravchenko     

Gender specificity in value structures

Separate factor analyses of the value rankings of 53 male and 77 female college students yielded three factors for each gender. Interpretation suggested Creative Self-Determination versus Submissive Dependency, Personal Gratification versus Sociopolitical Consciousness, and Existential Responsibility versus Traditionalism as core concepts for the female respondents; while males' axiological dimensions were labeled Communal Idealism versus Entrepreneural Pragmatism, Hedonism versus Egalitarianism, and Sybaritic Bohemianism versus Traditional Sobriety. Each pole of the female factors was interpreted as reflecting a major ideological referent component of the Women's Liberation Movement, while male factors were construed as constituting perspectives for interpreting varieties of response to feminist ideology. Techniques for increasing individuals' levels of self-actualization by direct intervention in axiological organization were discussed.     

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.     

On relative universality and Q-universality

Adams and Dziobiak proved that any finite-to-finite universal quasivariety must be Q-universal, and then asked whether a somewhat weaker hypothesis could lead to the same conclusion. We show that their original hypothesis cannot be weakened to its naturally extreme form.To Professor Ale Pultr on his 65th birthdayThe authors gratefully acknowledge the support of the NSERC of Canada, of the project LN00A056 of the Czech Ministry of Education, and also of the Grant Agency of Czech Republic under the grant 201/02/0148.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

Three prepositional calculi of probability

Attempts are made to transform the basis of elementary probability theory into the logical calculus.We obtain the propositional calculus NP by a naive approach. As rules of transformation, NP has rules of the classical propositional logic (for events), rules of the ukasiewicz logic ₀ (for probabilities) and axioms of probability theory, in the form of rules of inference. We prove equivalence of NP with a fragmentary probability theory, in which one may only add and subtract probabilities.The second calculus MP is a usual modal propositional calculus. It has the modal rules x x, x y x y, x x, x y (y x), (y x), in addition to the rules of classical propositional logic. One may read x as x is probable. Imbeddings of NP and of ₀ into MP are given.The third calculus P is a modal extension of ₀. It may be obtained by adding the rule ((xy)y) xy to the modal logic of quantum mechanics Q [5]. One may read x in P as x is observed. An imbedding of NP into P is given.     

The clinical usefulness of distinguishing between two types of dependency

The authors describe two very different dynamics that have been subsumed under the word, dependency. The good kind of dependency which enhances our self-esteem, is the need we all have for affection, admiration and emotional support. The bad kind is the need to have someone or something help us avoid our responsibility to deal with reality. This kind of dependency lowers our self-esteem. We have given six clinical examples of people who have problems with dependency—three who deny their need for nurture and three who abdicate their responsibility for their lives.     

The logic of linear tolerance

A nonempty sequence T₁,...,T_n of theories is tolerant, if there are consistent theories T ₁ ⁺ ,..., T _n ⁺ such that for each 1 i n, T _i ⁺ is an extension of T_i in the same language and, if i n, T _i ⁺ interprets T _i+1 ⁺ . We consider a propositional language with the modality , the arity of which is not fixed, and axiomatically define in this language the decidable logics TOL and TOL. It is shown that TOL (resp. TOL) yields exactly the schemata of PA-provable (resp. true) arithmetical sentences, if (A₁,..., A_n) is understood as (a formalization of) PA+A₁, ..., PA+A_n is tolerant.     

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).     

O pojęciu zdania analitycznego

Rezultaty przedstawione w pracy niniejszej pokrywaj si czciowo z wynikami osignitymi przezR. Wójcickiego w pracy:Analityczne komponenty definicji arbitralnych. Studia Logica, t. XIV. Dotyczy to gównie rezultatów zawartych w czci pierwszej. Chciabym podkreli, i wyniki R. Wójcickiego uzyskane zostay cakowicie niezalenie od rezultatów przedstawionych w pracy obecnej.Allatum est die 16 Aprilis 1962     

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.     

Children's knowledge of prepositional phrase structure: An experimental test

A test of prepositional phrase structure in 4- to 6-year-old children's language is reported. Children's productions of PP and verb-particle sequences were elicited. Children produced pronominal and full NP objects of sequences corresponding to PPs and verb-plus-particle in the adult grammar. Prepositions freely took both pronominal and full NP objects (He's jumping over it. He's jumping over the table). In particle verb constructions, pronominal objects were placed immediately after the verb in all but a few cases (He's pushing it overnot He's pushing over it). With full NP objects, the preference was to place the verb after the particle (He's pushing over the table). These facts support an analysis in which if the child constructs a PP-over-P—NP structure for prepositional phrases but not for verb-particle sequences, and follows adultlike rules for these structures.This research was supported in its initial stages by NIH grant No. HD90647-03 to T. Roeper and S.J. Keyser and was completed while the author was supported in part by grants from the Graduate School Research Committee of the University of Wisconsin-Madison and from the Spencer Foundation through the University of Wisconsin School of Education.     

