We interpret solution rules on a class of simple allocation problems as data on the choices of a policy maker. We analyze conditions under which the policy maker’s choices are (i) rational (ii) transitive-rational, and (iii) representable; that is, they coincide with maximization of a (i) binary relation, (ii) transitive binary relation, and (iii) numerical function on the allocation space. Our main results are as follows: (i) a well-known property, contraction independence (a.k.a. IIA) is equivalent to rationality; (ii) every (...) contraction independent and other-c monotonic rule is transitive-rational; and (iii) every contraction independent and other-c monotonic rule, if additionally continuous, can be represented by a numerical function. (shrink)

According to Brehm's intensity of emotion theory, if an emotion has motivational properties, its intensity should be non-monotonically affected by factors similar to those determining the intensity of motivational states. These factors are called deterrents. In the case of emotion, one category of deterrents consists of factors that can potentially interfere with feeling the emotion, such as reasons for not feeling the emotion. Two experiments were carried out to examine whether happiness is a motivational state and, thus, if its intensity (...) is non-monotonically determined by the importance of reasons for not feeling happy. We expected happiness to be reduced by a low importance reason for not feeling happy, to remain high in the presence of a moderately important reason, and to be reduced or eliminated by a very important reason. Both experiments supported the cubic function that results from these expectations, and when the results of the two studies were combined, each of the individual legs of the cubic function was found to be reliable along with the cubic function itself. The theoretical implications of these results are discussed. (shrink)

This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms in mathematical psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of continuity (full, separate, Wold, weak Wold, Archimedean, mixture) with those of solvability (restricted, unrestricted) under the completeness and transitivity of a binary relation. Theorem 2 uses the primitive notion of a separately continuous function to answer the question when an analogous property on a relation is fully continuous. Theorem 3 (...) provides a portmanteau theorem on the equivalence between restricted solvability and various notions of continuity under weak monotonicity. Finally, Theorem 4 presents a variant of Theorem 3 that follows Theorem 1 in dispensing with the dimensionality requirement and in providing partial equivalences between solvability and continuity notions. These theorems are motivated for their potential use in representation theorems. (shrink)

Limitwise monotonic sets and functions constitute an important tool in computable structure theory. We investigate limitwise monotonic numberings. A numbering ν of a family is limitwise monotonic (l.m.) if every set is the range of a limitwise monotonic function, uniformly in k. The set of all l.m. numberings of S induces the Rogers semilattice. The semilattices exhibit a peculiar behavior, which puts them in‐between the classical Rogers semilattices (for computable families) and Rogers semilattices of ‐computable families. We show that (...) every Rogers semilattice of a ‐computable family is isomorphic to some semilattice. On the other hand, there are infinitely many isomorphism types of classical Rogers semilattices which can be realized as semilattices. In particular, there is an l.m. family S such that is isomorphic to the upper semilattice of c.e. m‐degrees. We prove that if an l.m. family S contains more than one element, then the poset is infinite, and it is not a lattice. The l.m. numberings form an ideal (w.r.t. reducibility between numberings) inside the class of all ‐computable numberings. We prove that inside this class, the index set of l.m. numberings is ‐complete. (shrink)

In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.

Let Ω be the least uncountable ordinal. Let K(Ω) be the category where the objects are the countable ordinals and where the morphisms are the strictly monotonic increasing functions. A dilator is a functor on K(Ω) which preserves direct limits and pullbacks. Let $\tau \Omega: \xi = \omega^\xi\}$ . Then τ has a unique "term"-representation in Ω. λξη.ω ξ + η and countable ordinals called the constituents of τ. Let $\delta and K(τ) be the set of the constituents of τ. (...) Let β = max K(τ). Let [ β ] be an occurrence of β in τ such that τ [ β] = τ. Let $\bar \theta$ be the fixed point-free version of the binary Aczel-Buchholz-Feferman-function (which is defined explicitly in the text below) which generates the Bachman-hierarchy of ordinals. It is shown by elementary calculations that $\xi \mapsto \bar \theta(\tau \lbrack \gamma + \xi \rbrack)\delta$ is a dilator for every $\gamma > \max\{\beta. \delta.\omega\}$. (shrink)

