HYPERCOMPARATIVES

In natural language we rarely use relation-words with more than three argument places. This paper studies one systematic device, rooted in natural language, by which relations of greater adicity can be expressed. It is based on a higher-order relation between 1-place, 2-place, and 4-place relations (and so on) of which the relation between the positive and comparative degrees of a predicate is a special case. Two formal languages are presented in this connection, one of which represents the language of communication and the other the contextual information against which the first language is interpreted. A semantical theory is described, which treats the two languages in an interdependent way. Logical consequence is non-compact. Connections with issues about vagueness are made.     

A context-free language for binary multinomial processing tree models

This paper provides a new formalization for the class of binary multinomial processing tree (BMPT) models, and theorems for the class are developed using the formalism. MPT models are a popular class of information processing models for categorical data in specific cognitive paradigms. They have a recursive structure that is productively described with the tools of formal language and computation theory. We provide an axiomatization that characterizes BMPT models as strings in a context-free language, and then we add model-theoretic axioms and definitions to interpret the strings as parameterized probabilistic models for categorical data. The language for BMPT models is related to the Full Binary Tree language, a well-studied context-free language. Once BMPT models are viewed from the perspective of the Full Binary Tree language, a number of theoretical and computational results can be developed. In particular, we have a number of results concerning the enumerations of BMPT models as well as the identifiability of subclasses of these models.     

On the role of language in social choice theory

Axiomatic characterization results in social choice theory are usually compared either regarding the normative plausibility or regarding the logical strength of the axioms involved. Here, instead, we propose to compare axiomatizations according to the language used for expressing the axioms. In order to carry out such a comparison, we suggest a formalist approach to axiomatization results which uses a restricted formal logical language to express axioms. Axiomatic characterization results in social choice theory then turn into definability results of formal logic. The advantages of this approach include the possibility of non-axiomatizability results, a distinction between absolute and relative axiomatizations, and the possibility to ask how rich a language needs to be to express certain axioms. We argue for formal minimalism, i.e., for favoring axiomatizations in the weakest language possible.     

Inclusion and Exclusion in Natural Language

We present a formal system for reasoning about inclusion and exclusion in natural language, following work by MacCartney and Manning. In particular, we show that an extension of the Monotonicity Calculus, augmented by six new type markings, is sufficient to derive novel inferences beyond monotonicity reasoning, and moreover gives rise to an interesting logic of its own. We prove soundness of the resulting calculus and discuss further logical and linguistic issues, including a new connection to the classes of weak, strong, and superstrong negative polarity items.     

Now is the time

The aim of this paper is to consider some logical aspects of the debate between the view that the present is the only ‘real’ time, and the view that the present is not in any way metaphysically privileged. In particular I shall set out a language of first-order predicate tense logic with a now predicate, and a first order (extensional) language with an abstraction operator, in such a way that each language can be shewn to be exactly translatable into the other. I shew that this translation is preserved at the metalinguistic level, so that equivalent truth conditions can be defined in a tensed metalanguage or an indexical metalanguage. I then make some remarks about the connection between proofs of relative consistency and metaphysical truth; and some historical remarks about Arthur Prior's use of formal logic in expressing his presentist views.     

Cellular spaces

This paper is an introduction into the theory of cellular spaces. From the more general model of nets of abstract cells which are interpreted by finite automata, it is shown how the model of cellular spaces is achieved by specialization. Cellular spaces are extremely homogeneous in function and in geometry. The relation between local and global behavior is regarded as the main topic of the theory. After a formal definition of cellular spaces, it is shown that not all functions of the configuration space are induced by cellular spaces. In addition, the Garden-of-Eden problem is discussed, and a simple self-reproduction property is explained.     

Transfers between Logics and their Applications

In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attributes such as consequence operator, syntactical structure, and internal transformations. In particular, we treat Belief Revision Systems (BRS) as our main example, defining the Wide Belief Revision Systems (WBRS's). This generalization allows us to define BRS's in an abstract setting for classical and non-standard logics. We also show how the concept of translation between logics can be obtained as a particular case of transfers.     