An effective fixed-point theorem in intuitionistic diagonalizable algebras

Summary Within the technical frame supplied by the algebraic variety of diagonalizable algebras, defined by R. Magari in [2], we prove the following:LetT be any first-order theory with a predicate Pr satisfying the canonical derivability conditions, including Löb's property. Then any formula inT built up from the propositional variables q, p₁, ..., p_n, using logical connectives and the predicate Pr, has the same fixed-points relative to q (that is, formulas (p₁ ..., p_n) for which for all p₁, ..., p_n T((p₁, ..., p_n), p₁, ..., p_n) (p₁, ..., p_n)) of a formula ^* of the same kind, obtained from in an effective way.Moreover, such ^* is provably equivalent to the formula obtained from substituting with ^* itself all the occurrences of q which are under Pr. In the particular case where q is always under Pr in , ^* is the unique (up to provable equivalence) fixedpoint of .Since this result is proved only assumingPr to be canonical, it can be deduced that Löb's property is, in a sense, equivalent to Gödel's diagonalization lemma.All the results are proved more generally in the intuitionistic case.The algebraization of the theories which express Theor, IXAllatum est die 19 Decembris 1975     

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.     

The Decades of Life: Relocating Erikson's Stages

Erik H. Erikson's life cycle schema consists of eight stages. Three are located in infancy and early childhood (ages 1–5), one in childhood (5–12), one in adolescence, and three in adulthood. This essay proposes a relocation of the stages in terms of decades. The eight psychosocial crises in Erikson's model are retained, but each crisis and its resolution is the central theme of a decade of life. This relocation of Erikson's stages orients the life cycle schema more toward adulthood than to early childhood, as six of the stages now occur in the adult years. It also reflects Erikson's theoretical shift in emphasis from the ego to the sense of I in his later writings. A proposal for how the ninth and tenth decades fit into the schema is also offered.     

Some modifications of Scott's theorem on injective spaces

D. Scott in his paper [5] on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.In this paper we prove a generalization of this theorem for the category of , -closure spaces. The main theorem says that, for some cardinal numbers , , absolute extensors for the category of , -closure spaces are exactly , -closure spaces of , -filters in , >-semidistributive lattices (Theorem 3.5).If = and = we obtain Scott's Theorem (Corollary 2.1). If = 0 and = we obtain a characterization of closure spaces of filters in a complete Heyting lattice (Corollary 3.4). If = 0 and = we obtain a characterization of closure space of all principial filters in a completely distributive complete lattice (Corollary 3.3).     

Heidegger's Brightness as a Responsibility of the Therapist in Existential Family Therapy

The author reflects upon the Heideggerian concepts of thrown-ness, death imagery, arrogance and brightness and their usefulness in existential family therapy. The article describes and illustrates with clinical material the process of helping a couple or family to move from an arrogance response to thrownness and death imagery to the response of brightness as attendants of Being. The responsibilities of the therapist in facilitating such a process are also described.Director of the Worthington Logotherapy Institute, co-director of Lantz and Lantz Counseling Associates, and a professor at The Ohio State University. College of Social Work     

The group member's view of inner and outer reality: The Janus phenomenon applied to the group

This paper surveys some theoretical aspects of psychodynamic group treatment from the vantage point of the Janus phenomenon. This focus may provide some clarification in understanding how group therapy facilitates growth, especially in the relationships between inner realities and the realities of the external world. The paper explores and seeks bridges and connections between the dynamics of the group and intrapsychic dynamics. The inner view may be understood as intimately connected with intrapsychic concerns, whereas the issues for patients in groups do, to a degree, concern interpersonal processes in and projections onto the external world. The paper concludes that, thus far, we must accept less than perfect integration of theory and settle for limited domain reasoning (Scheidlinger, 1982). Erlebnis is the term coined by Paul Federn (1952) to refer to subjective experience of the self.     

The Therapeutic Relationship as Viewed by Existential Psychotherapy: Re-Embracing the World

Existential psychotherapy places pivotal significance upon the interrelational aspects of human experience. By so doing, the therapeutic relationship itself becomes the principal means through which the client's presenting symptoms and disorders are disclosed as direct expressions and outcomes of the client's overall way of being rather than as isolated and disruptive impediments. This paper examines the therapeutic relationship as viewed from four primary interrelational dimensions. Further, it focuses upon psychotherapy's tendency to exclude the world from the therapeutic relationship and provides two novel and challenging alternatives whose principal aim is to bring the world back into the therapeutic relationship.     

Syntactic criteria in prearticulatory editing: Evidence from laboratory-induced slips of the tongue

Earlier studies of laboratory-induced verbal slips have provided a partial model of prearticulatory editing in speech production—a cognitive process by which impending phoneme strings are evaluated for their linguistic and extralinguistic integrity prior to articulation. These studies have provided evidence of editing based upon phonotactic, lexical, and semantic criteria. The present study demonstrates the existence of syntactic editing criteria via laboratory-induced spoonerisms. Experiment I demonstrates that syntactically legitimate spoonerism errors (e.g., mice saw) are more frequent than syntactically anomalous spoonerism errors (e.g., mice sees), suggesting that prearticulatory phonological processing decisions are modified on the basis of syntactic criteria. Experiment II demonstrates that the criteria for syntactically legnitimate spoonerisms can be influenced by aspects of the syntactic context. Implications are discussed.