We upgrade [3] to a complete proof of the conjecture NP = PSPACE that is known as one of the fundamental open problems in the mathematical theory of computational complexity; this proof is based on [2]. Since minimal propositional logic is known to be PSPACE complete, while PSPACE to include NP, it suffices to show that every valid purely implicational formula ρ has a proof whose weight and time complexity of the provability involved are both polynomial in the weight of (...) ρ. As is [3], we use proof theoretic approach. Recall that in [3] we considered any valid ρ in question that had a “short” tree-like proof π in the Hudelmaier-style cutfree sequent calculus for minimal logic. The “shortness” means that the height of π and the total weight of different formulas occurring in it are both polynomial in the weight of ρ. However, the size, and hence also the weight, of π could be exponential in that of ρ. To overcome this trouble we embedded π into Prawitz’s proof system of natural deductions containing single formulas, instead of sequents. As in π, the height and the total weight of different formulas of the resulting tree-like natural deduction ∂1 were polynomial, although the size of ∂1 still could be exponential, in the weight of ρ. In our next, crucial move, ∂1 was deterministically compressed into a “small”, although multipremise, dag-like deduction ∂ whose horizontal levels contained only mutually different formulas, which made the whole weight polynomial in that of ρ. However, ∂ required a more complicated verification of the underlying provability of ρ. In this paper we present a nondeterministic compression of ∂ into a desired standard dag-like deduction ∂0 that deterministically proves ρ in time and space polynomial in the weight of ρ.2 Together with [3] this completes the proof of NP = PSPACE.Natural deductions are essential for our proof. Tree-to-dag horizontal compression of π merging equal sequents, instead of formulas, is not sufficient, since the total number of different sequents in π might be exponential in the weight of ρ – even assuming that all formulas occurring in sequents are subformulas of ρ. On the other hand, we need Hudelmaier’s cutfree sequent calculus in order to control both the height and total weight of different formulas of the initial tree-like proof π, since standard Prawitz’s normalization although providing natural deductions with the subformula property does not preserve polynomial heights. It is not clear yet if we can omit references to π even in the proof of the weaker result NP = coNP. (shrink)

In our previous work we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier’s cut-free sequent calculus for minimal logic with the horizontal compressing in the corresponding minimal Prawitz-style natural deduction. In this Addendum we show how to prove a weaker result NP = coNP without referring to HSC. The underlying idea is to omit full minimal logic and compress only “naive” normal tree-like ND refutations of the existence of Hamiltonian cycles in given non-Hamiltonian graphs, (...) since the Hamiltonian graph problem in NPcomplete. Thus, loosely speaking, the proof of NP = coNP can be obtained by HSC-elimination from our proof of NP = PSPACE. (shrink)

Abstract‘Raising aspirations’ for education among young people in low socioeconomic regions has become a widespread policy prescription for increasing human capital investment and economic competitiveness in so-called ‘knowledge economies’. However, policy tends not to address difficult social, cultural, economic and political conditions for aspiring, based in structural changes associated with globalization. Drawing conceptually on the works of Pierre Bourdieu, Raymond Williams, Arjun Appadurai and authors in the Funds of Knowledge tradition, this article theorizes two logics for aspiring that are recognizable (...) in research with young people and families: a doxic logic, grounded in populist–ideological mediations; and a habituated logic, grounded in biographic–historical legacies and embodied as habitus. A less tangible third ‘logic’ is also theorized: emergent senses of future potential, grounded in lived cultures, which hold possibility for imagining and pursuing alternative futures. The article offers a sociological framework for understanding aspirations as complex social–cultural phenomena, and for capacitating emergent and hopeful aspirations through school- and community-based research and dialogue. (shrink)

Children like Baby G, born with complex chronic medical conditions that compromise function in the long term, are an increasing presence in tertiary-level neonatal intensive care units. The parents and health-care providers of these children are faced with profoundly difficult decisions. Whether severe congenital anomalies with poor prognosis are diagnosed antenatally or are discovered at the time of birth, the issues are vexing, and the impact decisions will have on everyone in the family is profound. What should such decisions be (...) based upon? What values and principles might guide the decision-making process? What moral justifications allow for pursuing.. (shrink)

