It is shown that in any model of constructive mathematics in which a certain omniscience principle is false, for strongly extensional functions on an interval the distinction between sequentially continuous and regulated disappears. It follows, without the use of Markov's Principle, that any recursive function of bounded variation on a bounded closed interval is recursively sequentially continuous.

Uniform sequential continuity, a property classically equivalent to sequential continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.

It is shown constructively that, on a metric space that is dense in itself, if every pointwise continuous, real-valued function is uniformly sequentially continuous, then the space has the anti-Specker property. The converse is also discussed. Finally, we show that the anti-Specker property implies a restricted form of countable compactness.

The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for iterated contours of sequential cascades. A related problem of continuous extension of maps between maximal elements of sequential cascades to full subcascades is solved in full generality.

The main result of this paper is a weak constructive version of the uniform continuity theorem for pointwise continuous, real-valued functions on a convex subset of a normed linear space. Recursive examples are given to show that the hypotheses of this theorem are necessary. The remainder of the paper discusses conditions which ensure that a sequentially continuous function is continuous. MSC: 03F60, 26E40, 46S30.

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We show that every mapping is sequentially continuous if and only if it is sequentially nondiscontinuous and strongly extensional, and that "every mapping is strongly extensional", "every sequentially nondiscontinuous mapping is sequentially continuous", and a weak version of Markov's principle are equivalent. Also, assuming a consequence of Church's thesis, we prove a version of the Kreisel-Lacombe-Shoenfield-Tsĕitin theorem.

Continuous subgraph matching problem on dynamic graph has become a popular research topic in the field of graph analysis, which has a wide range of applications including information retrieval and community detection. Specifically, given a query graph q, an initial graph G 0, and a graph update stream △ G i, the problem of continuous subgraph matching is to sequentially conduct all possible isomorphic subgraphs covering △ G i of q on G i. Since knowledge graph is a directed labeled (...) multigraph having multiple edges between a pair of vertices, it brings new challenges for the problem focusing on dynamic knowledge graph. One challenge is that the multigraph characteristic of knowledge graph intensifies the complexity of candidate calculation, which is the combination of complex topological and attributed structures. Another challenge is that the isomorphic subgraphs covering a given region are conducted on a huge search space of seed candidates, which causes a lot of time consumption for searching the unpromising candidates. To address these challenges, a method of subgraph-indexed sequential subdivision is proposed to accelerating the continuous subgraph matching on dynamic knowledge graph. Firstly, a flow graph index is proposed to arrange the search space of seed candidates in topological knowledge graph and an adjacent index is designed to accelerate the identification of candidate activation states in attributed knowledge graph. Secondly, the sequential subdivision of flow graph index and the transition state model are employed to incrementally conduct subgraph matching and maintain the regional influence of changed candidates, respectively. Finally, extensive empirical studies on real and synthetic graphs demonstrate that our techniques outperform the state-of-the-art algorithms. (shrink)

The relation between near continuity and sequential continuity for mappings between metric spaces is explored constructively. It is also shown that the classical implications “near continuity implies sequential continuity” and “near continuity implies apart continuity” are essentially nonconstructive.

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We deal with principles which are equivalent to the statements "every mapping is sequentially nondiscontinuous", "every sequentially nondiscontinuous mapping is sequentially continuous", and "every sequentially continuous mapping is continuous". As corollaries, we show that every mapping of a complete separable space is continuous in constructive recursive mathematics (the Kreisel-Lacombe-Schoenfield-Tsejtin theorem) and in intuitionism.

