Chemical brain preservation allows the brain to be preserved for millennia. In the coming decades; the information in a chemically preserved brain may be able to be decoded and emulated in a computer. I first examine the history of brain preservation and recent advances that indicate this may soon be a real possibility. I then argue that chemical brain preservation should be viewed as a life-saving medical procedure. Any technology that significantly extends the human life span faces many potential criticisms. (...) However; standard medical ethics entails that individuals should have the autonomy to choose chemical brain preservation. Only if the harm to society caused by brain preservation and future emulation greatly outweighed any potential benefit would it be ethically acceptable to refuse individuals this medical intervention. Since no such harm exists; it is ethical for individuals to choose chemical brain preservation. (shrink)

Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers and Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under integration. In this paper, we will present a natural refinement of their definition that allows for stability results to hold within the wider class of [Formula: see text]-minimal structures. One of the main technical improvements is that we remove the requirement of definable Skolem functions from (...) the proofs. As a result, we obtain stability in particular for all intermediate structures between the semi-algebraic and the sub-analytic languages. (shrink)

We explain how the field of logarithmic-exponential series constructed in 20 and 21 embeds as an exponential field in any field of exponential-logarithmic series constructed in 9, 6, and 13. On the other hand, we explain why no field of exponential-logarithmic series embeds in the field of logarithmic-exponential series. This clarifies why the two constructions are intrinsically different, in the sense that they produce non-isomorphic models of Thequation image; the elementary theory of the ordered field (...) of real numbers, with the exponential function and restricted analytic functions. (shrink)

All known structural extensions of the substructural logic $\textbf{FL}_{\textbf{e}}$, the Full Lambek calculus with exchange/commutativity (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$ -equations), have decidable theoremhood; in particular all the ones defined by knotted axioms enjoy strong decidability properties (such as the finite embeddability property). We provide infinitely many such extensions that have undecidable theoremhood, by encoding machines with undecidable halting problem. An even bigger class of extensions is shown to have undecidable deducibility problem (the (...) corresponding varieties of residuated lattices have undecidable word problem); actually with very few exceptions, such as the knotted axioms and the other prespinal axioms, we prove that undecidability is ubiquitous. Known undecidability results for non-commutative extensions use an encoding that fails in the presence of commutativity, so and-branching counter machines are employed. Even these machines provide encodings that fail to capture proper extensions of commutativity, therefore we introduce a new variant that works on an exponential scale. The correctness of the encoding is established by employing the theory of residuated frames. (shrink)

An exponential $\exp $ on an ordered field $$. The structure$$ is then called an ordered exponential field. A linearly ordered structure $$ is called o-minimal if every parametrically definable subset of M is a finite union of points and open intervals of M.The main subject of this thesis is the algebraic and model theoretic examination of o-minimal exponential fields $$ whose exponential satisfies the differential equation $\exp ' = \exp $ with initial condition $\exp (...) = 1$. This study is mainly motivated by the Transfer Conjecture, which states as follows:Any o-minimal exponential field $$ whose exponential satisfies the differential equation $\exp ' = \exp $ with initial condition $\exp =1$ is elementarily equivalent to $\mathbb {R}_{\exp }$.Here, $\mathbb {R}_{\exp }$ denotes the real exponential field $$, where $\exp $ denotes the standard exponential $x \mapsto \mathrm {e}^x$ on $\mathbb {R}$. Moreover, elementary equivalence means that any first-order sentence in the language $\mathcal {L}_{\exp } = \{+,-,\cdot,0,1, <,\exp \}$ holds for $$ if and only if it holds for $\mathbb {R}_{\exp }$.The Transfer Conjecture, and thus the study of o-minimal exponential fields, is of particular interest in the light of the decidability of $\mathbb {R}_{\exp }$. To the date, it is not known if $\mathbb {R}_{\exp }$ is decidable, i.e., whether there exists a procedure determining for a given first-order $\mathcal {L}_{\exp }$ -sentence whether it is true or false in $\mathbb {R}_{\exp }$. However, under the assumption of Schanuel’s Conjecture—a famous open conjecture from Transcendental Number Theory—a decision procedure for $\mathbb {R}_{\exp }$ exists. Also a positive answer to the Transfer Conjecture would result in the decidability of $\mathbb {R}_{\exp }$. Thus, we study o-minimal exponential fields with regard to the Transfer Conjecture, Schanuel’s Conjecture, and the decidability question of $\mathbb {R}_{\exp }$.Overall, we shed light on the valuation theoretic invariants of o-minimal exponential fields—the residue field and the value group—with additional induced structure. Moreover, we explore elementary substructures and extensions of o-minimal exponential fields to the maximal ends—the smallest elementary substructures being prime models and the maximal elementary extensions being contained in the surreal numbers. Further, we draw connections to models of Peano Arithmetic, integer parts, density in real closure, definable Henselian valuations, and strongly NIP ordered fields.Parts of this thesis were published in [2–5].Abstract prepared by Lothar Sebastian KrappE-mail: sebastian.krapp@uni-konstanz.deURL: https://d-nb.info/1202012558/34. (shrink)

