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.

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.

It is shown that—over Bishop's constructive mathematics—the indecomposability of ℝ is equivalent to the statement that all functions from a complete metric space into a metric space are sequentially nondiscontinuous. Furthermore we prove that the indecomposability of ℝ \ {0} is equivalent to the negation of the disjunctive version of Markov's Principle. These results contribute to the programme of Constructive Reverse Mathematics.

It will be shown that the Peres–Mermin square admits value-definite noncontextual hidden-variable models if the observables associated with the operators can be measured only sequentially but not simultaneously. Namely, sequential measurements allow for noncontextual models in which hidden states update between consecutive measurements. Two recent experiments realizing the Peres–Mermin square by sequential measurements will also be analyzed along with other hidden-variable models accounting for these experiments.

According to T. M. Scanlon’s anti-aggregation principle, it is wrong to save a larger number of people from minor harms rather than a smaller number from much more serious harms. This principle is a central part of many influential and anti-utilitarian ethical theories. According to the sequential-dominance principle, one does something wrong if one knowingly performs a sequence of acts whose outcome would be worse for everyone than the outcome of an alternative sequence of acts. The intuitive appeal of the (...) sequential-dominance principle should be obvious; everyone is knowingly made worse off if it is violated. In this paper, I present a number of cases where one is forced to violate either the anti-aggregation principle or the sequential-dominance principle. I show that these principles conflict regardless of whether one accepts a counterfactual or a temporal, worsening view of harm. Moreover, I show that this result holds regardless of how much worse a harm has to be in order to count as a much more serious harm. (shrink)

Prediction‐based processes appear to play an important role in language. Few studies, however, have sought to test the relationship within individuals between prediction learning and natural language processing. This paper builds upon existing statistical learning work using a novel paradigm for studying the on‐line learning of predictive dependencies. Within this paradigm, a new “prediction task” is introduced that provides a sensitive index of individual differences for developing probabilistic sequential expectations. Across three interrelated experiments, the prediction task and results thereof are (...) used to bridge knowledge of the empirical relation between statistical learning and language within the context of nonadjacency processing. We first chart the trajectory for learning nonadjacencies, documenting individual differences in prediction learning. Subsequent simple recurrent network simulations then closely capture human performance patterns in the new paradigm. Finally, individual differences in prediction performances are shown to strongly correlate with participants’ sentence processing of complex, long‐distance dependencies in natural language. (shrink)

It is widely assumed that language in some form or other originated by piggybacking on pre-existing learning mechanism not dedicated to language. Using evolutionary connectionist simulations, we explore the implications of such assumptions by determining the effect of constraints derived from an earlier evolved mechanism for sequential learning on the interaction between biological and linguistic adaptation across generations of language learners. Artificial neural networks were initially allowed to evolve “biologically” to improve their sequential learning abilities, after which language was introduced (...) into the population. We compared the relative contribution of biological and linguistic adaptation by allowing both networks and language to change over time. The simulation results support two main conclusions: First, over generations, a consistent head-ordering emerged due to linguistic adaptation. This is consistent with previous studies suggesting that some apparently arbitrary aspects of linguistic structure may arise from cognitive constraints on sequential learning. Second, when networks were selected to maintain a good level of performance on the sequential learning task, language learnability is significantly improved by linguistic adaptation but not by biological adaptation. Indeed, the pressure toward maintaining a high level of sequential learning performance prevented biological assimilation of linguistic-specific knowledge from occurring. (shrink)

Causal Decision Theory reckons the choice-worthiness of an option to be completely independent of its evidential bearing on its non-effects. But after one has made a choice this bearing is relevant to future decisions. Therefore it is possible to construct problems of sequential choice in which Causal Decision Theory makes a guaranteed loss. So Causal Decision Theory is wrong. The source of the problem is the idea that agents have a special perspective on their own contemplated actions, from which evidential (...) connections that observers can see are either irrelevant or invisible. (shrink)