Hunting and gathering is, evolutionarily, the defining subsistence strategy of our species. Studying how children learn foraging skills can, therefore, provide us with key data to test theories about the evolution of human life history, cognition, and social behavior. Modern foragers, with their vast cultural and environmental diversity, have mostly been studied individually. However, cross-cultural studies allow us to extrapolate forager-wide trends in how, when, and from whom hunter-gatherer children learn their subsistence skills. We perform a meta-ethnography, which allows us (...) to systematically extract, summarize, and compare both quantitative and qualitative literature. We found 58 publications focusing on learning subsistence skills. Learning begins early in infancy, when parents take children on foraging expeditions and give them toy versions of tools. In early and middle childhood, children transition into the multi-age playgroup, where they learn skills through play, observation, and participation. By the end of middle childhood, most children are proficient food collectors. However, it is not until adolescence that adults (not necessarily parents) begin directly teaching children complex skills such as hunting and complex tool manufacture. Adolescents seek to learn innovations from adults, but they themselves do not innovate. These findings support predictive models that find social learning should occur before individual learning. Furthermore, these results show that teaching does indeed exist in hunter-gatherer societies. And, finally, though children are competent foragers by late childhood, learning to extract more complex resources, such as hunting large game, takes a lifetime. (shrink)

At the beginning of the third millennium we are entering a new era. I call it "The Integration/Disintegration Era" because the Integration/ Disintegration Problem is one of the basic problems our world is facing today. Philosophy attempts to work out an integrated view of the universe, of human nature, and of society. The specific philosophical science which has concerned itself with integration/ disintegration, is Integratism. This is the common denominator of different particular problems in the integration /disintegration of the universe, (...) society and personality; and it supplies a possible philosophical solution to the general problem of disintegration. The main concept of integratism is integration [Lat. integer, complete]. My theoretical and empirical study of various aspects of integration/ disintegration problems in modern science and education has led to the formulation of a new, rather systematic and, I believe, quite useful conception of contemporary integratism that contributes not only to the attempt to develop a theory of integration/disintegration processes in various biological and social systems but also to practical problems of developing contemporary integrated educational systems. Further concepts of contemporary integratism are: integrative level, IDon, adaptive disintegration, ADon, disadaptive disintegration, adaptive reintegration, sanosphere, pathosphere, etc. The philosophy of integratism might provide a possible philosophical solution to the general problem of disintegration and in this way assign priority to certain particular problems concerning the disintegration of the world. (shrink)

At the beginning of the third millennium we are entering a new era. I call it "The Integration/Disintegration Era" because the Integration/ Disintegration Problem is one of the basic problems our world is facing today. Philosophy attempts to work out an integrated view of the universe, of human nature, and of society. The specific philosophical science which has concerned itself with integration/ disintegration, is Integratism. This is the common denominator of different particular problems in the integration /disintegration of the universe, (...) society and personality; and it supplies a possible philosophical solution to the general problem of disintegration. The main concept of integratism is integration [Lat. integer, complete]. My theoretical and empirical study of various aspects of integration/ disintegration problems in modern science and education has led to the formulation of a new, rather systematic and, I believe, quite useful conception of contemporary integratism that contributes not only to the attempt to develop a theory of integration/disintegration processes in various biological and social systems but also to practical problems of developing contemporary integrated educational systems. Further concepts of contemporary integratism are: integrative level, IDon, adaptive disintegration, ADon, disadaptive disintegration, adaptive reintegration, sanosphere, pathosphere, etc. The philosophy of integratism might provide a possible philosophical solution to the general problem of disintegration and in this way assign priority to certain particular problems concerning the disintegration of the world. (shrink)

Infants have been described as 'statistical learners' capable of extracting structure (such as words) from patterned input (such as language). Here, we investigated whether prior knowledge influences how infants track transitional probabilities in word segmentation tasks. Are infants biased by prior experience when engaging in sequential statistical learning? In a laboratory simulation of learning across time, we exposed 9- and 10-month-old infants to a list of either disyllabic or trisyllabic nonsense words, followed by a pause-free speech stream composed of a (...) different set of disyllabic or trisyllabic nonsense words. Listening times revealed successful segmentation of words from fluent speech only when words were uniformly disyllabic or trisyllabic throughout both phases of the experiment. Hearing trisyllabic words during the pre-exposure phase derailed infants' abilities to segment speech into disyllabic words, and vice versa. We conclude that prior knowledge about word length equips infants with perceptual expectations that facilitate efficient processing of subsequent language input. (shrink)