Once assessments and continuers are focussed on as distinguishable phenomena it becomes clear that they differ from each other not just in the details of their sequential placement within an extended turn, but in other significant ways as well.First, though assessments can take the form of talk with clear lexical content (for example `Oh wow' and assessment adjectives such as ‘beautiful’), they can also be done with sounds such as ‘Ah:::’ whose main function seems to be the carrying of (...) an appropriate intonation contour, as well as gesturally (cf. M. Goodwin, 1980). In this they resemble continuers, which can be performed both with talk whose lexical status is not always granted, and with appropriate gestures such as nods. In view of the way in which both continuers and brief assessments are characteristically situated within a rather specialized environment, the ongoing talk of another, it is not surprising that they share these characteristics. Indeed in so far as these features provide minimal lexical and auditory interference with the other talk already in progress, they are precisely some of the adaptations that would be expected of action able to function in such an environment. Given such structural similarity in action that is also quite brief, the clarity with which assessments can be distinguished from continuers becomes interesting. If in fact these objects are doing different work in the same environment, the salience of their distinctness from each other becomes an important feature of the structure of each. In view of the economy and clarity that brief assessments require, it is all the more remarkable that many of them, through the details of the way in which they are pronounced and their intonation contour, are able to convey quite detailed, even intricate, information about their speaker's involvement in both the assessment and the talk of the moment.Second, while ‘uh huh’ seems to be restricted to placement in the midst of extended talk by another, assessments can occur at the completion of such extended turns as well. Indeed assessments are one of the prototypical ways of bringing an extended turn such as a story to completion. Such differential placement is quite compatible with what has already been noted about the organization of these phenomena. For example, insofar as a continuer treats the talk just heard as preliminary to further talk it would be quite inappropriate as a technique for marking completion of an extended turn. On the other hand by virtue of the way in which they appreciate the details of what has just been said without marking that talk as a prelude to something else, assessments are apt structures for doing terminal work on an extended sequence.Third, ‘uh huh’ seems to be an exclusively recipient action — indeed its work as a continuer is accomplished precisely through placement relative to more extended talk by another speaker. Assessments, however, can be done by speaker as well as recipient.Fourth, though analysis in the present paper has focussed on brief assessments (the type of assessment most similar in form to continuers), assessments unlike continuers can in fact take many shapes, some of them quite elaborate with, for example, extended sentences and even sequences of turns being devoted exclusively to the activity of doing an assessment.In sum, alternative types of action are available to recipients for constructing responses in the midst of another's extended talk. Though the responses themselves are typically brief, the presence of alternatives that can be placed in a variety of sequential positions provides recipients with resources that enable them to participate in speaker's emerging talk in a differentiated fashion, something which has consequences for speaker's actions as well. (shrink)

The anti-Specker property, a constructive version of sequential compactness, is used to prove constructively that a pointwise continuous, order-dense preference relation on a compact metric space is uniformly sequentially continuous. It is then shown that Ishihara's principle BD-ℕ implies that a uniformly sequentially continuous, order-dense preference relation on a separable metric space is uniformly continuous. Converses of these two theorems are also proved.

In this paper we suggest a model of sequential auctions with endogenous participation where each bidder conjectures about the number of participants at each round. Then, after learning his value, each bidder decides whether or not to participate in the auction. In the calculation of his expected value, each bidder uses his conjectures about the number of participants for each possible subgroup. In equilibrium, the conjectured probability is compatible with the probability of staying in the auction. In our model, (...) players face participation costs, bidders may buy as many objects as they wish and they are allowed to drop out at any round. Bidders can drop out at any time, but they cannot come back to the auction. In particular we can determine the number of participants and expected prices in equilibrium. We show that for any bidding strategy, there exists such a probability of staying in the auction. For the case of stochastically independent objects, we show that in equilibrium every bidder who decides to continue submits a bid that is equal to his value at each round. When objects are stochastically identical, we are able to show that expected prices are decreasing. (shrink)

We respond to recent comments on our proposal to improve justice in ventilator triage, in which we used as an example New Jersey’s publicly available and legally binding Directive Number 2020-03. We agree with Bernard Lo and Doug White that equity implications of triage frameworks should be continually reassessed, which is why we offered six concrete options for improvement, and called for monitoring the consequences of adopted triage models. We disagree with their assessment that we mis-characterised their Model Guidance, as (...) included in the NJ Directive, in ways that undermine our conclusions. They suggest we erroneously described their model as a two-criterion allocation framework; that recognising other operant criterion reveals it ‘likely mitigate[s] rather than exacerbate[s] racial disparities during triage’, and allege that concerns about inequitable outcomes are ‘without evidence’. We highlight two major studies robustly demonstrating why concerns about disparate outcomes are justified. We also show that White and Lo seek to retrospectively—and counterfactually—correct the version of the Model Guideline included in the NJ Directive. However, as our facsimile reproductions show, neither the alleged four-criteria form, nor other key changes, such as dropping the Sequential Organ Failure Assessment score, are found in the Directive. These points matter because our conclusions hence stand, because the public version of the Model Guidance had not been updated to reduce the risk of inequitable outcomes until June 2021 and NJ’s Directive still does not reflect these revisions, and, hence, represents a less equitable version, as acknowledged by its authors. We comment on broader policy implications and call for ways of ensuring accurate, transparent and timely updates for users of high-stakes guidelines. (shrink)