The paper analyses the impact of the discovery of the division of infusoria on eighteenth century microscopical iconography. In Autumn 1765, when reproducing the antispontaneist experiments of Lazzaro Spallanzani, Horace-Bénédict de Saussure (1740-1799) discovered a new method of generation of the animalcules of the infusions, namely their division. Drawing a dividing animalcule raised particular problems, notably the question of how to depict the time sequence of a microscopical creature. Although Saussure's journal of microscopical experiments remained unpublished, the discovery was soon (...) diffused and acknowledged by the European naturalists who began to repeat the observations and quickly faced iconographic problems similar to those experienced by Saussure. Indeed, linearity, used to picture time, is a construction, and, notably for public images, scholars had to contend with the conventions of drawers and engravers. The analysis of microscopical iconographic material of the period 1740-1786 shows that during this period, certain naturalists invented new solutions for depicting time, but diffusion of their innovations was not immediate. Nevertheless, in regards to the illustration of microscopical creatures, it is between 1765 and 1776 that the use of linearity was established as a solution enabling an audience to read an iconographic time process as a text. (shrink)

Independence is the condition that, if X is preferred to Y, then a lottery between X and Z is preferred to a lottery between Y and Z given the same probability of Z. Is it rationally required that one’s preferences conform to Independence? The main objection to this requirement is that it would rule out the alleged rationality of Allais and Ellsberg Preferences. In this paper, I put forward a sequential dominance argument with fairly weak assumptions for a variant of (...) Independence (called Independence for Constant Prospects), which shows that Allais and Ellsberg Preferences are irrational. Hence this influential objection (that is, the alleged rationality of Allais and Ellsberg Preferences) can be rebutted. I also put forward a number of sequential dominance arguments that various versions of Independence are requirements of rationality. One of these arguments is based on very minimal assumptions, but the arguments for the versions of Independence which are strong enough to serve in the standard axiomatization of Expected Utility Theory need notably stronger assumptions. (shrink)

It is widely assumed that language in some form or other originated by piggybacking on pre-existing learning mechanism not dedicated to language. Using evolutionary connectionist simulations, we explore the implications of such assumptions by determining the effect of constraints derived from an earlier evolved mechanism for sequential learning on the interaction between biological and linguistic adaptation across generations of language learners. Artificial neural networks were initially allowed to evolve “biologically” to improve their sequential learning abilities, after which language was introduced (...) into the population. We compared the relative contribution of biological and linguistic adaptation by allowing both networks and language to change over time. The simulation results support two main conclusions: First, over generations, a consistent head-ordering emerged due to linguistic adaptation. This is consistent with previous studies suggesting that some apparently arbitrary aspects of linguistic structure may arise from cognitive constraints on sequential learning. Second, when networks were selected to maintain a good level of performance on the sequential learning task, language learnability is significantly improved by linguistic adaptation but not by biological adaptation. Indeed, the pressure toward maintaining a high level of sequential learning performance prevented biological assimilation of linguistic-specific knowledge from occurring. (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)

In the first author's thesis [10], a sequential language, LRT, for real number computation is investigated. That thesis includes a proof that all polynomials are programmable, but that work comes short of giving a complete characterization of the expressive power of the language even for first-order functions. The technical problem is that LRT is non-deterministic. So a natural characterization of its expressive power should be in terms of relations rather than in terms of functions. In [2], Brattka examines a formalization (...) of recursive relations in the style of Kleene's recursive functions on the natural numbers. This paper is an expanded version of [13] which establishes the expressive power of LRTp, a variant of LRT, in terms of Brattka's recursive relations. Because Brattka already did the work of establishing the precise connection between his recursive relations and Type 2 Theory of Effectivity, we thus obtain a complete characterization of first-order definability in LRTp. (shrink)

Neural network models of memory are notorious for catastrophic interference: Old items are forgotten as new items are memorized (French, 1999; McCloskey & Cohen, 1989). While working memory (WM) in human adults shows severe capacity limitations, these capacity limitations do not reflect neural network style catastrophic interference. However, our ability to quickly apprehend the numerosity of small sets of objects (i.e., subitizing) does show catastrophic capacity limitations, and this subitizing capacity and WM might reflect a common capacity. Accordingly, computational investigations (...) (Knops, Piazza, Sengupta, Eger & Melcher, 2014; Sengupta, Surampudi & Melcher, 2014) suggest that mutual inhibition among neurons can explain both kinds of capacity limitations as well as why our ability to estimate the numerosity of larger sets is limited according to a Weber ratio signature. Based on simulations with a saliency map‐like network and mathematical proofs, we provide three results. First, mutual inhibition among neurons leads to catastrophic interference when items are presented simultaneously. The network can remember a limited number of items, but when more items are presented, the network forgets all of them. Second, if memory items are presented sequentially rather than simultaneously, the network remembers the most recent items rather than forgetting all of them. Hence, the tendency in WM tasks to sequentially attend even to simultaneously presented items might not only reflect attentional limitations, but also an adaptive strategy to avoid catastrophic interference. Third, the mean activation level in the network can be used to estimate the number of items in small sets, but it does not accurately reflect the number of items in larger sets. Rather, we suggest that the Weber ratio signature of large number discrimination emerges naturally from the interaction between the limited precision of a numeric estimation system and a multiplicative gain control mechanism. (shrink)