We show that arbitrary tautologies of Johansson’s minimal propositional logic are provable by “small” polynomial-size dag-like natural deductions in Prawitz’s system for minimal propositional logic. These “small” deductions arise from standard “large” tree-like inputs by horizontal dag-like compression that is obtained by merging distinct nodes labeled with identical formulas occurring in horizontal sections of deductions involved. The underlying geometric idea: if the height, h(∂), and the total number of distinct formulas, ϕ(∂), of a given tree-like deduction ∂ of a minimal (...) tautology ρ are both polynomial in the length of ρ, |ρ|, then the size of the horizontal dag-like compression ∂ᶜ is at most h(∂)×ϕ(∂), and hence polynomial in |ρ|. That minimal tautologies ρ are provable by tree-like natural deductions ∂ with |ρ|-polynomial h(∂) and ϕ(∂) follows via embedding from Hudelmaier’s result that there are analogous sequent calculus deductions of sequent ⇒ρ. The notion of dag-like provability involved is more sophisticated than Prawitz’s tree-like one and its complexity is not clear yet. Our approach nevertheless provides a convergent sequence of NP lower approximations of PSPACE-complete validity of minimal logic. (shrink)

Work-themed play may allow children to learn complex skills, and ethno-typical and gender-typical behaviors. Thus, play may have made important contributions to the evolution of childhood through the development of embodied capital. Using data from Aka foragers and Ngandu farmer children from the Central African Republic, we ask whether children perform ethno- and gender-typical play and work activities, and whether play prepares children for complex work. Focal follows of 50 Aka and 48 Ngandu children were conducted with the aim of (...) recording children’s participation in 12 categories of work and work-themed play. Using these data, we test a set of hypotheses regarding how age, gender, ethnicity, and task complexity influence children’s activities. As hypothesized, we find performance of work-themed play is negatively correlated with age. Contrary to our hypothesis, children do not play more than they work at complex tasks, but they work more than they play at simple ones. Gender and ethnicity are associated with play and work at culturally salient activities, despite availability of other-gender and other-ethnicity social partners. Our findings show that ethnic and gender biases are apparent in the play and work behavior of Aka and Ngandu children. Moreover, our results show that play helps both forager and farmer children learn complex skills, consistent with play having an adaptive learning function. (shrink)

This paper analyses how the discursive construction, valuation and subjective experience of human capital is evolving in parallel with crises of capital as a world-system. Ideology critique provides tools for analysing policy ‘fictions’ that aim to sustain investment in human capital through education. Foucauldian analytical tools enable analysis of how human capital has become a project of self-appreciation and cultivation of positive psychological traits. We argue that the work of Lauren Berlant provides an important complement to these approaches and enables (...) us to analyse how crises of capital are being lived as the cruelling of optimism about social mobility through investment in oneself as human capital. The paper points to an educational politics and pedagogy for living through infrastructural breakdown in darkly uncertain historical times. (shrink)

Ethical decision-making is a multi-faceted phenomenon, and our understanding of ethics rests on diverse perspectives. While considering how leaders ought to act, scholars have created integrated models of moral reasoning processes that encompass diverse influences on ethical choice. With this, there has been a call to continually develop an understanding of the micro-level factors that determine moral decisions. Both rationalist, such as moral processing, and non-rationalist factors, such as virtue and humanity, shape ethical decision-making. Focusing on the role of moral (...) judgement and moral intent in moral reasoning, this study asks what bearings a trait of mindfulness and a sense of moral responsibility may have on this process. A survey measuring mindfulness, moral responsibility and moral judgement completed by 171 respondents was used for four hypotheses on moral judgement and intent in relation to moral responsibility and mindfulness. The results indicate that mindfulness predict moral responsibility but not moral judgement. Moral responsibility does not predict moral judgement, but moral judgement predicts moral intent. The findings give further insight into the outcomes of mindfulness and expand insights into the models of ethical decision-making. We offer suggestions for further research on the role of mindfulness and moral responsibility in ethical decision-making. (shrink)