Continuity is perhaps the most familiar characterization of the finitary character of the operations performed in computation. We sketch the historical and conceptual development of this notion by interpreting it as a unifying theme across three main varieties of semantical theories of programming: denotational, axiomatic and event-based. Our exploration spans the development of this notion from its origins in recursion theory to the forms it takes in the context of the more recent event-based analyses of sequential and concurrent (...) computations, touching upon the relations of continuity with non-determinism. (shrink)

This paper develops a deontic logic based on dynamic logic for reasoning about permission and prohibition of sequential actions. Our approach is characterized by two main features. First, permission and prohibition of sequential actions are not necessarily reduced to permission and prohibition of the actions’ constituent parts. Second, we incorporate the idea that actions may be permitted or prohibited conditional on another action being performed first. The logic interprets actions in terms of sequences of states, and the deontic (...) component of the logic is introduced by relating sequences of states to their legal and illegal future continuations. We consider various different logics obtained by imposing natural constraints on models, and formulate complete axiom systems for several of these logics. (shrink)

The glueing of (sequentially, pointwise, or uniformly) continuous functions that coincide on the intersection of their closed domains is examined in the light of Bishop-style constructive analysis. This requires us to pay attention to the way that the two domains intersect.

We prove two embedding and extension theorems in the context of the constructive theory of metric spaces. The first states that Cantor space embeds in any inhabited complete separable metric space (CSM) without isolated points, X, in such a way that every sequentially continuous function from Cantor space to ℤ extends to a sequentially continuous function from X to ℝ. The second asserts an analogous property for Baire space relative to any inhabited locally non‐compact CSM. Both results rely on having (...) careful constructive formulations of the concepts involved.As a first application, we derive new relationships between “continuity principles” asserting that all functions between specified metric spaces are pointwise continuous. In particular, we give conditions that imply the failure of the continuity principle “all functions from X to ℝ are continuous”, when X is an inhabited CSM without isolated points, and when X is an inhabited locally non‐compact CSM. One situation in which the latter case applies is in models based on “domain realizability”, in which the failure of the continuity principle for any inhabited locally non‐compact CSM, X, generalizes a result previously obtained by Escardó and Streicher in the special case X = C[0, 1].As a second application, we show that, when the notion of inhabited complete separable metric space without isolated points is interpreted in a recursion‐theoretic setting, then, for any such space X, there exists a Banach‐Mazur computable function from X to the computable real numbers that is not Markov computable. This generalizes a result obtained by Hertling in the special case that X is the space of computable real numbers. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

This article investigates how text messages and mobile phone calls interrelate as parts of continuous communication sequences. Based on the recorded mobile communication of 14-year-olds in Denmark and a conversation-analytic approach, the article will show that after a text message in a continuous communication sequence, four different types of conversation may follow: the answer, the reminder, the resumption of conversation and the confirmation. In itself, the change from text message to conversation requires no interactional efforts from the participants. However, changes (...) of mode are related to the different communicative possibilities the text message and the phone call offer: text messages and calls have distinct formal qualities that govern their uses, and participants in a given sequence move between the two modes, exploiting the potential of each as they ascribe meaning to the written and spoken media. (shrink)

The present study explores the influence of challenge stressors on identity orientation directly and via thriving at work and employee investment. Drawing on the broaden–and–build theory of positive emotions, this study proposes challenge stressors as a critical predictor of identity orientation. The purpose of this article is to explore if a particular identity is salient in different contextual factors, and this study suggests that challenge stressors stimulate personal, relational, and collective identities to respond to a situation. The relationships hypothesized in (...) this study were tested using a sample of 225 employees from the banking sector of Pakistan. A time-lagged research design consisting of two waves of data collection was employed. A structural equation modeling technique was used to test the hypotheses regarding the relationship between challenge stressors and identity orientation, including the role of thriving at work and employee investment as intervening mechanisms of this relationship. Results showed that challenge stressors had a significant positive relationship with identity orientation. The results also confirmed the sequential mediation of thriving at work and employee investment in the relationship between challenge stressors and identity orientation. The findings suggest that the positive side of stress as a strength motivates employees for continued self-development. Importantly, challenge stressors enhance employees’ ability to thrive at work and, in turn, they invest in the work more and identify themselves strongly with their organization and work. (shrink)