The effect of recent experience on current behavior has been studied extensively in simple laboratory tasks. We explore the nature of sequential effects in the more naturalistic setting of automobile driving. Driving is a safety-critical task in which delayed response times may have severe consequences. Using a realistic driving simulator, we find significant sequential effects in pedal-press response times that depend on the history of recent stimuli and responses. Response times are slowed up to 100 ms in particular cases, a (...) delay that has dangerous practical consequences. Further, we observe a significant number of history-related pedal misapplications, which have recently been noted as a cause for concern in the automotive safety community. By anticipating these consequences of sequential context, driver assistance systems could mitigate the effects of performance degradations and thus critically improve driver safety. (shrink)

With reference to Mead, Peirce, speech act theory, conversation analysis, and Luhmann's phenomenological grounded version of systems theory, the paper tries to reconstruct actions as products of communication. A triadic sequence is identified as the elementary unit for the intersubjective constitution of an act. This unit combines three achievements: (a) the constitution of meaning by sequential attribution, (b) the intersubjective coordination of attributed meanings, and (c) the reproduction of rules, guiding the process of constitution and coordination of attributed meanings. Then, (...) using the tools of systems theory and applying them to empirical results of ethnomethodology and conversation analysis, it is shown how the rule scheme is integrated in a triadic sequence, functioning on three different levels of communication. Finally, a specific form of repair after next turn is discussed, relating it to the function of preserving the structure of conversational types. The analysis of such conversational types opens a possible realm of cooperation between conversation analysis and Luhmann's version of systems theory. (shrink)

By examining the activity of direction-giving and asking we can discover some of the sequential and other structures which characterize the activity. The insertion sequence, as a sequential structure, can be found to be used by interactants in more than one way to accomplish different results. We can therefore consider the insertion sequence as a sequential structure and, by attending to the activity in which the interactants are engaged, discover the relation between sequential and activity system structures. In this way (...) we can relate what persons are doing and how they are doing it (i.e. the activity being accomplished in and through their talk) to some of the basic structures of conversational interaction (e.g. insertion sequences). (shrink)

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)

This article uses transcriptions from video recordings of airline pilots at work, on actual flights, to consider some locations and the interactional significance of a feature of routine talk in the airline cockpit: and-prefaced turns. As pilots’ work is formally organized for them as many discrete and ordered tasks, and-prefacing is a local means for maintaining an ongoing sense of their conduct of a flight as a whole. By and-prefacing their talk, pilots present some new talk or task as connected (...) and relevantly next in a larger macro-sequence of work for their flight. And-prefacing is evidence of pilots’ orientation to a sense of sequence that can extend well beyond pairs of turns at talk and/or non-talk activities, or even a series of such paired sequences. It allows pilots to make salient the sequentiality of their work where the officially prescribed wordings they must use can leave this implicit. (shrink)

We deal with situations incongruent with our automatic response tendencies much better right after having done so on a previous trial than after having reacted to a congruent trial. The nature of the mechanisms responsible for these sequential congruency effects is currently a hot topic of debate. According to the conflict monitoring model these effects depend on the adjustment of control triggered by the detection of conflict on the preceding situation. We tested whether these conflict monitoring processes can operate implicitly (...) in an implicit learning procedure, modulating the expression of knowledge of which participants are not aware. We reanalyze recently published data, and present an experiment with a probabilistic sequence learning procedure, both showing consistent effects of implicit sequence learning. Despite being implicit, the expression of learning was reduced or completely eliminated right after trials incongruent with the learned sequence, thus showing that sequential congruency effects can be obtained even when the source of congruency itself remains implicit. (shrink)

We show that the property of sequential compactness for subspaces of.

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.