We prove that the continuous function${\rm{\hat \Omega }}:2^\omega \to $ that is defined via$X \mapsto \mathop \sum \limits_n 2^{ - K\left} $ for all $X \in {2^\omega }$ is differentiable exactly at the Martin-Löf random reals with the derivative having value 0; that it is nowhere monotonic; and that $\mathop \smallint \nolimits _0^1{\rm{\hat{\Omega }}}\left\,{\rm{d}}X$ is a left-c.e. $wtt$-complete real having effective Hausdorff dimension ${1 / 2}$.We further investigate the algorithmic properties of ${\rm{\hat{\Omega }}}$. For example, we show that the (...) maximal value of ${\rm{\hat{\Omega }}}$ must be random, the minimal value must be Turing complete, and that ${\rm{\hat{\Omega }}}\left \oplus X{ \ge _T}\emptyset \prime$ for every X. We also obtain some machine-dependent results, including that for every $\varepsilon > 0$, there is a universal machine V such that ${{\rm{\hat{\Omega }}}_V}$ maps every real X having effective Hausdorff dimension greater than ε to a real of effective Hausdorff dimension 0 with the property that $X{ \le _{tt}}{{\rm{\hat{\Omega }}}_V}\left$; and that there is a real X and a universal machine V such that ${{\rm{\Omega }}_V}\left$ is rational. (shrink)

We extend the notion of limitwise monotonic functions to include arbitrary computable domains. We then study which sets and degrees are support increasing limitwise monotonic on various computable domains. As applications, we provide a characterization of the sets S with computable increasing η-representations using support increasing limitwise monotonic sets on ℚ and note relationships between the class of order-computable sets and the class of support increasing limitwise monotonic sets on certain domains.

This paper investigates structural properties of monotone function classes within the framework of three-valued logic (3VL), aiming to characterize dependencies and constraints that ensure structural finiteness and order-preserving properties. This research delves into characteristics of structurally finite classes of order-preserving 3VL map. Monotonicity plays a critical role in understanding functional behaviour, which is essential for structuring closed logical operations within $ P_{k} $. We define $ F $ as a closed class in $ P_{k} $, consisting only of (...) mappings that comply with specified operations and are strictly confined to $ P_{k} $. The notation $ F(n) $ represents the subset of mappings in $ F $ dependent on $ n $ variables, highlighting the limited scope of inputs and their respective outputs. Further analysis through $ CR(F) $ facilitates the identification of precursor subclasses within $ F $, which have not yet achieved closure under all necessary operations—a pivotal step in constructing intermediate mapping classes. Within the framework of 3VL, the study examines order-preserving maps $ f_{D}, f_{K}, f_{M^{(2)}}, f_{DM^{(2)}}, f_{KM^{(2)}} $, deliberately excluding the sets $ D, K, M^{(2)} $, where $ DM^{(2)} $ is defined as $ D \cap M^{(2)} $ and $ KM^{(2)} $ as $ K \cap M^{(2)} $. The lattice framework in $ P_{k}(1) $ for $ k = 3 $ systematically organizes these mapping classes based on their completeness properties, with particular emphasis on classes such as $ M $, which is characterized as a comprehensive set governed by the operations of maximum and minimum. Our theorems establish structural finiteness for classes of unary order-preserving maps, emphasizing their two-variable dependency in class construction. This study extends existing findings on single-variable monotonic functions within 3VL by integrating criteria of linear order. Key results include the classification of mapping classes $ F \subseteq M $ containing $ M^{(1)}_{3} $, categorized into distinct groups: $ M^{(1)}_{3}, KM^{(2)}, DM^{(2)}, M^{(2)}, K, D, M $. Inclusion relations are visualized diagrammatically, showing the hierarchical structure of these monotone classes, ultimately validating the structural finiteness of classes incorporating all unary order-preserving maps within the broader context of 3VL. (shrink)