The goal of the present set of studies is to explore the boundary conditions of category transfer in causal learning. Previous research has shown that people are capable of inducing categories based on causal learning input, and they often transfer these categories to new causal learning tasks. However, occasionally learners abandon the learned categories and induce new ones. Whereas previously it has been argued that transfer is only observed with essentialist categories in which the hidden properties are causally relevant for (...) the target effect in the transfer relation, we here propose an alternative explanation, the unbroken mechanism hypothesis. This hypothesis claims that categories are transferred from a previously learned causal relation to a new causal relation when learners assume a causal mechanism linking the two relations that is continuous and unbroken. The findings of two causal learning experiments support the unbroken mechanism hypothesis. (shrink)

This paper introduces a hybrid model that unifies connectionist, symbolic, and reinforcement learning into an integrated architecture for bottom-up skill learning in reactive sequential decision tasks. The model is designed for an agent to learn continuously from on-going experience in the world, without the use of preconceived concepts and knowledge. Both procedural skills and high-level knowledge are acquired through an agent’s experience interacting with the world. Computational experiments with the model in two domains are reported.

We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are contextual, namely they depend strongly on the specific measurement scheme through which they are determined. We construct Positive-Operator-Valued measures (POVM) that provide such probabilities. For observables with continuous spectrum, the constructed POVMs depend strongly on the resolution of the measurement device, a conclusion that persists even if (...) we consider a quantum mechanical measurement device or the presence of an environment. We then examine the same issues in alternative interpretations of quantum theory. We first show that multi-time probabilities cannot be naturally defined in terms of a frequency operator. We next prove that local hidden variable theories cannot reproduce the predictions of quantum theory for sequential measurements, even when the degrees of freedom of the measuring apparatus are taken into account. Bohmian mechanics, however, does not fall in this category. We finally examine an alternative proposal that sequential measurements can be modeled by a process that does not satisfy the Kolmogorov axioms of probability. This removes contextuality without introducing non-locality, but implies that the empirical probabilities cannot be always defined (the event frequencies do not converge). We argue that the predictions of this hypothesis are not ruled out by existing experimental results (examining in particular the “which way” experiments); they are, however, distinguishable in principle. (shrink)

The quantum theory of sequential measurements is worked out and is employed to provide an operational analysis of basic measurement theoretical notions such as coexistence, correlations, repeatability, and ideality. The problem of the operational definition of continuous observables is briefly revisited, with a special emphasis on the localization observable. Finally, a brief overview is given of possible applications of the theory to various fields and problems in quantum physics.

Conversation analysis is now what Kuhn once called a normal science. It has a discernible body of concepts, methods, and recognizable objects of analysis. More importantly, its considerable archive of accumulated findings has a very high degree of redundancy-in the positive sense that researchers have continually replicated the findings of their colleagues. It ought, then, in every respect, to be the envy of the social sciences generally and not easily dismissed as an abstruse and recondite branch of language studies or (...) "discourse analysis" concerned with merely trivial fragments of recorded talk as such. To help CA be respecified in this way, the present paper unearths a relatively unknown part of its history in the partial book manuscript of Harvey Sacks's "Aspects of the Sequential Organization of Conversation," circulated in mimeo to colleagues in 1970. There we find innumerable appeals to the now well-recognized fact that the practical actions of everyday talk have significant, culturewide, formal structures that are the proper objects of the discipline. Or, in Sacks's own terms, seemingly insignificant mundane events are generated by a powerful social "machinery." The purpose of this paper is, then, to extract a sample of these aspects of Sacks's "Aspects" in order to illustrate, sketch, or give a preliminary sense of just that point. (shrink)