We elaborate Weiermann-style phase transitions for well-partial-orderings (wpo) determined by iterated finite sequences under Higman-Friedman style embedding with Gordeev’s symmetric gap condition. For every d-times iterated wpo \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}\right)}$$\end{document} in question, d > 1, we fix a natural extension of Peano Arithmetic, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T \supseteq \sf{PA}}$$\end{document}, that proves the corresponding second-order sentence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} (...) \begin{document}$${\sf{WPO}\left({\rm S}{\textsc{eq}}^{d}, \trianglelefteq _{d}\right) }$$\end{document}. Having this we consider the following parametrized first-order slow well-partial-ordering sentence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}, r\right):}$$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \forall K > 0 \right) \left( \exists M > 0\right) \left( \forall x_{0},\ldots,x_{M}\in {\rm S}\text{\textsc{eq}}^{d}\right)$$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \left( \forall i\leq M\right) \left( \left| x_{i}\right| 1}$$\end{document} then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d},r \right) }$$\end{document} is not provable in T.Moreover, by the well-known proof theoretic equivalences we can just as well replace T by PA or ACA0 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta _{1}^{1}\sf{CA}}$$\end{document}, if d = 2 and d = 3, respectively.In the limit case d → ∞ we replaceEFA-provably computable reals r by EFA-provably computable functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f: \mathbb{N} \rightarrow \mathbb{R}_{+}}$$\end{document} and prove analogous theorems. (In the sequel we denote by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}_{+}}$$\end{document} the set of EFA-provably computable positive reals). In the basic case T = PA we strengthen the basic phase transition result by adding the following static threshold clause\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2}, 1\right)}$$\end{document} is still provable in T = PA (actually in EFA). Furthermore we prove the following dynamic threshold clauses which, loosely speaking are obtained by replacing the static threshold t by slowly growing functions 1α given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1_{\alpha }\left( i\right)\,{:=}\,1+\frac{1}{H_{\alpha }^{-1}\left(i\right) }, H_{\alpha}}$$\end{document} being the familiar fast growing Hardy function and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H_{\alpha }^{-1}\left( i\right)\,{:=}\,\rm min \left\{ j \mid H_{\alpha } \left ( j\right) \geq i \right\}}$$\end{document} the corresponding slowly growing inversion. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha < \varepsilon _{0}}$$\end{document}, then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2}, 1_{\alpha}\right)}$$\end{document} is provable in T = PA. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left( {\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2},1_{\varepsilon _{0}}\right)}$$\end{document} is not provable in T = PA. We conjecture that this pattern is characteristic for all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T\supseteq \sf{PA}}$$\end{document} under consideration and their proof-theoretical ordinals o (T ), instead of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon _{0}}$$\end{document}. (shrink)

Aspects of human life history and cognition, such as our long childhoods and extensive use of teaching, theoretically evolved to facilitate the acquisition of complex tasks. The present paper empirically examines the relationship between subsistence task difficulty and age of acquisition, rates of teaching, and rates of oblique transmission among Hadza and BaYaka foragers from Tanzania and the Republic of Congo. We further examine cross-cultural variation in how and from whom learning occurred. Learning patterns and community perceptions of task difficulty (...) were assessed through interviews. We found no relationship between task difficulty, age of acquisition, and oblique transmission, and a weak but positive relationship between task difficulty and rates of teaching. While same-sex transmission was normative in both societies, tasks ranked as more difficult were more likely to be transmitted by men among the BaYaka, but not among the Hadza, potentially reflecting cross-cultural differences in the sexual division of subsistence and teaching labor. Further, the BaYaka were more likely to report learning via teaching, and less likely to report learning via observation, than the Hadza, possibly owing to differences in socialization practices. (shrink)

This paper provides a roadmap for engaging in cross-cultural, developmental research in practical, ethical, and community-engaged ways. To cultivate the flexibility necessary for conducting cross-cultural research, we structure our roadmap as a series of questions that each research program might consider prior to embarking on cross-cultural examinations in developmental science. Within each topic, we focus on the challenges and opportunities inherent to different types of study designs, fieldwork, and collaborations because our collective experience in conducting research in multiple cultural contexts (...) has taught us that there can be no single “best practice”. Here we identify the challenges that are unique to cross-cultural research as well as present a series of recommendations and guidelines. We also bring to the forefront ethical considerations which are rarely encountered in the laboratory context, but which researchers face daily while conducting research in a cultural context which one is not a member. As each research context requires unique solutions to these recurring challenges, we urge researchers to use this set of questions as a starting point, and to expand and tailor the questions and potential solutions with community members to support their own research design or cultural context. This will allow us to move the field towards more inclusive and ethical research practices. (shrink)