A new three-parameter extension of the generalized-exponential distribution, which has various hazard rates that can be increasing, decreasing, bathtub, or inverted tub, known as the Marshall-Olkin generalized-exponential distribution has been considered. So, this article addresses the problem of estimating the unknown parameters and survival characteristics of the three-parameter MOGE lifetime distribution when the sample is obtained from progressive type-II censoring via maximum likelihood and Bayesian approaches. Making use of the s-normality of classical estimators, two types of approximate (...) confidence intervals are constructed via the observed Fisher information matrix. Using gamma conjugate priors, the Bayes estimators against the squared-error and linear-exponential loss functions are derived. As expected, the Bayes estimates are not explicitly expressed, thus the Markov chain Monte Carlo techniques are implemented to approximate the Bayes point estimates and to construct the associated highest posterior density credible intervals. The performance of proposed estimators is evaluated via some numerical comparisons and some specific recommendations are also made. We further discuss the issue of determining the optimum progressive censoring plan among different competing censoring plans using three optimality criteria. Finally, two real-life datasets are analyzed to demonstrate how the proposed methods can be used in real-life scenarios. (shrink)

To express fine-grained resource-sensitive reasoning, a temporal soft linear logic (TSLL) is introduced as an extension of both Girard's (propositional classical) linear logic (CLL) and Lafont's (propositional classical) soft linear logic (SLL). It is known that the linear exponential operator in CLL can express a specific infinitely reusable resource, i.e. it is reusable not only for any number, but also many times. In contrast, the soft exponential operator in SLL, which is a weak version of the linear (...) exponential operator, can express a specific usable resource, i.e. it is usable in any number, but only once (i.e. it is consumed after use). In TSLL, the resource operators (i.e. linear and soft exponentials) and some temporal operators are combined based on the interpretation that “time” is regarded as a “resource”. The completeness theorem (with respect to phase semantics) for TSLL and the cut-elimination and decidability theorems for some subsystems of TSLL are proved as the main results of this paper. A decidable subsystem, called a bounded soft linear logic (BSLL), which has a restricted soft exponential operator, can represent a specific finitely usable resource. (shrink)

Under the presupposition that human time perception is distorted in intertemporal choice, this study constructs a time scale in the framework of axiomatic measurement. First, the conditions (homogeneity of degree one or two) to identify the form of a time scale are proposed so that one can determine whether the hyperbolic or exponential is a more suitable function for modeling people’s discounting. Homogeneity of degree one implies that subjective time delay is measured by a power scale and its discount (...) function becomes a power-exponential type, whereas homogeneity of degree two implies that subjective time delay is measured by a log scale and its discount function becomes a hyperbolic type. Second, a method is shown for constructing a model that can reflect subadditive and superadditive discounting. A non-commutative and non-associative concatenation operation is provided to generate a time string consisting of subdivided durations that incorporates the effect of repeated delay with a subdivided duration. The discounting model is yielded by substituting these strings in an exponential model equipped with a generalized time scale, and the determination of subadditivity or superadditivity depends on whether the discount function value of a product by the non-commutative and non-associative operation is, respectively, smaller or greater than that of a product by an operation of the usual extensive structure. (shrink)

We present a semantic study of a family of modal intuitionistic linear systems, providing various logics with both an algebraic semantics and a relational semantics, to obtain completeness results. We call modality a unary operator on formulas which satisfies only one rale (regularity), and we consider any subsetW of a list of axioms which defines the exponential of course of linear logic. We define an algebraic semantics by interpreting the modality as a unary operation on an IL-algebra. Then we (...) introduce a relational semantics based on pretopologies with an additional binary relationr between information states. The interpretation of is defined in a suitable way, which differs from the traditional one in classical modal logic. We prove that such models provide a complete semantics for our minimal modal system, as well as, by requiring the suitable conditions onr (in the spirit of correspondence theory), for any of its extensions axiomatized by any subsetW as above. We also prove an embedding theorem for modal IL-algebras into complete ones and, after introducing the notion of general frame, we apply it to obtain a duality between general frames and modal IL-algebras. (shrink)

Every model of IΔ0 is the tally part of a model of the stringlanguage theory Th-FO . We show how to “smoothly” introduce in Th-FO the binary length function, whereby it is possible to make exponential assumptions in models of Th-FO. These considerations entail that every model of IΔ0 + ¬exp is a proper initial segment of a model of Th-FO and that a modicum of bounded collection is true in these models.