We prove a result relating the author's monotone functional interpretation to the bounded functional interpretation due to Ferreira and Oliva. More precisely we show that largely a solution for the bounded interpretation also is a solution for the monotone functional interpretation although the latter uses the existence of an underlying precise witness. This makes it possible to focus on the extraction of bounds while using the conceptual benefit of having precise realizers at the same time without having to (...) construct them. (shrink)

A famous theorem by van der Waerden states the following: Given any finite coloring of the integers, one color contains arbitrarily long arithmetic progressions. Equivalently, for every q,k, there is an N = N(q,k) such that for every q-coloring of an interval of length N one color contains a progression of length k. An obvious question is what is the growth rate of N = N(q,k). Some proofs, like van der Waerden's combinatorial argument, answer this question directly, while the topological (...) proof by Furstenberg and Weiss does not. We present an analysis of (Girard's variant of) Furstenberg and Weiss's proof based on monotone functional interpretation, both yielding bounds and providing a general illustration of proof mining in topological dynamics. The bounds do not improve previous results by Girard, but only—as is also revealed by the analysis—because the combinatorial proof and the topological dynamics proof in principle are identical. (shrink)

In this paper an attempt is made to provide an analysis of the meaning of the term function and related terms as they are used by R. K. Merton in the first chapter of his book Social Theory and Social Structure. Several problems are suggested which must be solved if statements about functions are to be considered scientifically adequate. Secondly the term functionalism is defined and several of Merton's functionalist explanations of social phenomena are stated and criticized.

In this article we, given a free ultrafilter p on ω, consider the following classes of ultrafilters:(1) T(p) - the set of ultrafilters Rudin-Keisler equivalent to p,(2) S(p)={q ∈ ω*:∃ f ∈ ω ω , strictly increasing, such that q=f β (p)},(3) I(p) - the set of strong Rudin-Blass predecessors of p,(4) R(p) - the set of ultrafilters equivalent to p in the strong Rudin-Blass order,(5) P RB (p) - the set of Rudin-Blass predecessors of p, and(6) P RK (p) (...) - the set of Rudin-Keisler predecessors of p,and analyze relationships between them. We introduce the semi-P-points as those ultrafilters p ∈ ω* for which P RB (p)=P RK (p), and investigate their relations with P-points, weak-P-points and Q-points. In particular, we prove that for every semi-P-point p its α-th left power α p is a semi-P-point, and we prove that non-semi-P-points exist in ZFC. Further, we define an order ⊴ in T(p) by r⊴q if and only if r ∈ S(q). We prove that (S(p),⊴) is always downwards directed, (R(p),⊴) is always downwards and upwards directed, and (T(p),⊴) is linear if and only if p is selective.We also characterize rapid ultrafilters as those ultrafilters p ∈ ω* for which R(p)∖S(p) is a dense subset of ω*.A space X is M-pseudocompact (for ) if for every sequence (U n ) n < ω of disjoint open subsets of X, there are q ∈ M and x ∈ X such that x=q-lim (U n ); that is, for every neighborhood V of x. The P RK (p)-pseudocompact spaces were studied in [ST].In this article we analyze M-pseudocompactness when M is one of the classes S(p), R(p), T(p), I(p), P RB (p) and P RK (p). We prove that every Frolik space is S(p)-pseudocompact for every p ∈ ω*, and determine when a subspace with is M-pseudocompact. (shrink)

