The Lattice of Subvarieties of the Variety Defined by Externally Compatible Identities of Abelian Groups of Exponent <Emphasis Type="Italic">n</Emphasis>

The lattices of varieties were studied in many works (see [4], [5], [11], [24], [31]). In this paper we describe the lattice of all subvarieties of the variety defined by so called externally compatible identities of Abelian groups and the identity x ⁿ ≈ y ⁿ . The notation in this paper is the same as in [2]. Presented by W. Dziobiak     

Towards a Rough Mereology-Based Logic for Approximate Solution Synthesis. Part 1

We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature e.g. Dempster-Shafer theory [29], [42], bayesian-based reasoning [21], [29], belief networks [29], many-valued logics and fuzzy logics [6], non-monotonic logics [29], neural network logics [14]. We propose rough mereology developed by the last two authors [22-25] as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes, among others, proofs understood as schemes constructed in order to support within our knowledge assertions/hypotheses about reality described by our knowledge incompletely.     

Measures of kearnels of reducibility axioms and singlets

The present paper is a generalization and further development of the theory of Kernel measures of reducibility axioms formulated in [1], [2], [3] in. the years 1969–1973. In this paper logical connections of Kernel measures with some set-theoretical notions are studied and some suggestions related to these connections are formulated.     

ON SCIENCE AS A GUIDE TO UNDERSTANDING THE ORDER AMIDST THE DIVERSITY OF LIFE

This paper is the reprinting under a new title of the “Foreword” of Paul A. Weiss's Life, Order, and Understanding: A Theme in Three Variations, published in 1970 as volume 8 supplement of The Graduate Journal of the University of Texas (Austin, Texas, #5.00 [hardcover], #2.50 [paperback], 157 pages). We reprint this paper here for two reasons. The first is that its beautiful, scientifically grounded imagery of living systems in relation to wave dynamics provides a significant supplement to this issue of Zygon on human values in the context of thermodynamics. The second is that it is hoped this foreword will serve better than would a book review to introduce Zygon readers to the philosophical and scientific wisdom contained in Life, Order, and Understanding.–Editor.     

Retracts of the closure space of filters in the lattice of all subsets

We give an idea of uniform approach to the problem of characterization of absolute extensors for categories of topological spaces [21], closure spaces [15], Boolean algebras [22], and distributive lattices [4]. In this characterization we use the notion of retract of the closure space of filters in the lattice of all subsets.     

From Adolescence to Later Adulthood: Femininity, Masculinity, and Androgyny in Six Age Groups

We drew from developmental theory regarding the timing of historical events in individuals’ lives to examine age-related differences in self-reported masculine, feminine, and androgynous personality traits in a cross-sectional sample of American men (N?=?357) and women (N?=?404) representing six age groups (adolescents [12–17 years], younger [18–29 years], middle-aged [40–59], young-old [60–69], old-old [70–79], and oldest-old [80 and older] adults). Oldest-old women were less likely than younger and middle-aged women to endorse masculine and androgynous traits. Men in their 70s (old-old) were more likely than adolescents and younger men to endorse androgynous traits. Discussion of the results emphasizes the implications of the second wave of the women’s movement for understanding life-span gender development.     

Plain Semi-Post algebras as a poset-based generalization of post algebras and their representability

Semi-Post algebras of any type T being a poset have been introduced and investigated in [CR87a], [CR87b]. Plain Semi-Post algebras are in this paper singled out among semi-Post algebras because of their simplicity, greatest similarity with Post algebras as well as their importance in logics for approximation reasoning ([Ra87a], [Ra87b], [RaEp87]). They are pseudo-Boolean algebras generated in a sense by corresponding Boolean algebras and a poset T. Every element has a unique descending representation by means of elements in a corresponding Boolean algebra and primitive Post constants which form a poset T. An axiomatization and another characterization, subalgebras, homomorphisms, congruences determined by special filters and a representability theory of these algebras, connected with that for Boolean algebras, are the subject of this paper.To the memory of Jerzy SupeckiResearch reported here has been supported by Polish Government Grant CPBP 01.01     

Gaifman's theorem on categorial grammars revisited

The equivalence of (classical) categorial grammars and context-free grammars, proved by Gaifman [4], is a very basic result of the theory of formal grammars (an essentially equivalent result is known as the Greibach normal form theorem [1], [14]). We analyse the contents of Gaifman's theorem within the framework of structure and type transformations. We give a new proof of this theorem which relies on the algebra of phrase structures and exhibit a possibility to justify the key construction used in Gaifman's proof by means of the Lambek calculus of syntactic types [15].     

Weakly higher order cylindric algebras and finite axiomatization of the representables

We show that the variety of n-dimensional weakly higher order cylindric algebras, introduced in Németi [9], [8], is finitely axiomatizable when n > 2. Our result implies that in certain non-well-founded set theories the finitization problem of algebraic logic admits a positive solution; and it shows that this variety is a good candidate for being the cylindric algebra theoretic counterpart of Tarski’s quasi-projective relation algebras. Supported by the Hungarian National Foundation for Scientific Research grant T73601.     