In computer-mediated communication, users cannot ensure that responsive postings are placed in a directly adjacent position. Yet, paired actions are discernible in which a first pair part makes a second pair part conditionally relevant. While previous studies of short messaging service communication show that users usually send clusters of FPPs and that SPPs are ordered in the same chronology, little is known about sequential practices of dealing with multiple FPPs in text-based WhatsApp communication. This article shows that in German WhatsApp (...) dialogues, users apply a chronological as well as a reversed ordering of SPPs. It is argued that this result can only be partly attributed to the affordances of the mobile messenger. Rather, users arrange SPPs in order to foreground particular topics in extended, chat-like dialogues. (shrink)

We introduce a notion of complexity for interpretations, which is used to prove some new results about interpretations of sequential theories. In particular, we give a new, elementary proof of Pudlák's theorem that sequential theories are connected. We also demonstrate a counterexample to the infinitary distributive law $a \vee \bigwedge_{i \in I} b_i = \bigwedge_{i \in I} (a \vee b_i)$ in the lattice of chapters, in which the chapters a and b i are compact. (Counterexamples in which a is not (...) compact have been found previously.). (shrink)

The constructions of sequential calculi are based on the idea of application to the deduction process not only single logical constants but complexes of them as well. Surely, making use of this idea is not obligatory in paraconsistent logic. Nevertheless, using it in this field gives us a convenient tool for seeking proofs in formulation of many paraconsistent logics. Each of sequential propositional logics discussed in this paper is obtained as a result of a transformation of a starting calculus GCL (...) – one of sequential formalizations of classical propositional logic. Let α be a standard propositional language with a vocabulary {p1, p2, p3, . . . , −,∨, &, ⊃,¬,), we shall denote any formulas of α and by the letters Γ,∆, Σ, Θ finite sets of α-formulas. (shrink)

How do activist groups instigate institutional change within an organizational field? Studying the global sports and apparel industry, we explore how activist groups applied different tactics over time, including conflict and collaboration, and how the accumulation of these tactics led to the build-up of pressure on firms within the industry to change their policies and activities on labor issues in their supply chains. Building on interorganizational conflict literature, we show how an industry-level approach is helpful to understand the sequential patterning (...) of tactical choices in evoking institutional change. These findings contribute to the growing literature of activists’ influence strategies. (shrink)

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.

Two recent conversation analytical studies draw contrary conclusions from seemingly very similar materials. Hutchby and Barnett ‘show that, far from revolutionizing the organization of telephone conversation, mobile phone talk retains many of the norms associated with landline phone talk’. Arminen and Leinonen, however, state that landline and mobile calls differ systematically from each other. These incommensurate findings raise the question of why the comparisons between landline and mobile call openings have not been able to determine whether social and communicative practices (...) are changing. It is suggested that auxiliary elements in CA allow the emergence of incompatible findings. The auxiliary assumptions enable authors to construct the phenomenon examined from their chosen perspective. Further, it will be shown that unquestioned assumptions materialize into theoretical notions that guide the research. CA studies seem to conceptualize the relationship between sequential order and sequence structure in different ways, which leads to different findings and results. (shrink)

We relate two sequential models of PCF: the sequential algorithm model due to Berry and Curien and the strongly stable model due to Bucciarelli and the author. More precisely, we show that all the morphisms araising in the strongly stable model of PCF are sequential in the sense that they are the “extensional projections” of some sequential algorithms. We define a model of PCF where morphisms are “extensional” sequential algorithms and prove that any equation between PCF terms which holds in (...) this model also holds in the strongly stable model. (shrink)

Previous studies of Hebrew nu investigate this discourse marker in casual conversation. The current study explores nu on Israeli political phone-in radio programs and broadens our knowledge both about the functions and grammaticization processes of discourse markers and about some particularities of Israeli political talk radio. The comparison to casual talk reveals both qualitative and quantitative differences. In casual talk, the main function of nu is a sequential one – urging further development of an ongoing topic. In the radiophonic data, (...) the most common role of nu is as a keying token, functioning in the affective realm. Furthermore, the talk-radio data show a wider variety of keys constructed by nu – which range from joking to sheer contempt – clustering closer towards the latter, in contrast to the case of casual talk, manifesting mostly the joking key. Structurally, whereas sequential functions are generally accomplished by stand-alone nu, affective tokens are accompanied by same-speaker talk. The analysis sheds new light on how a sequential token might come to function in the affective realm. (shrink)