We give a constructive analysis of learning as it arises in various computational interpretations of classical Peano Arithmetic, such as Aschieri and Berardi learning based realizability, Avigad’s update procedures and epsilon substitution method. In particular, we show how to compute in Gödel’s system T upper bounds on the length of learning processes, which are themselves represented in T through learning based realizability. The result is achieved by the introduction of a new non standard model of Gödel’s T, whose (...) new basic objects are pairs of non standard natural numbers and moduli of convergence, where the latter are objects giving constructive information about the former. As a foundational corollary, we obtain that that learning based realizability is a constructive interpretation of Heyting Arithmetic plus excluded middle over Σ10 formulas and of all Peano Arithmetic when combined with Gödel’s double negation translation. As a byproduct of our approach, we also obtain a new proof of Avigad’s theorem for update procedures and thus of the termination of the epsilon substitution method for PA. (shrink)

The present study is concerned the viability of the primary method in contemporary philosophy, i.e., conceptual analysis. Starting out by tracing the roots of this methodology to Platonic philosophy, the study questions whether such a methodology makes sense when divorced from Platonic philosophy, and develops a framework for a kind of analysis that is more in keeping with recent psychological research on categorization. Finally, it is shown that this kind of analysis can be applied to the concept (...) of justification in a manner that furthers the epistemological goal of providing intellectual guidance. (shrink)

Journal Name: Cognitive Linguistics Issue: Ahead of print.

Five recursively axiomatizable theories extending Kleene's intuitionistic theory FIM of numbers and numbertheoretic sequences are introduced and shown to be consistent, by a modified relative realizability interpretation which verifies that every sequence classically defined by a Π11 formula is unavoidable and that no sequence can fail to be classically Δ11. The analytical form of Markov's Principle fails under the interpretation. The notion of strongly inadmissible rule of inference is introduced, with examples.

This note explores the common core of constructive, intuitionistic, recursive and classical analysis from an axiomatic standpoint. In addition to clarifying the relation between Kleene’s and Troelstra’s minimal formal theories of numbers and number-theoretic sequences, we propose some modified choice principles and other function existence axioms which may be of use in reverse constructive analysis. Specifically, we consider the function comprehension principles assumed by the two minimal theories EL and M, introduce an axiom schema CFd asserting (...) that every decidable property of numbers has a characteristic function, and use it to describe a precise relationship between the minimal theories. We show that the axiom schema AC00 of countable choice can be decomposed into a monotone choice schema AC00m (which guarantees that every Cauchy sequence has a modulus) and a bounded choice schema BC00. We relate various (classically correct) axiom schemas of continuous choice to versions of the bar and fan theorems, suggest a constructive choice schema AC1/2,0 (which incidentally guarantees that every continuous function has a modulus of continuity), and observe a constructive equivalence between restricted versions of the fan theorem and correspondingly restricted bounding axioms \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${AB_{1/2,0}^{2^{\mathbb{n}}}}$$\end{document}. We also introduce a version WKL!! of Weak König’s Lemma with uniqueness which is intermediate in strength between WKL and the decidable fan theorem FTd. (shrink)

Constructional approaches to genre model genre knowledge in terms of genre-based constructions. Like all constructions, these represent conventionalized pairings of meaning and form, of varying degrees of length and schematicity, whose pragmatic specifications include their association with a particular socio-cultural context. In this state-of-the-art article I review genre-related constructional work, discussing grammatical patterns that are licensed only in particular contexts, including conversational genres, as well as expressions that qualify as constructions simply on the basis of socio-cultural currency. The appropriateness of (...) constructional analysis for the language of genre derives from the definitional incorporation of discourse-pragmatic information in constructional descriptions and the possibility of relating genre-bound, idiosyncratic patterns to the rest of the constructions in a language through relations of inheritance. I further highlight the compatibility of Frame Semantics with the notion of genre and critically discuss the concept of conventionality as it applies to genre language. (shrink)

Within Bishop's constructive mathematics we provide conditions that ensure weak continuity properties of mappings between metric and normed spaces.

Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and (...) LLPO. Furthermore, we give a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum. (shrink)

Constructive Analysis and Nonstandard Analysis are often characterized as completely antipodal approaches to analysis. We discuss the possibility of capturing the central notion of Constructive Analysis (i.e. algorithm, finite procedure or explicit construction) by a simple concept inside Nonstandard Analysis. To this end, we introduce Omega-invariance and argue that it partially satisfies our goal. Our results provide a dual approach to Erik Palmgren's development of Nonstandard Analysis inside constructive mathematics.

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.

It has been argued that globalization assists the USA to gain a hegemonic position, allowing it to export its culture. Because this exportation leads to the domination by American culture of the local cultures of importing countries, which are the key element in sustaining their citizens’ national identity, citizens of these countries are unable to protect state sovereignty from this cultural invasion. In order to prevent a political crisis arising from such an invasion, these countries will adopt the strategy of (...) cultural localization. However, this top-down approach overestimates the influence of hegemonic cultures and, thus, overlooks the dynamic nature of cultural development that is generated by people’s agency. This essay rejects this top-down model by arguing that texts cannot dominate people, and that people influence their existence and value. (shrink)

Africana scholars often address their texts to a reader who is implicitly white. This tendency, which this article characterizes as the “discursive orientation toward whiteness,” has the pernicious effect of limiting the range and rigor of scholars’ research questions and proposal. This analysis examines the other discursive “face,” following J. Saunders Redding’s observation from almost eighty years ago, which remains unnervingly insightful: “Negro [sic] writers have been obliged to have two faces... to satisfy two different (and opposed when not (...) entirely opposite) audiences, the [B]lack and the white.” Scholars have described this second face in the text in a number of ways—variously as a temperament, a rhythm, or an “aesthetic.” Through an analysis of a few exemplary texts, the current study will describe a few of the most salient characteristics, ultimately in the service of equipping the “Black” scholar with a few effective, liberatory rhetorical strategies. (shrink)

In a previous paper we constructed a full and faithful functor ℳ from the category of locally compact metric spaces to the category of formal topologies . Here we show that for a real-valued continuous function f, ℳ factors through the localic positive reals if, and only if, f has a uniform positive lower bound on each ball in the locally compact space. We work within the framework of Bishop constructive mathematics, where the latter notion is strictly stronger than (...) point-wise positivity. (shrink)

In 1991, Jones developed an issue-contingent model of ethical decision making in which moral intensity is posited to affect the four stages of Rest's 1986 model. Jones claimed that moral intensity, which is "the extent of issue-related moral imperative in a situation", consists of six characteristics: magnitude of consequences, social consensus, probability of effect, temporal immediacy, proximity, and concentration of effect. This article reports the findings of two studies that analyzed the factor structure of moral intensity, operationalized by a 12-item (...) Perceived Moral Intensity Scale adapted from the work of Sing-hapakdi et al. [1996, Journal of Business Research, 36, 245-255] and Frey [2000, Journal of Business Ethics, 26, 181-195]. The two items that were purported to measure CE were dropped due to their inability to effectively tap into the characteristic proposed by Jones. Factor analyses of the remaining 10 items supported a 3-factor structure, with the MC, PE, and TI items loading on the first factor, the PX items loading on the second factor, and the SC items loading on the third factor. These factors were labeled: Probable Magnitude of Consequences, Proximity, and Social Consensus. The authors conclude that moral intensity consists of three characteristics, rather than the six posited by Jones. (shrink)

The child directed speech of twelve English‐speaking motherswas analyzed in terms of utterance‐level constructions. First, the mothers' utterances were categorized in terms of general constructional categories such as Wh‐questions, copulas and transitives. Second, mothers' utterances within these categories were further specified in terms of the initial words that framed the utterance, item‐based phrases such as Are you …, I'll …, It's …, Let's …, What did … The findings were: (i) overall, only about 15% of all maternal utterances had SVO (...) form (most were questions, imperatives, copulas, and fragments); (ii) 51% of all maternal utterances began with one of 52 item‐based phrases, mostly consisting of two words or morphemes (45% began with one of just 17 words); and (iii) children used many of these same item‐based phrases, in some cases at a rate that correlated highly with their own mother's frequency of use. We suggest that analyses of adult–child linguistic interaction should take into account not just general constructional categories, but also the item‐based constructions that adults and children use and the frequency with which they use them. (shrink)

