On the Expressive Power of Monotone Natural Language Quantifiers over Finite Models

We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties – here called CE quantifiers – one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further identify a stronger form of monotonicity, called smoothness, which also has linguistic relevance, and we extend our considerations to smooth quantifiers. The results lead us to propose two tentative universals concerning monotonicity and natural language quantification. The notions involved as well as our proofs are presented using a graphical representation of quantifiers in the so-called number triangle.     

Quantifiers and Congruence Closure

We prove some results about the limitations of the expressive power of quantifiers on finite structures. We define the concept of a bounded quantifier and prove that every relativizing quantifier which is bounded is already first-order definable (Theorem 3.8). We weaken the concept of congruence closed (see [6]) to weakly congruence closed by restricting to congruence relations where all classes have the same size. Adapting the concept of a thin quantifier (Caicedo [1]) to the framework of finite structures, we define the concept of a meager quantifier. We show that no proper extension of first-order logic by means of meager quantifiers is weakly congruence closed (Theorem 4.9). We prove the failure of the full congruence closure property for logics which extend first-order logic by means of meager quantifiers, arbitrary monadic quantifiers, and the Härtig quantifier (Theorem 6.1).     

阅读理解中汉语量词的眼动特点分析

采用眼动记录技术探讨被试阅读不同汉语量词的即时加工过程。考查名量词和动量词,以及名量词内部的差异。结果发现:(1)被试在阅读理解过程中对名量词和动量词的眼动特点存在显著差异,名量词获得更多的加工;(2)被试在阅读理解过程中对不同名量词的眼动特点也存在显著差异,个体量词比集合量词和临时量词获得更少的加工。由此可知,不同量词在阅读理解中的信息加工难度是不同的,对于篇章理解而言,其信息含量和信息的重要性也是不同的。     

Symmetric Propositions and Logical Quantifiers

Symmetric propositions over domain and signature are characterized following Zermelo, and a correlation of such propositions with logical type- quantifiers over is described. Boolean algebras of symmetric propositions over and Σ are shown to be isomorphic to algebras of logical type- quantifiers over . This last result may provide empirical support for Tarski’s claim that logical terms over fixed domain are all and only those invariant under domain permutations.     

Plausible Reasoning and the Resolution of Quantifier Scope Ambiguities

Despite overwhelming evidence suggesting that quantifier scope is a phenomenon that must be treated at the pragmatic level, most computational treatments of scope ambiguities have thus far been a collection of syntactically motivated preference rules. This might be in part due to the prevailing wisdom that a commonsense inferencing strategy would require the storage of and reasoning with a vast amount of background knowledge. In this paper we hope to demonstrate that the challenge in developing a commonsense inferencing strategy is in the discovery of the relevant commonsense data and in a proper formulation of the inferencing strategy itself, and that a massive amount of background knowledge is not always required. In particular, we present a very effective procedure for resolving quantifier scope ambiguities at the pragmatic level using simple quantitative data that is readily available in most database environments.     

Second-Order Quantifier Elimination in Higher-Order Contexts with Applications to the Semantical Analysis of Conditionals

Second-order quantifier elimination in the context of classical logic emerged as a powerful technique in many applications, including the correspondence theory, relational databases, deductive and knowledge databases, knowledge representation, commonsense reasoning and approximate reasoning. In the current paper we first generalize the result of Nonnengart and Szałas [17] by allowing second-order variables to appear within higher-order contexts. Then we focus on a semantical analysis of conditionals, using the introduced technique and Gabbay’s semantics provided in [10] and substantially using a third-order accessibility relation. The analysis is done via finding correspondences between axioms involving conditionals and properties of the underlying third-order relation. Presented by Wojciech Buszkowski     

LÉVY HIERARCHY IN WEAK SET THEORIES

We investigate the interactions of formula complexity in weak set theories with the axioms available there. In particular, we show that swapping bounded and unbounded quantification preserves formula complexity in presence of the axiom of foundation weakened to an arbitrary set base, while it does not if the axiom of foundation is further weakened to a proper class base. More attention is being paid to the necessary axioms employed in the positive results, than to the combinatorial strength of the positive results themselves.     

The Craig Interpolation Theorem in abstract model theory

The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics is small.     

Question answering and database querying: Bridging the gap with generalized quantification

Even though Questions Answering and Database Querying have very different goals and frameworks, collaboration between the two fields could be mutually beneficial. However, the different assumptions in each field makes such collaboration difficult. In this paper, we introduce a query language with generalized quantifiers (QLGQ) and show how it could be used to help bridge the gap between the two fields.     

Most family physicians report communicating the risks of adverse drug reactions in words (vs. numbers)

Family physicians can communicate to patients the risk of adverse drug reactions using words or numbers, and this format has important implications for patients' ability to make informed decisions. The present study (a) assessed which formats family physicians preferred to communicate the risk of a given side effect, (b) tested whether the severity of this adverse drug reaction affected this preference, and (c) investigated the type of quantifiers physicians preferred to use in general (e.g., ratios, percentages). In a format selection task, a sample of 131 family physicians reported that they mostly use words to communicate to patients the risk of mild and severe adverse drug reactions, but the verbal preference was weaker for severe adverse drug reactions. The quantifier selection task showed that the most common quantifiers were verbal frequencies and verbal probabilities. Family physicians and patients should be aware of the implications of this preference.     