Potential romantic partners often employ specific communicative strategies in computer-mediated communication based on their anticipation of future interactions. This conversation analytic study examines the practice of assessments used in WeChat conversations between potential romantic partners. We found that people recurrently mobilize the action of assessment to maintain or terminate their relationships. Especially, people tend to provide more assessments after an initial assessment, which we term ‘continuing assessment’. We show that continuing assessments are sequentially organized in conversational context between co-participants and (...) are essential for relational developments. When potential partners aim to maintain or advance their relationships, continuing assessments are used to prevent a structurally integrated conversation from falling into closure. In contrast, continuing assessments are applied to put an end to the dialogue and to manage face work. Our study furthers the understanding of the communicative strategies of online dating. (shrink)

In this note we show that the Axiom of Countable Choice is equivalent to two statements from the theory of pseudometric spaces: the first of them is a well-known characterization of uniform continuity for functions between metric spaces, and the second declares that sequentially compact pseudometric spaces are \—meaning that all real valued, continuous functions defined on these spaces are necessarily uniformly continuous.

We propose that all actual causes are simultaneous with their direct effects, as illustrated by both everyday examples and the laws of physics. We contrast this view with the sequential conception of causation, according to which causes must occur prior to their effects. The key difference between the two views of causation lies in differing assumptions about the mathematical structure of time.

This study aimed to analyze the mediating effect of tolerance of uncertainty and trait anxiety on future self-continuity and intention to use Internet wealth management systems. A questionnaire survey was distributed online and a total of 388 participants completed questionnaire, The questionnaire included the following scales: Chinese version of the FSC, Intention to Use the Internet Wealth Management, TU, and TA. Pearson correlation was used to investigate the correlation coefficient between variables while the sequential regression method was used (...) to analyze relationship between variables. To analyze the collected data, the SPSS 26.0 was used. A two-step procedure was applied to analyze the mediation effect. Confirmatory factor analysis was conducted to test the measurement model. Afterward, the Maximum Likelihood method was used for path analysis, and the Bias-corrected Bootstrap method was used to investigate determine the estimated value and confidence interval of the mediating effect. To analyze the mediation effect, the Mplus 7.0 was used. The results showed that FSC positively predicted individuals’ Internet wealth management systems. Furthermore, TU and TA played complete serial multiple mediating roles between FSC and IUIWM. The role of TA and TU have negative impact on intention to use. This study provides a theoretical basis in personality psychology that Internet financial product suppliers can use to improve the attractiveness of their products. Product managers can subdivide users according to these personality traits to provide customized products. (shrink)

The existence of either a maximum or a minimum for a uniformly continuous mapping f of a compact interval into ${\mathbb{R}}$ is established constructively under the hypotheses that f′ is sequentially continuous and f has at most one critical point.

Ishiharaʼs boundedness principleBD-N was introduced in Ishihara [5] and has turned out to be most useful for constructive analysis, see e.g. Ishihara [6]. It is equivalent to the statement that every sequentially continuous function from NN to N is continuous w.r.t. the usual metric topology on NN. We construct models for higher order arithmetic and intuitionistic set theory in which both every function from NN to N is sequentially continuous and in which the axiom of choice from NN to N (...) holds. Since the latter is known to be inconsistent with the statement that all functions from NN to N are continuous these models refute BD-N. (shrink)

We prove two embedding and extension theorems in the context of the constructive theory of metric spaces. The first states that Cantor space embeds in any inhabited complete separable metric space (CSM) without isolated points, X, in such a way that every sequentially continuous function from Cantor space to ℤ extends to a sequentially continuous function from X to ℝ. The second asserts an analogous property for Baire space relative to any inhabited locally non‐compact CSM. Both results rely on having (...) careful constructive formulations of the concepts involved.As a first application, we derive new relationships between “continuity principles” asserting that all functions between specified metric spaces are pointwise continuous. In particular, we give conditions that imply the failure of the continuity principle “all functions from X to ℝ are continuous”, when X is an inhabited CSM without isolated points, and when X is an inhabited locally non‐compact CSM. One situation in which the latter case applies is in models based on “domain realizability”, in which the failure of the continuity principle for any inhabited locally non‐compact CSM, X, generalizes a result previously obtained by Escardó and Streicher in the special case X = C[0, 1].As a second application, we show that, when the notion of inhabited complete separable metric space without isolated points is interpreted in a recursion‐theoretic setting, then, for any such space X, there exists a Banach‐Mazur computable function from X to the computable real numbers that is not Markov computable. This generalizes a result obtained by Hertling in the special case that X is the space of computable real numbers. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