The International Criminal Tribunal for Yugoslavia was established by the UN Security Council in 1993 to prosecute persons responsible for war crimes committed in the former Yugoslavia during the Balkan wars. As the first international war crimes tribunal since the Nuremburg and Tokyo tribunals set up after WWII, the ICTY has attracted immense interest among legal scholars since its inception, but has failed to garner the same level of attention from researchers in other disciplines, notably linguistics. This represents a significant (...) research gap, as the Tribunal’s public discourse can open up interesting avenues of analysis to researchers of law, language, and legal discourse alike. On its official website, the Tribunal claims that it has “irreversibly changed the landscape of international humanitarian law” and lists six specific achievements: “Holding leaders accountable; bringing justice to victims; giving victims a voice; establishing the facts; developing international law and strengthening the rule of the law”. While a number of legal scholars have studied and critiqued the level of ‘achievement’ actually attained by the Tribunal against these metrics and others, of interest to linguists is the ways in which this work might be conveyed discursively. In this paper, we demonstrate how methods from the linguistic field of corpus-based critical discourse analysis can be utilised to explore the discursive construction of such achievements in the language of the ICTY. (shrink)

In the present paper we introduce a constructive theory of nonstandard arithmetic in higher types. The theory is intended as a framework for developing elementary nonstandard analysis constructively. More specifically, the theory introduced is a conservative extension of HAω + AC. A predicate for distinguishing standard objects is added as in Nelson's internal set theory. Weak transfer and idealisation principles are proved from the axioms. Finally, the use of the theory is illustrated by extending Bishop's constructive (...) class='Hi'>analysis with infinitesimals. (shrink)

The constructions of genders and sexualities in different global spaces continue to be influenced by Christian and imperial ideologies. In Africa, genders and sexualities were (mis)construed by colonial and missionary enterprises, and they continue to be defined according to Eurocentric terms and perceptions. This has produced ‘modern sexual repression’. The use of Biblical discourses to construct African genders and sexualities is one way that this repression is mirrored in South Africa. Because of this, African genders and sexualities are marginalised, treated (...) as taboo and depicted as backward and uncivilised, thus, promoting hegemonic heteronormative and monogamous marriages. This article examined how Biblical discourses contributed to this narrative. It further advanced a call for transforming this dominant narrative by engaging theology, gender and sexuality studies and socio-political sciences from the premise of a multidisciplinary epoch. The decolonial motif, with a focus on delinking African genders and sexualities from the Western agenda of sexual repression, serves as the theoretical framework for this research. On the other hand, race, gender and sexuality serve as lenses used to better understand the phenomenon and to explore the use of biblical discourses in this context. Thus, the article makes use of a secondary research approach to carry out this task.Contribution: This article seeks to add to the body of knowledge that endeavours to change the way that biblical discourses are used in South Africa today to construct a narrative that represses non-normative genders and sexualities. (shrink)

Complex-transitive argument structures have received a large amount of attention from syntacticians of both formalist and cognitive-functional orientations. To account for expressions with causative resultative meanings, construction grammar has postulated a family of argument-structure constructions whose core is constituted by the Caused-Motion Construction and the Resultative Construction, exhibiting a locative complement and a predicative complement in the form of an AjP, respectively. Argument structures with NP complements, however, have been largely neglected. The present study investigates these patterns in the International (...) Corpus of English (ICE-GB) by means “collostruction analysis”. It shows that the formal distinction between AjP and NP complements corresponds to a constructional distinction hitherto unrevealed, viz. that between the Resultative Construction and another argument-structure construction, here called the “Denominative Construction”. Apart from improving existing descriptions of the network of complex-transitive argument-structure constructions, this study demonstrates that collostruction analysis can be employed in an exploratory way to discover constructions. (shrink)