On modal μ-calculus with explicit interpolants

This paper deals with the extension of Kozen's μ-calculus with the so-called “existential bisimulation quantifier”. By using this quantifier one can express the uniform interpolant of any formula of the μ-calculus. In this work we provide an explicit form for the uniform interpolant of a disjunctive formula and see that it belongs to the same level of the fixpoint alternation hierarchy of the μ-calculus than the original formula. We show that this result cannot be generalized to the whole logic, because the closure of the third level of the hierarchy under the existential bisimulation quantifier is the whole μ-calculus. However, we prove that the first two levels of the hierarchy are closed. We also provide the μ-logic extended with the bisimulation quantifier with a complete calculus.     

Together – apart: in touch in a time of separation

This paper explores the experience of working as a Jungian analyst through the various phases of the global COVID-19 pandemic, examining the importance of the physical containing space alongside the analyst’s internal mind and how technology can both help and hinder understanding. A number of clinical vignettes illustrate the challenge of communicating over a distance, paying particular attention to the way countertransference phenomena can become re-attuned. Reference is made to mythology and symbols of hope, and consideration given to the meaning and purpose of the pandemic.     

The Possibility of Meaning in Human Evolution

Science undermines the certitude of non-naturalistic answers to the question of whether human life has meaning. I explore whether evolution can provide a naturalistic basis for existential meaning. Using the work of philosopher Daniel Dennett and scientist Ursula Goodenough, I argue that evolution is the locus of the possibility of meaning because it has produced intentionality, the matrix of consciousness. I conclude that the question of the meaning of human life is an existentialist one: existential meaning is a product of the individual and collective tasks human beings undertake.     

Phenotypic plasticity and archetype: a response to common objections to the biological theory of archetype and instinct

Since Jung’s death in 1961, scholars have attempted to integrate growing biological science data into Jungian concepts such as the collective unconscious, instincts and the archetypes. This enterprise has been challenging due to persistent false dichotomies of gene and environment occasionally arising. Recent works by Roesler (2022a, 2022b) for example, have raised objections to the biological theory of archetypes, but the objections are plagued by such dichotomies. The concept of phenotypic plasticity, however, helps to both avoid this problem as well as bridge the gap between competing theories into a more integrated model with solid biological foundations.     

When is it time to stop? When good enough becomes bad enough

This article draws on Winnicott’s concept of the good enough mother to discuss how to know whether a therapeutic situation is good enough to continue or bad enough to end. This dilemma is explored in terms of clinical syndromes, such as anorexia and pathological gambling, but focuses mainly on analyst-initiated endings, which are termed the ‘Casablanca dilemma’, based on an amplification of the ending of the film Casablanca. The author goes on to discuss such one-sided endings, drawing on interviews with 40 analysts and therapists about their clinical experience. A typology of bad enough endings is presented. The psychological differences between a good enough analysis as opposed to a bad enough one are explored through the ideas of Winnicott and Neumann.     

Kann Es Ein Argument Für Den Skeptizismus Geben? Das Epistemische Problem Der Irrtumsmöglichkeit

Summary  Is there any argument for scepticism? The epistemic problem of the possibility of error. Arguments for scepticism rest on the assumption that knowledge claims are fallible. For this reason the concept of knowledge appears to be questionable. Since it is necessary to distinguish doubts from possible doubts, the arguments for scepticism appear to be unconvincing. If we take it into account that we know something that is immune to doubt, we should draw the conclusion that, contrary to scepticism, knowledge claims have to be compatible with being fallible. Thus any knowledge claim is capable of being doubted.     

The transcendent function in Spitteler’s Prometheus and Epimetheus

In August 2020, John Beebe and Steve Myers met via Zoom to discuss their differing interpretations of psychological typology and the different sources within Jung’s writings that influenced their books: Integrity in Depth: Energies and Patterns in Psychological Type (Beebe), and Myers-Briggs Typology vs Jungian Individuation (Myers). The discussion centred on Spitteler’s epic poem Prometheus und Epimetheus, which forms the basis of chapter V of Psychological Types. This is both the largest chapter and one of two chapters that Jung highlighted in the Argentine foreword as containing the essence of the book. Jung’s book is primarily about the transformation of personality rather than the categorization of people. Although it contains a critical psychology that deconstructs the nature of consciousness, that is only one half of the book and a stepping-stone to the other half, which is the reconciliation of opposites with particular emphasis on the relation of consciousness and the unconscious. Jung assumed that readers were already familiar with Prometheus und Epimetheus, an understanding of which sheds light on the nature of the transformation that Jung described – the development of a new attitude towards attitude itself.