We consider notions of boundedness of subsets of the natural numbers ℕ that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ℕ to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential (...) class='Hi'>continuity. Most of the results do not require countable choice. (shrink)

Continuous poleward motion of microtubules in metazoan mitotic spindles has been fascinating generations of cell biologists over the last several decades. In human cells, this so‐called poleward flux was recently shown to be driven by the coordinated action of four mitotic kinesins. The sliding activities of kinesin‐5/EG5 and kinesin‐12/KIF15 are sequentially supported by kinesin‐7/CENP‐E at kinetochores and kinesin‐4/KIF4A on chromosome arms, with the individual contributions peaking during prometaphase and metaphase, respectively. Although recent data elucidate the molecular mechanism underlying this cellular (...) phenomenon, the functional roles of microtubule poleward flux during cell division remain largely elusive. Here, we discuss potential contribution of microtubule flux engine to various essential processes at different stages of mitosis. (shrink)

Most models of response time (RT) in elementary cognitive tasks implicitly assume that the speed-accuracy trade-off is continuous: When payoffs or instructions gradually increase the level of speed stress, people are assumed to gradually sacrifice response accuracy in exchange for gradual increases in response speed. This trade-off presumably operates over the entire range from accurate but slow responding to fast but chance-level responding (i.e., guessing). In this article, we challenge the assumption of continuity and propose a phase transition model (...) for RTs and accuracy. Analogous to the fast guess model (Ollman, 1966), our model postulates two modes of processing: a guess mode and a stimulus-controlled mode. From catastrophe theory, we derive two important predictions that allow us to test our model against the fast guess model and against the popular class of sequential sampling models. The first prediction—hysteresis in the transitions between guessing and stimulus-controlled behavior—was confirmed in an experiment that gradually changed the reward for speed versus accuracy. The second prediction—bimodal RT distributions—was confirmed in an experiment that required participants to respond in a way that is intermediate between guessing and accurate responding. (shrink)

Individual differences in the strategies that control sequential behavior were investigated in an experiment in which participants memorized sentences and then wrote them by hand, in a non‐cursive style. Thirty‐two participants each wrote eight sentences, which had hierarchical structures with five levels. The dataset included over 31,000 letters. Despite the deliberately constrained nature of the task and stimuli, 23 patterns of behavior were identified from the durations of pauses that occurred before the inscription of letters at four chunk levels, (...) spanning letters, words, phrases, and sentences. A critical path task analytic model, Graphical Production of Memorized Sentences (GPoMS), shows that the control of writing relies on cues that continuously switch between motor actions and chunk retrievals in a just‐in‐time fashion at the level of letter information. GPoMS explains the individual differences in terms of variants of a motor production mechanism and variants of a chunk retrieval mechanism, which involve varying degrees of parallelism between cognitive actions and motor actions. A graphical technique for constructing GPoMS models was developed that enabled the estimation of ongoing working memory demands during production. (shrink)

Many philosophers have argued that the past must be finite in duration because otherwise reaching the present moment would have involved something impossible, namely, the sequential occurrence of an actual infinity of events. In reply, some philosophers have objected that there can be nothing amiss in such an occurrence, since actually infinite sequences are ‘traversed’ all the time in nature, for example, whenever an object moves from one location in space to another. This essay focuses on one of the (...) two available replies to this objection, namely, the claim that actual infinities are not traversed in nature because space, time, and other continuous wholes divide into parts only in so far as we divide them in thought, and thus divide into only a finite number of parts. I grant that this reply succeeds in blunting the anti-finitist objection, but I argue that it also subverts the very argument against an eternal past that it was intended to save. (shrink)

In this paper we investigate conditions for Lp-computability which are in accordance with the classical Grzegorczyk notion of computability for a continuous function. For a given computable real number p ≥ 1 and a compact computable rectangle I ⊂ ℝq, we show that an Lp function f ∈ Lp is LP-computable if and only if f is sequentially computable as a linear functional and the Lp-modulus function of f is effectively continuous at the origin of ℝq.