The uses of statistical distributions for modeling real phenomena of nature have received considerable attention in the literature. The recent studies have pointed out the potential of statistical distributions in modeling data in applied sciences, particularly in financial sciences. Among them, the two-parameter Lomax distribution is one of the prominent models that can be used quite effectively for modeling data in management sciences, banking, finance, and actuarial sciences, among others. In the present article, we introduce a new three-parameter extension (...) of the Lomax distribution via using a class of claim distributions. The new model may be called the Lomax-Claim distribution. The parameters of the Lomax-Claim model are estimated using the maximum likelihood estimation method. The behaviors of the maximum likelihood estimators are examined by conducting a brief Monte Carlo study. The potentiality and applicability of the Lomax claim model are illustrated by analyzing a dataset taken from financial sciences representing the vehicle insurance loss data. For this dataset, the proposed model is compared with the Lomax, power Lomax, transmuted Lomax, and exponentiated Lomax distributions. To show the best fit of the competing distributions, we consider certain analytical tools such as the Anderson–Darling test statistic, Cramer–Von Mises test statistic, and Kolmogorov–Smirnov test statistic. Based on these analytical measures, we observed that the new model outperforms the competitive models. Furthermore, a bivariate extension of the proposed model called the Farlie–Gumble–Morgenstern bivariate Lomax-Claim distribution is also introduced, and different shapes for the density function are plotted. An application of the bivariate model to GDP and export of goods and services is provided. (shrink)

The exponential accumulation, processing and accrual of big data in healthcare are only possible through an equally rapidly evolving field of big data analytics. The latter offers the capacity to rationalize, understand and use big data to serve many different purposes, from improved services modelling to prediction of treatment outcomes, to greater patient and disease stratification. In the area of infectious diseases, the application of big data analytics has introduced a number of changes in the information accumulation models. These (...) are discussed by comparing the traditional and new models of data accumulation. Big data analytics is fast becoming a crucial component for the modelling of transmission—aiding infection control measures and policies—emergency response analyses required during local or international outbreaks. However, the application of big data analytics in infectious diseases is coupled with a number of ethical impacts. Four key areas are discussed in this paper: automation and algorithmic reliance impacting freedom of choice, big data analytics complexity impacting informed consent, reliance on profiling impacting individual and group identities and justice/fair access and increased surveillance and population intervention capabilities impacting behavioural norms and practices. Furthermore, the extension of big data analytics to include information derived from personal devices, such as mobile phones and wearables as part of infectious disease frameworks in the near future and their potential ethical impacts are discussed. Considered together, the need for a constructive and transparent inclusion of ethical questioning in this rapidly evolving field becomes an increasing necessity in order to provide a moral foundation for the societal acceptance and responsible development of the technological advancement. (shrink)

Extensive empirical work has shown that species richness decreases roughly exponentially or quadratically with latitude. What appears to be a latitudinal gradient in fact may simply be a negative correlation of latitude with area at that latitude, due to convergence of lines of meridian at the poles. There is simply less area at high latitudes, which means fewer niches and fewer opportunities for speciation, hence diminished biodiversity at high latitudes. Similarly, analytic geometry of a cone shows that species number should (...) decrease linearly with altitude on a conical mountain. Here, I provide an explicit mathematical model of the area hypothesis of species richness along latitude and altitude gradients. I re-analyze a previously published latitudinal gradient dataset and show that species number is a linear function of the predicted area and that species number is more fully explained by predicted area than by a quadratic function of latitude. However, analytic geometry is not needed if precise measures of area are known. (shrink)

An extensive survey by Heathcote et al. (in press) found that the Law of Practice is closer to an exponential than a power form. We show that this result is hard to obtain for models using leaky competitive units when practice affects only the input, but that it can be accommodated when practice affects shunting self-excitation.