Is perfectionism categorical or dimensional? A taxometric analysis

Considerable debate exists within the perfectionism literature regarding whether perfectionism is most accurately conceptualized as a dimensional or categorical construct. Specifically, some researchers have viewed perfectionism as a continuous construct, with extreme scores being associated with negative psychological outcomes (e.g., obsessive-compulsive disorder, eating disorders, etc.). In contrast, others have argued that two distinct forms of perfectionism exist (i.e., adaptive vs. maladaptive perfectionism) that are associated with both positive and negative outcomes. The purpose of this study was to examine the latent structure of perfectionism using taxometric procedures to determine whether perfectionism is most accurately conceptualized as taxonic (categorical) or dimensional (continuous). We applied four taxometric procedures (maximum eigenvalue [Waller & Meehl, 1998], maximum covariance [Meehl & Yonce, 1996], mean above minus below a cut [Meehl & Yonce, 1994], and latent-mode factor analysis [Waller & Meehl, 1998]) to perfectionism data collected from 2 large nonclinical samples. Results provided convergent evidence for a dimensional conceptualization of perfectionism across samples, perfectionism measures, and statistical procedures. We discuss the implications of these findings for the theory, assessment, and investigation of perfectionism are discussed.     

Model theory for tense logic: Saturated and special models with applications to the tense hierarchy

The aims of this paper are: (1) to present tense-logical versions of such classical notions as saturated and special models; (2) to establish several fundamental existence theorems about these notions; (3) to apply these powerful techniques to tense complexity.In this paper we are concerned exclusively with quantifiedK ₁ (for linear time) with constant domain. Our present research owes much to Bowen [2], Fine [5] and Gabbay [6].     

A modern elaboration of the ramified theory of types

The paper first formalizes the ramified type theory as (informally) described in the Principia Mathematica [32]. This formalization is close to the ideas of the Principia, but also meets contemporary requirements on formality and accuracy, and therefore is a new supply to the known literature on the Principia (like [25], [19], [6] and [7]).As an alternative, notions from the ramified type theory are expressed in a lambda calculus style. This situates the type system of Russell and Whitehead in a modern setting. Both formalizations are inspired by current developments in research on type theory and typed lambda calculus; see [3].Supported by the Co-operation Centre Tilburg and Eindhoven Universities. ¹[32], Introduction, Chapter II, Section I, p. 37.Presented by Wolfgang Rautenberg     

Galois structures

This paper is a continuation of investigations on Galois connections from [1], [3], [10]. It is a continuation of [2]. We have shown many results that link properties of a given closure space with that of the dual space. For example: for every -disjunctive closure space X the dual closure space is topological iff the base of X generated by this dual space consists of the -prime sets in X (Theorem 2). Moreover the characterizations of the satisfiability relation for classical logic are shown. Roughly speaking our main result here is the following: a satisfiability relation in a logic L with, a countable language is a fragment of the classical one iff the compactness theorem for L holds (Theorems 3–8).     

Type Logics and Pregroups

We discuss the logic of pregroups, introduced by Lambek [34], and its connections with other type logics and formal grammars. The paper contains some new ideas and results: the cut-elimination theorem and a normalization theorem for an extended system of this logic, its P-TIME decidability, its interpretation in L1, and a general construction of (preordered) bilinear algebras and pregroups whose universe is an arbitrary monoid. Special Issue Categorial Grammars and Pregroups Edited by Wojciech Buszkowski and Anne Preller     

Selective adaptation of English consonants using real speech

Most English consonant-vowel (CV) syllables have other CV syllables embedded within them. For example, splicing sufficient energy from the onset of [k^ha] yields [p^ha], splicing into [ma] or [va] yields [ba], and splicing into [?a] yields [da]. We spliced successively longer segments from naturally spoken CV syllables to produce sequences of CV syllables which varied in discrete acoustic steps from [k^ha] to [p^ha], from [?a] to [da], from [ma] to [ba], from [fa] to [ba], and from [va] to [ba]. Random presentation of syllables in each series resulted in identification functions with typically sharp phoneme boundaries. For example, in the seven-syllable [?a]-[da] series (where [?a] was the original or first syllable), there were98% [?a] responses to Syllable 3, but only 12% [?a] responses (88% [da] responses) to Syllable 5. Following the identification test, subjects listened to 180 repetitions of either the first or last syllable in the test series, and were again required to identify randomly presented syllables from the test series. A shift in the phoneme boundary toward the repeated (adapting) syllable was observed for 11 of the 12 repeated syllables. Repeated presentation of [?a], for example, resulted in fewer [?a] responses to syllables in the [?a]-[da] series, compared to performance on the previous identification test. Likewise, repeated listening to [da] resulted in a decrease in [da] responses. Adaptation was selective in that syllables near the phoneme boundary were most affected by the adapting syllable. A shift in the phoneme boundary was also observed for two different continua when the adapting stimulus contained an acoustic feature identical to syllables in the test series. Thus, selective adaptation was found along a [ma]-[ba] continuum following repeated presentation of [na] and following repeated presentation of nasal resonance removed from its syllable context. A second major result, observed in five different experiments, was an asymmetrical adaptation effect. A greater shift in the phoneme boundary was observed following repeated presentation of the first syllable in each series (e.g., [?a]) than for the final embedded syllable (e.g., [da]). The results were discussed in terms of two different models of-selective adaptation.     

Graded modalities. III (the completeness and compactness of S40)

We go on along the trend of [2] and [1], giving an axiomatization of S4 ⁰ and proving its completeness and compactness with respect to the usual reflexive and transitive Kripke models. To reach this results, we use techniques from [1], with suitable adaptations to our specific case.The present work was carried out while the author had a grant of the Foundation U. Bordoni.