We introduce the appropriate iterated version of the system of ordinal notations from [G1] whose order type is the familiar Howard ordinal. As in [G1], our ordinal notations are partly inspired by the ideas from [P] where certain crucial properties of the traditional Munich' ordinal notations are isolated and used in the cut-elimination proofs. As compared to the corresponding “impredicative” Munich' ordinal notations (see e.g. [B1, B2, J, Sch1, Sch2, BSch]), our ordinal notations arearbitrary terms in the appropriate simple term (...) algebra based on the notion of collapsing functions (which we would rather identify as projective functions). In Sect. 1 below we define the systems of ordinal notationsPRJ( ), for any primitive recursive limit wellordering . In Sect. 2 we prove the crucial well-foundness property by using the appropriate well-quasi-ordering property of the corresponding binary labeled trees [G3]. In Sect. 3 we interprete inPRJ( ) the familiar Veblen-Bachmann hierarchy of ordinal functions, and in Sect. 4 we show that the corresponding Buchholz's system of ordinal notationsOT( ) is a proper subsystem ofPRJ( ), although it has the same order type according to [G3] together with the interpretation from Sect. 2 in the terms of labeled trees. In Sect. 5 we use Friedman's approach in order to obtain an appropriate purely combinatorial statement which is not provable in the theory of iterated inductive definitions ID< λ, for arbitrarily large limit ordinalλ. Formal theories, axioms, etc. used below are familiar in the proof theory of subsystems of analysis (see [BFPS, T, BSch]). (shrink)

Kruskal proved that finite trees are well-quasi-ordered by hom(e)omorphic embeddability. Friedman observed that this statement is not provable in predicative analysis. Friedman also proposed (see in [Simpson]) some stronger variants of the Kruskal theorem dealing with finite labeled trees under home(e)omorphic embeddability with a certain gap-condition, where labels are arbitrary finite ordinals from a fixed initial segment of ω. The corresponding limit statement, expressing that for all initial segments of ω these labeled trees are well-quasi-ordered, is provable in Π 1 (...) 1 -CA, but not in the analogous theory Π 1 1 -CA 0 with induction restricted to sets. Schutte and Simpson proved that the one-dimensional case of Friedman's limit statement dealing with finite labeled intervals is not provable in Peano arithmetic. However, Friedman's gap-condition fails for finite trees labeled with transfinite ordinals. In [Gordeev 1] I proposed another gap-condition and proved the resulting one-dimensional modified statements for all (countable) transfinite ordinal-labels. The corresponding universal modified one-dimensional statement UM 1 is provable in (in fact, is equivalent to) the familiar theory ATR 0 whose proof-theoretic ordinal is Γ 0 . In [Gordeev 1] I also announced that, in the general case of arbitrarily-branching finite trees labeled with transfinite ordinals, in the proof-theoretic sense the hierarchy of the limit modified statements $\mathbf{M}_{ (which are denoted by LM λ in the present note) is as strong as the hierarchy of the familiar theories of iterated inductive definitions (more precisely, see [Gordeev 1, Concluding Remark 3]). In this note I present a "positive" proof of the full universal modified statement UM, together with a short proof of the crucial "reverse" results which is based on Okada's interpretation of the well-established ordinal notations of Buchholz corresponding to the theories of iterated inductive definitions. Formally the results are summarized in $\S5$ below. (shrink)

The paper aims to provide precise proof theoretic characterizations of Myhill–Friedman-style “weak” constructive extensional set theories and Aczel–Rathjen analogous constructive set theories both enriched by Mostowski-style collapsing axioms and/or related anti-foundation axioms. The main results include full intuitionistic conservations over the corresponding purely arithmetical formalisms that are well known in the reverse mathematics – which strengthens analogous results obtained by the author in the 80s. The present research was inspired by the more recent Sato-style “weak weak” classical extensional set theories (...) whose proof theoretic strengths are shown to strongly exceed the ones of the intuitionistic counterparts in the presence of the collapsing axioms. (shrink)

Michael A. Petersa and Fazal Rizvib aBeijing Normal University, Beijing, PR China; bMelbourne University, Melbourne, Australia Our minds are still racing back and forth, longing for a return to ‘no...