This study investigated the roles of the executive functions of inhibition and switching, and of verbal and visuo-spatial working memory capacities, in insight and non-insight tasks. A total of 18 insight tasks, 10 non-insight tasks, and measures of individual differences in working memory capacities, switching, and inhibition were administered to 120 participants. Performance on insight problems was not linked with executive functions of inhibition or switching but was linked positively to measures of verbal and visuo-spatial working memory capacities. Non-insight task (...) performance was positively linked to the executive function of switching (but not to inhibition) and to verbal and visuo-spatial working memory capacities. These patterns regarding executive functions were maintained when the insight and non-insight composites were split into verbal and spatial insight and non-insight composite scores. The results are discussed in relation to dual processing accounts of thinking. (shrink)

Memory represents a key psychological process. It allows us to recall things from the past which may have taken place hours, days, months, or even many years ago. Our memories are intrinsically personal, subjective, and internal, yet without the primary capacity of memory, other important activities such as speech, perception, concept formation, and reasoning would be impossible. The range of different aspects of memory is huge, from our vocabulary and knowledge about language and the world to our personal histories, skills (...) such as walking and talking, and the more simple memory capacities found in lower animals. Amongst the diversity of memory processes, the principal focus in this volume is the long-term representation of complex associative human memory. This refers to the permanently stored representation of individual items and events. The books in the Oxford Debates in Psychology series aim to provide students and researchers with a stimulating, self-contained, and balanced summary of the various theoretical and empirical positions that shape the most controversial and contested areas of research. Memory: Systems, Process, or Function? presents a a debate about the cognitive architecture of the human long-term memory system. The individual chapter authors represent some of the leading researchers and theorists in the field. Each chapter concentates upon the central theoretical question of how long-term memory can best be conceptualized. In particular, is long-term memory best regarded as comprising multiple independent systems, as a processing framework which can be tapped via different levels of processing, or as a complex fnction which can be used in a flexible and task-appropriate manner? The authors of each chapter present their own answers to this and related research questions. The book concludes with an integrated synopsis and appraisal of the different facets of this fascinating debate. (shrink)

We review evidence for multifaceted functional specialization of somatosensory information processing, both within and outside classical somatosensory cortex. We argue that the nature of such specialization has not yet been clarified adequately to regard the proposed action/perception dichotomy as being established. However, we believe this is a good working hypothesis that can motivate further work.

Postulating the subcortical organization of human consciousness provides a critical link for the construal of pain in patients with impaired cortical function or cortical immaturity during early development. Practical implications of the centrencephalic proposal include the redefinition of pain, improved pain assessment in nonverbal humans, and benefits of adequate analgesia/anesthesia for these patients, which certainly justify the rigorous scientific efforts required. (Published Online May 1 2007).

AGM-theory, named after its founders Carlos Alchourrón, Peter Gärdenfors and David Makinson, is the leading contemporary paradigm in the theory of belief-revision. The theory is reformulated here so as to deal with the central relational notions 'J is a contraction of K with respect to A' and 'J is a revision of K with respect to A'. The new theory is based on a principal-case analysis of the domains of definition of the three main kinds of theory-change (expansion, contraction and (...) revision). The new theory is stated by means of introduction and elimination rules for the relational notions. In this new setting one can re-examine the relationship between contraction and revision, using the appropriate versions of the so-called Levi and Harper identities. Among the positive results are the following. One can derive the extensionality of contraction and revision, rather than merely postulating it. Moreover, one can demonstrate the existence of revision-functions satisfying a principle of monotonicity. The full set of AGM-postulates for revision-functions allow for completely bizarre revisions. This motivates a Principle of Minimal Bloating, which needs to be stated as a separate postulate for revision. Moreover, contractions obtained in the usual way from the bizarre revisions, by using the Harper identity, satisfy Recovery. This provides a new reason (in addition to several others already adduced in the literature) for thinking that the contraction postulate of Recovery fails to capture the Principle of Minimal Mutilation. So the search is still on for a proper explication of the notion of minimal mutilation, to do service in both the theory of contraction and the theory of revision. The new relational formulation of AGM-theory, based on principal-case analysis, shares with the original, functional form of AGM-theory the idealizing assumption that the belief-sets of rational agents are to be modelled as consistent, logically closed sets of sentences. The upshot of the results presented here is that the new relational theory does a better job of making important matters clear than does the original functional theory. A new setting has been provided within which one can profitably address two pressing questions for A GM-theory: (1) how is the notion of minimal mutilation (by both contractions and revisions) best analyzed? and (2) how is one to rule out unnecessary bloating by revisions? (shrink)