The problem of when a recursive graph has a recursive k-coloring has been extensively studied by Bean, Schmerl, Kierstead, Remmel, and others. In this paper, we study the polynomial time analogue of that problem. We develop a number of negative and positive results about colorings of polynomial time graphs. For example, we show that for any recursive graph G and for any k, there is a polynomial time graph G′ whose vertex set is {0,1}* such that there is an effective (...) degree preserving correspondence between the set of k-colorings of G and the set of k-colorings of G′ and hence there are many examples of k-colorable polynomial time graphs with no recursive k-colorings. Moreover, even though every connected 2-colorable recursive graph is recursively 2-colorable, there are connected 2-colorable polynomial time graphs which have no primitive recursive 2-coloring. We also give some sufficient conditions which will guarantee that a polynomial time graph has a polynomial time or exponential time coloring. (shrink)

We prove an exponential lower bound on the length of cutting plane proofs. The proof uses an extension of a lower bound for monotone circuits to circuits which compute with real numbers and use nondecreasing functions as gates. The latter result is of independent interest, since, in particular, it implies an exponential lower bound for some arithmetic circuits.

We study the extension 123) of the theory S21 by instances of the dual weak pigeonhole principle for p-time functions, dWPHPx2x. We propose a natural framework for formalization of randomized algorithms in bounded arithmetic, and use it to provide a strengthening of Wilkie's witnessing theorem for S21+dWPHP. We construct a propositional proof system WF , which captures the Π1b-consequences of S21+dWPHP. We also show that WF p-simulates the Unstructured Extended Nullstellensatz proof system of Buss et al. 256). We prove (...) that dWPHP is equivalent to a statement asserting the existence of a family of Boolean functions with exponential circuit complexity. Building on this result, we formalize the Nisan–Wigderson construction in a conservative extension of S21+dWPHP. (shrink)

In this paper a method to construct Kripke models for subtheories of constructive set theory is introduced that uses constructions from classical model theory such as constructible sets and generic extensions. Under the main construction all axioms except the collection axioms can be shown to hold in the constructed Kripke model. It is shown that by carefully choosing the classical models various instances of the collection axioms, such as exponentiation, can be forced to hold as well. The paper does not (...) contain any deep results. It consists of first observations on the subject, and is meant to introduce some notions that could serve as a foundation for further research. (shrink)

We study the extension of public announcement logic PAL by public assignments, which we call PALA. Just as in the case of PAL, the standard procedure for deciding PALA validity, i.e. the use of so-called reduction axioms to translate PALA formulae into formulae in epistemic logic EL, may lead to exponential growth. In this paper, we show that such a price is not mandatory, for we provide a polynomial translation of PALA into EL. This is based on abbreviations (...) of subformulae by new propositional letters. Such optimal translation also enables us to show the computational complexity of the problem of deciding PALA validity, which turns out to be coNP-complete in the single-agent case and PSPACE-complete in the multiagent case. (shrink)

The capacity to collect and analyse data is growing exponentially. Referred to as ‘Big Data’, this scientific, social and technological trend has helped create destabilising amounts of information, which can challenge accepted social and ethical norms. Big Data remains a fuzzy idea, emerging across social, scientific, and business contexts sometimes seemingly related only by the gigantic size of the datasets being considered. As is often the case with the cutting edge of scientific and technological progress, understanding of the ethical implications (...) of Big Data lags behind. In order to bridge such a gap, this article systematically and comprehensively analyses academic literature concerning the ethical implications of Big Data, providing a watershed for future ethical investigations and regulations. Particular attention is paid to biomedical Big Data due to the inherent sensitivity of medical information. By means of a meta-analysis of the literature, a thematic narrative is provided to guide ethicists, data scientists, regulators and other stakeholders through what is already known or hypothesised about the ethical risks of this emerging and innovative phenomenon. Five key areas of concern are identified: informed consent, privacy, ownership, epistemology and objectivity, and ‘Big Data Divides’ created between those who have or lack the necessary resources to analyse increasingly large datasets. Critical gaps in the treatment of these themes are identified with suggestions for future research. Six additional areas of concern are then suggested which, although related have not yet attracted extensive debate in the existing literature. It is argued that they will require much closer scrutiny in the immediate future: the dangers of ignoring group-level ethical harms; the importance of epistemology in assessing the ethics of Big Data; the changing nature of fiduciary relationships that become increasingly data saturated; the need to distinguish between ‘academic’ and ‘commercial’ Big Data practices in terms of potential harm to data subjects; future problems with ownership of intellectual property generated from analysis of aggregated datasets; and the difficulty of providing meaningful access rights to individual data subjects that lack necessary resources. Considered together, these eleven themes provide a thorough critical framework to guide ethical assessment and governance of emerging Big Data practices. (shrink)