This article questions the aptness of ‘discourse analysis’ as a label for our field, and prefers the less reductionist concept of ‘Discourse Interpretation’. It does this through drawing on ideas from the field of philosophical hermeneutics – the theory and practice of interpreting texts. It operationalizes and adapts the construct of the Interpretive Arc from the philosophy of Paul Ricoeur in order to address issues that are central to discourse work, including that of how we warrant the validity of (...) our textual interpretations. The Interpretive Arc consists of six inter-linked phases, which the article presents and exemplifies through discussion of a single text – the story of Babel. Phase 1 of the arc defines readers as being in a state of Estrangement before the text because of the distancing created by its written or technological form. Phase 2 is that of Pre-view, the state of opinion or knowledge that readers bring to a text. At phase 3, a first reading forms readers’ Proto-understanding, their initial ‘guess’ at what the text means. Then processes of Analysis test and evidence the validity of alternative readings, limiting the interpretations which can plausibly be taken from a text. Three byways of interpretive analysis are challenged and discarded: the dominance of author intention, structuralist analysis and limitless polysemy. Analysis then leads into 5, the phase of informed Understanding of the matter or injunction of the text, of what is disclosed or unfolded before the text. The Interpretive Arc is completed in phase 6, Ownership. Here, through processes of critique of their own and the text’s ideologies and of fresh listening, readers are led to a new self formed by the matter of the text. There is a dialectic amongst Analysis, Understanding and Ownership, with each informing and modifying the other. The approach emphasizes interpretation as the heart of discourse work. The 3000-year-old narrative of Babel is a subject as well as an object here. It contributes to the matter of the article and its interpretation is interwoven with the theoretical substance. The story is shown to be an integrated narrative abounding in sophisticated linguistic techniques which show a delight in language. The traditional Christian and Western interpretation of Babel – as an affront to God which results in the curse of multilingualism – is challenged. A re-constructed interpretation informed by intertextual evidence reads the fault of Babel to be the people’s refusal to spread through the earth. Babel can be interpreted as a manifesto against the monolingual and monocultural impetus of empires ancient and contemporary. The multilingual outcome is a positive affirmation of sociocultural and linguistic diversity. (shrink)

Evolutionary change is opportunistic, but its course is strongly constrained in several fundamental ways. These constraints (historical/phylogenetic, functional/adaptive, constructional/morphogenetic) and their dynamic relationships are discussed here and shown to constitute the conceptual framework of Constructional Morphology. Notwithstanding recent published opinions which claim that the discovery of constraints renders Neodarwinian selection theory obsolete, we regard the insights of Constructional Morphology as being entirely consistent with this theory. As is shown here in the case of the Hyracoidea, formal analysis of the (...) constraints which have framed the evolution of various characters extends our understanding of the evolution of a taxon. (shrink)

The activities of Fulani nomads in Ghana have gained considerable media attention and engendered continuing public debate. In this paper, we analyze the prejudiced portrayals of the nomads in the Ghanaian news media, and how these contribute to an exclusionist and a discriminatory discourse that puts the nomads at the margins of Ghanaian society. The study employs a critical discourse analysis framework and draws on a dataset of 160 articles, including news stories, editorials and op-ed pieces. The analysis (...) reveals that the nomads are discursively constructed as undesirables through an othering process that centers on three discourses: a discourse of dangerousness/criminalization, a discourse of alienization, and a discourse of stigmatization. This anti-nomad/fulani rhetoric is evident in the choice of sensational headlines, alarmist news content, organization of arguments, and use of quotations. The paper concludes with a call for more balanced and critical news reporting on the nomads, especially since issues surrounding them border on national cohesion and security. (shrink)

The processes in construction are more likely than others to breed unsafe behaviors, and the consequences of these actions can be serious. This paper first reviews the research status on unsafe behavior in construction teams. It then analyzes the complex mechanisms that lead to unsafe behavior and constructs a three-layer structural model based on agent-based modeling technology. This modeling deals with complexity and elaborates on key points and potential research ideas in the study of unsafe behavior in construction teams. Using (...) the ABM method, the effects of different incentive strategies on the safe behavior of construction teams under different management scenarios were studied. The results showed that when members have a fair perception of the situation, the effect of the excess performance reward distribution, according to the member’s safety awareness level, is better than the average distribution effect. This is the case whether the member’s safety behavior level is positively or negatively related to the member’s safety awareness level. This study proves the feasibility, validity, and universality of the three-layer structural model. It also reaches certain management conclusions and ideas for further development. The purpose of this paper is to provide a reference for research on the containment and prevention of unsafe behavior in construction teams. (shrink)