Sequential von Neumann–Morgernstern (VM) games are a very general formalism for representing multi-agent interactions and planning problems in a variety of types of environments. We show that sequential VM games with countably many actions and continuous utility functions have a sound and complete axiomatization in the situation calculus. This axiomatization allows us to represent game-theoretic reasoning and solution concepts such as Nash equilibrium. We discuss the application of various concepts from VM game theory to the theory of planning (...) and multi-agent interactions, such as representing concurrent actions and using the Baire topology to define continuous payoff functions. (shrink)

Within the research field of computer-mediated communication, extensive attention has been paid to the differences between CMC and spoken conversation, particularly in terms of sequential structure. In this study, the aim is to analyse how participants maintain continuity and handle discontinuities in institutionally arranged, computer-mediated communication. The empirical material consists of chat log files from in-service training courses for professionals in the food production industry. In the chat sessions we analysed, participants initially had some problems in co-ordinating their (...) postings, that is, keeping track of the discussion’s threading.We also found, however, that methods for co-ordinating postings rather quickly were established among the participants. Two methods for making recognizable how postings were to be read were common in the material: 1) the use of personal names to address a specific participant, and 2) recycling part of the content of a previous posting or reformulating the content in the posting addressed in recognizable ways. We also found an emerging norm in their interaction: that of waiting for one’s turn. (shrink)

Our daily lives unfold continuously, yet our memories are organised into distinct events, situated in a specific context of space and time, and chunked when this context changes (at event boundaries). Previous research showed that this process, termed event segmentation, enhances object-context binding but impairs temporal order memory. Physiologically, peaks in pupil dilation index event segmentation, similar to emotion-induced bursts of autonomic arousal. Emotional arousal also modulates object-context binding and temporal order memory. Yet, these two critical factors have not been (...) systematically studied together. To address this gap, we ran a behavioural experiment using a paradigm validated to study event segmentation and extended it with emotion manipulation. During encoding, we sequentially presented greyscale objects embedded in coloured frames (colour changes defining events), with a neutral or aversive sound. During retrieval, we tested participants’ memory of temporal order memory and object-colour binding. We found opposite effects of emotion and event segmentation on episodic memory. While event segmentation enhanced object-context binding, emotion impaired it. On the contrary, event segmentation impaired temporal order memory, but emotion enhanced it. These findings increase our understanding of episodic memory organisation in laboratory settings, and potentially in real life with perceptual changes and emotion fluctuations constantly interacting. (shrink)

This article addressed the issue of how the author of the Gospel according to John portrayed dissent, in particular, how the author had his protagonists respond to the experience of rejection by those typically designated as ‘the Jews’. Research thus far has usually focused on the identity of the dissenters but rarely on the way dissent was handled. This article’s aim was to examine the range of responses to dissent. It employed a sequential reading of the text to identify (...) the various responses and then brought these findings into comparison with the way dissent was handled in related documents of the time, Matthew and Hebrews. It found that responses included not only argument and blame, including threat of divine wrath but also, beyond these, ad hominem allegations that those who dissent were inherently bad or beholden to the devil or had not been predestined or chosen by God to respond. Such categories were, however, not absolute, because the author assumed that people could choose to respond positively and so move from one apparently fixed and predetermined category to another. They served a rhetorical function. A further ploy was to reduce Israel’s tradition to witness and foreshadowing within the tension of asserting both continuity and discontinuity. Contribution: The article concluded that such strategies served in part to comfort and reassure hearers engaged in the process of grief at rejection. As such they warranted critical reflection. (shrink)

Chan Buddhist philosophy as expressed in the Blue Cliff Record and related gongan case commentarial literature is primarily based on the notion of the instantaneous pivot moment, in which a master creates a profound turnaround experience reflecting his own liberation so as to reveal the deficient tendencies of his dialogue partner in a way that leads both parties to enhance their spiritual awareness. What are the implications of the pivot experience for understanding the overall Chan view of time and space? (...) From the standpoint of temporality, Chan emphasizes the unity of momentary experience and continuity unbound yet not oblivious to sequential limitations. In terms of spatiality, the Chan pivot is a universal experience but is realized in particular manifestations of natural phenomena as perceived by an awakened observer. (shrink)