Society economics has been always connected with religious and ethic views of each people. A lot of philosophers and theologists closely studied the problem of synthesis and mutual influence of these social institutions. Within the frame of historical development of philosophy there were such periods. The most illustrative example of such synthesis, maybe, is the parallel development of Protestantism and capitalism. It is possible to note this world tendency in the places with strong protestant influence (in particular its conservative branch (...) – kalvinism). Capitalism influence is also strong enough. Kalvin was the first to speak against the capital growth condemnation. He considered economy to be a natural aspect of man’s life which should be regulated in agreement with Bible. It’s worth noting that Kalvinist approach to personal life bred a new type of ascets in secular world very wealthy people who consider their wealth as their duty to the God. The main goal of these people was accumulation for accumulation sake and for their possibility of soul salvation but not for their demand satisfaction. These people consider themselves as some kind of tool; their direct religious duty was to accumulate wealth. This was the essence of “protestant spirit”, the intersection point of capitalism and Protestantism, the starting point of political economics. (shrink)

We analyze N. C. A. da Costa and F. A. Doria’s “exotic formalization” of the conjecture P = NP [3–7]. For any standard axiomatic PA extension T and any number-theoretic sentence ${\varphi }$ , we let ${\varphi ^{\star} := \varphi \vee \lnot \mathsf{Con}\left( \mathsf{T}\right)}$ and prove the following “exotic” inferences 1–3. 1. ${\mathsf{T}+\varphi ^{\star}}$ is consistent, if so is T, 2. ${\mathsf{T}+\varphi}$ is consistent, provided that ${\mathsf{T}+\varphi ^{\star}}$ is ω-consistent, 3. ${\mathsf{T}+\varphi}$ is consistent, provided that T is consistent and has (...) the same provably total recursive functions as ${\mathsf{T}+\left( \varphi \leftrightarrow \varphi ^{\star }\right) }$ . Furthermore we show that 1–3 continue to hold for ${\varphi ^{\star} := \varphi _{S} :=\varphi \vee \lnot S}$ , where ${S=\forall x\exists yR\left( x,y\right)}$ is any ${\Pi _{2}^{0}}$ sentence satisfying: 4. ${\left( \forall n\in \omega \right) \left( \mathsf{T}\vdash S_{x}\left[ \underline{n}\right] \right) }$ , 5. ${\mathsf{Con}\left( \mathsf{T}\right) \Rightarrow \mathsf{T}\nvdash S}$ . We observe that if ${\varphi :=\left[ \mathsf{P}=\mathsf{NP}\right] }$ and ${S:= \left[\digamma total\right] }$ , where ${\digamma=\digamma _{\mathsf{T}}}$ is da Costa-Doria “exotic” function with respect to T, then 4, 5 are satisfied for most familiar (presumably) consistent T in question, while ${\varphi _{S}}$ becomes equivalent to da Costa-Doria “exotic formalization” ${\left[ \mathsf{P}=\mathsf{NP}\right]^{\digamma}}$ . Moreover, the corresponding “exotic” inferences 1–3 generalize analogous da Costa-Doria results. Hence these “exotic” inferences are universal for all number-theoretic sentences and not characteristic to the conjecture P = NP. Nor do they infer relative consistency of P = NP (see Conclusion 15 in the text). (shrink)

The research is focused on the problems of transforming a complex heterogeneous spatial system, urban agglomeration with a unique natural complex. The paper touches upon the following issues: restrictions on spatial development, zoning of territories, transformation of the settlement framework, social transformations, and integration of the most significant city-forming objects. To predict transformations in such a system, a complex multilevel model is considered — “the biosphere core vs. urban environment”. Forming such a model to analyze the prospective development of the (...) territory involves updating the methodology aimed at the systemic socio-ecological-economic analysis of developing heterogeneous spatial systems, integration of cartographic and digital information, adaptation of IT visualization technologies, including the “neogeography” toolkit. In the study the authors analyze the main prospects for the spatial territory development as exemplified by developing the urban environment of the Chelyabinsk agglomeration with a unique “green zone” (Chelyabinsk urban forest), complex multi-level socio-economic system. The main research results create the prerequisites for a significant expansion of the possibilities for analyzing the prospects for sustainable socio-ecological-economic development of complex spatial systems with unique natural objects and effective management of regional development. (shrink)