This paper argues that a behavioral or functional analysis of human action is compatible with human freedom. This thesis is quite contrary to what behaviorists such as B. F. Skinner as well as their critics such as D. C. Dennett have assumed to be the case. The essential argument involves three steps. First, the paper proceeds by presenting a novel analysis of intentional or mental states in terms of the principles of reinforcement. It is argued that with the acquisition of (...) language humans are able to think about, plan for, and make rational choices about the future. Second, the paper, while not trying to define freedom, nonetheless argues that freedom is essentially a function of three conditions. These include our power over the environment, our will power, and the ability to rationally determine our value priorities. Third, and finally, it is shown that there is nothing in a behavioral or functional analysis to prevent our satisfying these three basic conditions of which our freedom is a function. (shrink)

This paper critically appraises the arguments that have been offered for what can be called ‘the expressive function of punishment’. According to this view, what distinguishes punishment from other kinds of non-punitive hard treatment is that punishment conveys a censorial/reprobative message about what the punished has done, and that this expressive function should therefore be accepted as part of the nature and definition of punishment. Against this view, this papers argues that the standard account of punishment, according to (...) which punishment is a kind of hard treatment that is imposed on an alleged offender in response to her alleged wrongdoing, can already properly account for punishment and distinguish it from other kinds of hard treatment when it is properly clarified and understood. Thus there is no need to accept the expressive function of punishment in addition to the standard account when it comes to the nature and definition of punishment. (shrink)

Style and Function: A Study of the dominant stylistic features of the prose portions of Pali canonical sutta texts and their mnemonic function. Mark Allon. The Internatioal Institute for Buddhist Studies, Tokyo 1997. xiv, 394 pp. ISBN 4-906267-40-8.

We share Nair-Collins and Joffe's (2023) concern with the accuracy of the “whole brain-death” diagnosis, which fails to take into account current understandings of residual brain function (neurohor...

Jon Elster and Daniel Little have criticized social scientists for appealing to a mechanism of social selection in functional explanations of social practices. Both believe that there is no such mechanism operative in the social world. I develop and defend an account of functional explanation in which a mechanism of social selection figures centrally. In addition to developing an account of social selection, I clarify what functional hypotheses purport to claim, and re-examine the role of agents’ intentions in functional explanations (...) in an effort to show why a mechanism of social selection is indispensable to adequate functional explanations. (shrink)

A variety of semiotic resources makes the construction of scientific knowledge possible and meaning-making resources are conveyed by certain semiotic modes. Next, numerous studies have demonstrated the pedagogical importance of gestures in the demonstration of scientific knowledge in the classroom. Drawing on social semiotic systemic functional theory and legitimation code theory, this study explores the types and the role of gestures in the semiotic construction of scientific knowledge in pedagogic semiosis and their pedagogical values for the meaning-making of science content. (...) With this aim, a gesture observation protocol (GOP) is developed to annotate and analyze data. Two science lectures, which are broadcast remotely for middle school students including gifted students, are observed. Systemic Functional Multimodal Discourse Analysis (SF-MDA) method is employed to analyze and evaluate data. Results demonstrated that the deployment of gestures that contributes to the construction of scientific knowledge is low and deployed gestures mostly do not have pedagogical value. It is recommended that teachers should be more conscious and educated about deploying gestures to present scientific knowledge efficiently. (shrink)