Cognitive processing in literate and illiterate subjects: a review of some recent behavioral and functional neuroimaging data

The study of illiterate subjects, which for specific socio-cultural reasons did not have the opportunity to acquire basic reading and writing skills, represents one approach to study the interaction between neurobiological and cultural factors in cognitive development and the functional organization of the human brain. In addition the naturally occurring illiteracy may serve as a model for studying the influence of alphabetic orthography on auditory-verbal language. In this paper we have reviewed some recent behavioral and functional neuroimaging data indicating that learning an alphabetic written language modulates the auditory-verbal language system in a non-trivial way and provided support for the hypothesis that the functional architecture of the brain is modulated by literacy. We have also indicated that the effects of literacy and formal schooling is not limited to language related skills but appears to affect also other cognitive domains. In particular, we indicate that formal schooling influences 2D but not 3D visual naming skills. We have also pointed to the importance of using ecologically relevant tasks when comparing literate and illiterate subjects. We also demonstrate the applicability of a network approach in elucidating differences in the functional organization of the brain between groups. The strength of such an approach is the ability to study patterns of interactions between functionally specialized brain regions and the possibility to compare such patterns of brain interactions between groups or functional states. This complements the more commonly used activation approach to functional neuroimaging data, which characterize functionally specialized regions, and provides important data characterizing the functional interactions between these regions.     

L’instrumentalisation managériale des espaces de délibération formels: l’expérience des enseignantes du préscolaire/primaire

This study examines formal deliberation spaces’ structure and how they translate into collegial work structures. Based on a critical experientialist work theory and a materialist feminist perspective it considers formal deliberation spaces and teachers’ lived experiences. The methodology relies on a qualitative research design involving 25 primary school teachers and individual and group interviews. The results show many mandatory formal deliberation spaces within the work organization and highlight the limited possibilities for teachers to deliberate their day-to-day experiences within these spaces. The findings render visible the process by which the structure of formal deliberation spaces can be moulded and instrumentalized to benefit the administration and render invisible teachers’ lived experience, leading to institutional silencing.     

Implicit States of Connectivity in the Clinical Practice of Jungian Psychoanalysis and Andean Shamanism

This paper will describe the spiritual states of “oneness” experienced by Andean shamans in relation to oceanic states in early infancy and working with trauma in Jungian analysis. The author’s work exploring implicit energetic experience with Andean shamans will be referenced with comparisons made to depth psychology, in both theory and in practice. Definitions of Q’echua terms describing different psychic meditative states that Andean shamans enter into will be provided as Andean medicine people have a much more developed language for conceptualizing these experiences. A clinical vignette will be presented that demonstrates how the spaces of implicit connection that occur between an analyst and analysand in the analytic setting can be a catalyst for healing.     

Framework for formal ontology

The discussions which follow rest on a distinction, first expounded by Husserl, between formal logic and formal ontology. The former concerns itself with (formal) meaning-structures; the latter with formal structures amongst objects and their parts. The paper attempts to show how, when formal ontological considerations are brought into play, contemporary extensionalist theories of part and whole, and above all the mereology of Leniewski, can be generalised to embrace not only relations between concrete objects and object-pieces, but also relations between what we shall call dependent parts or moments. A two-dimensional formal language is canvassed for the resultant ontological theory, a language which owes more to the tradition of Euler, Boole and Venn than to the quantifier-centred languages which have predominated amongst analytic philosophers since the time of Frege and Russell. Analytic philosophical arguments against moments, and against the entire project of a formal ontology, are considered and rejected. The paper concludes with a brief account of some applications of the theory presented.     

A Note on the Correspondence among Entail Relations, Rough Set Dependencies, and Logical Consequence

In this note, we report that entail relations defined in the context of knowledge spaces are equivalent to the dependence relations of rough set data analysis and Tarski's consequence relation of monotone logic. We also discuss the connection between these and related structures. Copyright 2001 Academic Press.     

Plasticity and language: an example of the Baldwin effect?

In recent years, many scholars have suggested that the Baldwin effect may play an important role in the evolution of language. However, the Baldwin effect is a multifaceted and controversial process and the assessment of its connection with language is difficult without a formal model. This paper provides a first step in this direction. We examine a game-theoretic model of the interaction between plasticity (represented by Herrnstein reinforcement learning) and evolution in the context of a simple language game. Additionally, we describe three distinct aspects of the Baldwin effect: the Simpson–Baldwin effect, the Baldwin expediting effect and the Baldwin optimizing effect. We find that a simple model of the evolution of language lends theoretical plausibility to the existence of the Simpson–Baldwin and the Baldwin optimizing effects in this arena, but not the Baldwin expediting effect.     