Familiar proof theoretical and especially automated deduction methods sometimes accept infinity where, in fact, it can be omitted. Our first example deals with the infinite supply of individual variables admitted in 1-order deductions, the second one deals with infinite-branching rules in sequent calculi with number-theoretical induction. The contents of Section 1 summarize and extend basic ideas and results published elsewhere, whereas basic ideas and results of Section 2 are exposed for the first time in the present paper. We consider classical (...) formalisms only, to which constructive formalisms can be reduced by Shanin-style interpretations. (shrink)

The realities of the coronavirus crisis caused by the COVID-19 pandemic, in many cases, become decisive for adjusting the prospects for socio-economic development. The article presents the main results of studying the social aspect of the pandemic in the context of social heterogeneity and specific regional differences. The main points of the study are focused on analyzing the dynamics of the pandemic spreading in Russia’s regions, the specifics and effectiveness of social restrictions, and the transformation of social space. The analysis (...) of the pandemic dynamics was carried out taking into account the information from four large industrial regions in the center of Russia and the Urals. As part of the analysis, a number of problematic issues of the social constraints effectiveness are considered, among which there are the following ones: specificity of the pandemic dynamics by regions in the context of various options for self-isolation, factors of «Path Dependence» of the social space, the consequences of redundant restrictions, social «fatigue» and «erosion» of requirements for isolation. From the viewpoint of updating the transformation priorities - spatial transformations during a pandemic, the following aspects are considered: background for moving from isolation restrictions to spatial transformations, regional employment specificity, socio-economic priorities of spatial transformation, problem-oriented zoning of a heterogeneous socio-economic space. The study is aimed at developing an adequate authorities’ and society’s response to the problems of coronacrisis, forming a regionally adapted set of measures and strategies of socio-economic transformations during the pandemic, creating a basis for solving interdisciplinary issues in the subsequent situation of «normality 2020». (shrink)

In view of the twentieth anniversary of the Socium i Vlast’journal, on the day of the Russian science, a round table was held in the Chelyabinsk branch of the Russian Presidential Academy of National Economy and Public Administration in order to discuss topical issues of crisis dynamics and risks in the context of new global challenges. Below the main materials of the report based on the results of interdisciplinary research series as exemplified by the Chelyabinsk region are presented. The report (...) discusses the following issues: the economic dynamics of crisis processes, the analysis of trends variability, the assessment of the total income of organizations and individuals, the classification of development scenarios, the visualization of trajectories when analyzing the “picture of changes”. The issues of assessing the risks and prospective development scenarios are associated with the consideration and influence of the conditions of prolonged instability on it. (shrink)

This paper is a continuation of dag-like proof compression research initiated in [9]. We investigate proof compression phenomenon in a particular, most transparent case of propositional DNF Logic. We define and analyze a very efficient semi-analytic sequent calculus SEQ*0 for propositional DNF. The efficiency is achieved by adding two special rules CQ and CS; the latter rule is a variant of the weakened substitution rule WS from [9], while the former one being specially designed for DNF sequents. We show that (...) dag-like SEQ*0 has good deterministic proof search strategy. Furthermore, we expose six examples showing that dag-like deducibility in SEQ*0 admits exponential-size proof compression, as compared to familiar proof systems like cutfree sequent calculi, resolution and cutting plane proof systems. (shrink)

The authors present the results of studying migration processes as one of the factors that determine the transformation of the regional social space. Applying migration indicators to assessing prospective spatial changes presupposes a multivariate analysis of developing complex heterogeneous systems. The version of applying problem-oriented visualization tools presented by the authors significantly expands the possibilities of such an analysis. Assessment, systematization and subsequent classification of migration characteristics are considered within the framework of a multi-stage graphical digital analysis procedure. The problems (...) of migration dynamics characterize a number of problems of the incipient deformation of social space. The main provisions and results of the study are presented as exemplified by the five largest urban areas of the Chelyabinsk region. The key contradictions generated by the processes of regional migration are presented for various urban areas of one of the leading industrial regions of the Urals. These are contradictions: dynamics of population inflow — outflow; the ratio of the balance of migration and migration flows, etc. The results of the study make it possible to proceed to more complex models of spatial reconstruction and sustainable development of territories. Considering such models lays the groundwork for passing on to a controlled transformation in the spatial development of territories and reducing the signs of social space deformation. (shrink)