Conflict can profoundly affect individuals and their groups. Oftentimes, conflict involves a clash between one side seeking change and increased gains through victory and the other side defending the status quo and protecting against loss and defeat. However, theory and empirical research largely neglected these conflicts between attackers and defenders, and the strategic, social, and psychological consequences of attack and defense remain poorly understood. To fill this void, we model (1) the clashing of attack and defense as games of strategy (...) and reveal that (2) attack benefits from mismatching its target's level of defense, whereas defense benefits from matching the attacker's competitiveness. This suggests that (3) attack recruits neuroendocrine pathways underlying behavioral activation and overconfidence, whereas defense invokes neural networks for behavioral inhibition, vigilant scanning, and hostile attributions; and that (4) people invest less in attack than defense, and attack often fails. Finally, we propose that (5) in intergroup conflict, out-group attack needs institutional arrangements that motivate and coordinate collective action, whereas in-group defense benefits from endogenously emerging in-group identification. We discuss how games of attack and defense may have shaped human capacities for prosociality and aggression, and how third parties can regulate such conflicts and reduce their waste. (shrink)

Felicitas Goodman (1990) observed that naive participants experienced unique trance states, characterized by specific visionary content, when they assumed particular postures and listened to monotonous rattling. Students (n = 284), enrolled in various sections of the course Introduction to Psychology, experienced one of four conditions with their eyes closed: Sitting Quietly with and without Drumming, Standing (Feather Serpent) Posture plus Drumming with and without Suggested Experiences. Participants completed the Phenomenology of Consciousness Inventory (Pekala 1982, 1991c) and wrote narratives following their (...) respective stimulus conditions. Participants reported less imagery, joy, and absorption, but more internal dialogue, self‐awareness, and muscular tension in the posture, compared to the sitting quietly, conditions. Goodman's results of specific posture (content‐related) effects with naive participants were not replicated. (shrink)

Today we are in the midst of a far-reaching shift in scientific thought involving the recasting of many of our long-cherished ideas and preconceptions. To some this appears but the orderly evolution of scientific thought, while to others it portends a revolution in both the ideas and the methods of scientific inquiry.

Neuroscientists have long sought to study the dynamic activity of the human brain—what's happening in the brain, that is, while people are thinking, feeling, and acting. Ideally, an inside look at brain function would simultaneously and continuously measure the biochemical state of every cell in the central nervous system. While such a miraculous method is science fiction, a century of progress in neuroimaging technologies has made such simultaneous and continuous measurement a plausible fiction. Despite this progress, practitioners of modern (...) neuroimaging struggle with two kinds of limitations: those that attend the particular neuroimaging methods we have today and those that would limit any method of imaging neural activity, no matter how powerful.In this essay, I consider the liabilities and potential of techniques that measure human brain activity. I am concerned here only with methods that measure relevant physiologic states of the central nervous system and relate those measures to particular mental states. I will consider in particular the preeminent method of functional neuroimaging: BOLD fMRI. While there are several practical limits on the biological information that current technologies can measure, these limits—as important as they are—are minor in comparison to the fundamental logical restraints on the conclusions that can be drawn from brain imaging studies. (shrink)

A conservative extension of first order logic, suitable for circumscriptive inference, is introduced.

Nicotinic acetylcholine receptors (nAChRs) are ligand‐gated ion channels that bring about a diversity of fast synaptic actions. Analysis of the Caenorhabditis elegans genome has revealed one of the most‐extensive and diverse nAChR gene families known, consisting of at least 27 subunits. Striking variation with possible functional implications has been observed in normally conserved motifs at the acetylcholine‐binding site and in the channel‐lining region. Some nAChR subunits are particular to neurons whilst others are present in both neurons and muscles. The localization (...) of subunits in non‐synaptic regions suggests novel roles for nAChRs. Genetic and heterologous expression studies have identified a subset of nAChR subunits that are important drug targets while the study of mutants has identified genes functionally‐linked to nAChRs. Future studies using C. elegans offer the prospect of increasing our understanding of the functional diversity of a complex nAChR gene family as well as addressing the role of nAChRs and associated proteins in human disorders. BioEssays 26:39–49, 2004.© 2003 Wiley Periodicals, Inc. (shrink)