People tend to perceive ongoing continuous activity as series of discrete events. This partitioning of continuous activity may occur, in part, because events correspond to dynamic patterns that have recurred across different contexts. Recurring patterns may lead to reliable sequential dependencies in observers' experiences, which then can be used to guide perception. The current set of simulations investigated whether this statistical structure within events can be used 1) to develop stable internal representations that facilitate perception and 2) to learn (...) when to update such representations in a self-organizing manner. These simulations demonstrate that experience with recurring patterns enables a system to accurately predict upcoming stimuli within an event, to identify boundaries between such events based on transient increases in prediction error, and to use such boundaries to improve prediction about subsequent activities. (shrink)

Dynamic First Order Logic results from interpreting quantification over a variable v as change of valuation over the v position, conjunction as sequential composition, disjunction as non-deterministic choice, and negation as test for continuation. We present a tableau style calculus for DFOL with explicit binding, prove its soundness and completeness, and point out its relevance for programming with DFOL, for automated program analysis including loop invariant detection, and for semantics of natural language. We also extend this to an infinitary (...) calculus for DFOL with iteration and connect up with other work in dynamic logic. (shrink)

We experience the world around us as a smooth and continuous flow. However, there is growing evidence that the stream of sensory inputs is not elaborated in an analog way but is instead organized in discrete or quasi-discrete temporal processing windows. These discrete windows are suggested to depend on rhythmic neural activity in the alpha (and theta) frequency bands, which in turn reflect changes in neural activity within, and coupling between, cortical areas. In the present study, we investigated a possible (...) causal link between oscillatory brain activity in the alpha range (8–12 Hz) and the temporal resolution of visual perception, which determines whether sequential stimuli are perceived as distinct entities or combined into a single representation. To this aim, we employed a two-flash fusion task while participants received focal transcranial alternating current stimulation (tACS) in extra-striate visual regions including V5/MT of the right hemisphere. Our findings show that 10-Hz tACS, as opposed to a placebo (sham tACS), reduces the temporal resolution of perception, inducing participants to integrate the two stimuli into a unique percept more often. This pattern was observed only in the contralateral visual hemifield, providing further support for a specific effect of alpha tACS. The present findings corroborate the idea of a causal link between temporal windows of integration/segregation and oscillatory alpha activity in V5/MT and extra-striate visual regions. They also stimulate future research on possible ways to shape the temporal resolution of human vision in an individualized manner. (shrink)

As argued above, if we examine each "form of knowledge" within a modern historical context, it seems that we can see a sequentially transformational and coincident historical line that links the material, then the institutional, and then the cultural, while maintaining the sequential development of the linked trends from beginning to end. Even a summary of Lin Yusheng's hypothesis is a continuation of the "mind's" function orientation. This framework, however, must still answer the following question: In the process whereby (...) "forms of knowledge" become intimately connected with transformational events or time sequencing, do they appear in the form of a totalitarian theoretical model, or do they exert their influence in the form of the dispersed role of a discourse? More concretely, in the case of China: When the traditional "forms of knowledge" of modern Chinese intellectuals—for example, the methodology and behavior within the "thought discourses" of the Confucian School—faced the challenge of the West, did they use "a comprehensive theory" to undertake self-adjustment? Michel Foucault raised a query about the role of totalitarian discourse in saying: "At the beginning of any research I expressed a query about these long-established ‘unified’ models. Traditionally, according to these ‘unified’ models we differentiate infinite, repetitive and fecund territories within the discourse. Must we necessarily, on these ‘unities’ which actually are not unities, pile up yet another even more obscure and even more controversial ‘unitary’ model?". (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models. Higher-level analyses of these connectionist models reveal subtle relations to symbolic models. Parallel connectionist memory and linguistic processes are hypothesized to give rise to processes that are describable at a higher level as sequential rule application. At the lower level, computation has the character of massively parallel satisfaction of soft numerical constraints; at the higher level, this can lead to competence characterizable by hard rules. Performance will typically deviate from this competence since behavior is achieved not by interpreting hard rules but by satisfying soft constraints. The result is a picture in which traditional and connectionist theoretical constructs collaborate intimately to provide an understanding of cognition. (shrink)