试论语义悖论的弗完全理论

弗完全理论通过限制排中律的使用,弱化经典逻辑,采用非经典的三值语言来处理语义悖论,最终使得形式语言能够一致地包含自身的真谓词。文中我们讨论了弗完全理论的两种基本形式——基础的弗完全理论和高级的弗完全理论。基础的弗完全理论引入了＂真值空缺＂的思想,认为句子除了真假之外还有＂既不真也不假＂的第三值,像说谎者这样的语义悖论语句就落在真假之空缺中,该理论借助于对不动点的归纳构造过程证明了形式语言中真谓词的存在性。高级弗完全理论在前者的基础上引入一个适当的条件句,定义了一个＂更强的真＂,发展出了既满足真的素朴模式又具有不动点解释的、一致的高级弗完全理论。     

Hybrid Speech Acts: A Theory of Normative Thought and Language That ‘Has It Both Ways’

In this essay, I propose a novel hybrid metanormative theory. According to this theory, speakers making normative claims express both cognitive and motivational attitudes in virtue of the constitutive norms of the particular speech acts they perform. This view has four principal virtues: (1) it is consistent with traditional semantic theories, (2) it supports a form of motivational judgment internalism that does justice to externalist intuitions, (3) it illuminates the connection between normative language and normative thought, and (4) it explains how speakers can express different conative states when speaking in different normative domains. In the first section, I discuss the theories of Stephen Finlay and David Copp. I show that they each come very close to having it both ways but ultimately fail. Understanding the shortcomings of these views is instrumental to a clear presentation of my own Hybrid Speech Act theory in section two. In the final section, I demonstrate how my view achieves its four advantages.     

How Do Artificial Neural Networks Classify Musical Triads? A Case Study in Eluding Bonini's Paradox

How might artificial neural networks (ANNs) inform cognitive science? Often cognitive scientists use ANNs but do not examine their internal structures. In this paper, we use ANNs to explore how cognition might represent musical properties. We train ANNs to classify musical chords, and we interpret network structure to determine what representations ANNs discover and use. We find connection weights between input units and hidden units can be described using Fourier phase spaces, a representation studied in musical set theory. We find the total signal coming through these weighted connection weights is a measure of the similarity between two Fourier structures: the structure of the hidden unit's weights and the structure of the stimulus. This is surprising because neither of these Fourier structures is computed by the hidden unit. We then show how output units use such similarity measures to classify chords. However, we also find different types of units—units that use different activation functions—use this similarity measure very differently. This result, combined with other findings, indicates that while our networks are related to the Fourier analysis of musical sets, they do not perform Fourier analyses of the kind usually described in musical set theory. Our results show Fourier representations of music are not limited to musical set theory. Our results also suggest how cognitive psychologists might explore Fourier representations in musical cognition. Critically, such theoretical and empirical implications require researchers to understand how network structure converts stimuli into responses.     

Some Reasons for Distinguishing Between “Non-normative Response” and “Irrational Decision”

Three concerns that limit the implications of normative decision research were described in this study. First, because there is no unequivocal way to determine whether any particular base rate is appropriate in a particular instance, the significance of the apparent base rate underutilization reported by a number of investigators is unclear. Second, because there are discrepancies between natural language and formal logic, word problems are an uncertain domain within which to gauge human inferential skills. Third, because different people will have different strategies and preferences, no single solution may be correct or optimal for all persons. In light of these limitations, a more functional approach to decision interpretation is discussed.     

A re-evaluation of story grammars

Black and Wilensky (1979) have made serious methodological errors in analyzing story grammars, and in the process they have committed additional errors in applying formal language theory. Our arguments involve clarifying certain aspects of knowledge representation crucial to a proper treatment of story understanding. Particular criticisms focus on the following shortcomings of their presentation: 1) an erroneous statement from formal language theory, 2) misapplication of formal language theory to story grammars, 3) unsubstantiated and doubtful analogies with English grammar, 4) various non sequiturs concerning the generation of non-stories, 5) a false claim based on the artificial distinction between syntax and semantics, and 6) misinterpretation of the role of story grammars in story understanding. We conclude by suggesting appropriate criteria for the evaluation of story grammars.