abstract As history shows, some human beings are capable of acting very immorally. 1 Technological advance and consequent exponential growth in cognitive power means that even rare evil individuals can act with catastrophic effect. The advance of science makes biological, nuclear and other weapons of mass destruction easier and easier to fabricate and, thus, increases the probability that they will come into the hands of small terrorist groups and deranged individuals. Cognitive enhancement by means of drugs, implants and biological (...) (including genetic) interventions could thus accelerate the advance of science, or its application, and so increase the risk of the development or misuse of weapons of mass destruction. We argue that this is a reason which speaks against the desirability of cognitive enhancement, and the consequent speedier growth of knowledge, if it is not accompanied by an extensive moral enhancement of humankind. We review the possibilities for moral enhancement by biomedical and genetic means and conclude that, though it should be possible in principle, it is in practice probably distant. There is thus a reason not to support cognitive enhancement in the foreseeable future. However, we grant that there are also reasons in its favour, but we do not attempt to settle the balance between these reasons for and against. Rather, we conclude that if research into cognitive enhancement continues, as it is likely to, it must be accompanied by research into moral enhancement. (shrink)

The field of Neuroscience has experienced a growing interest in recent decades, which has led to an exponential growth in the amount of related information made available online as well as the market for Neuroscience-related courses. While this type of knowledge can be greatly beneficial to people working in science, health and education, it can also benefit individuals in other areas. For example, neuroscience knowledge can help people from all fields better understand and critique information about new discoveries or (...) products, and even make better education- and health-related decisions. Online platforms are fertile ground for the creation and spread of fake information, including misrepresentations of scientific knowledge or new discoveries. These types of false information, once spread, can be difficult to tear down and may have widespread negative effects. For example, even scientists are less likely to access retractions of peer-reviewed articles than the original discredited articles. In this study we surveyed general knowledge about neuroscience and the brain among volunteers in Brazil, Latin America’s largest country. We were interested in evaluating the prevalence of neuromyths in this region, and test whether knowledge/neuromyth endorsement differs by age, region, and/or profession. To that end, we created a 30-item survey that was anonymously answered online by 1128 individuals. While younger people generally responded more accurately than people 60 and older, people in the North responded significantly worse than those in the South and Southeast. Most interestingly, people in the biological sciences consistently responded best, but people in the health sciences responded no better than people in the exact sciences or humanities. Furthermore, years of schooling did not correlate with performance, suggesting that quantity may surpass quality when it comes to extension or graduate-level course offerings. We discuss how our findings can help guide efforts toward improving access to quality information and training in the region. (shrink)

In the nearly 40 years since implementation of federal regulations governing the protection of human participants in research, the number of clinical studies has grown exponentially. These studies have become more complex, with multisite trials now common, and there is increasing use of archived biospecimens and related data, including genomics data. In addition, growing emphasis on targeted cancer therapies requires greater collaboration and sharing of research data to ensure that rare patient subsets are adequately represented. Electronic records enable more extensive (...) data collection and mining, but also raise concerns about the potential for inappropriate or unauthorized use of data, bringing patient protections into a new landscape. There are also long-standing concerns about the processes and forms used to obtain informed consent from patients participating in clinical studies. These changes and challenges raise new ethical and practical questions for the oversight of clinical studies, and for protecting patients and their health information in an efficient manner that does not compromise the progress of biomedical research. Contemporary Issues for Protecting Patients in Cancer Research is the summary of a workshop convened by the National Cancer Policy Forum of the Institute of Medicine in February 2014 to explore contemporary issues in human subjects protections as they pertain to cancer research, with the goal of identifying potential relevant policy actions. Clinical researchers, government officials, members of Institutional Review Boards, and patient advocates met to discuss clinical cancer research and oversight. This report examines current regulatory provisions that may not adequately protect patients or may be hindering research, and discusses potential strategies and actions to address those challenges. (shrink)

In this important work, Dr. Felipe Fierro offers a comprehensive view on the subject of Introduction to the Study of Law, in which he revives the use of Gnoseology, Philosophy, History and Logic as Auxiliary Sciences; and exposes how the abandonment of such has contributed to the exponential growth of Skepticism and Relativism, currently prevailing in the legal world. The above, through extensive experience in teaching Law from the Aristotelian-Thomistic platform, based on the elementary assumption that we must first (...) prove the existence of the object of study, and contrast main legal branches in topics such as: what is Law?, why is Science?, what are Law, Justice, Facultative rights and the Common Good?; supported by extensive and select bibliography. In addition, the being, nature, concept, essence and properties of the sources, fundamentals and classification are described. But important elements such as knowledge, order, principles, Jurisprudence, and Natural law, fundamental legal concepts, the legislative process, the Constitution, interpretation and others are not absent. Morality and Legal Law are obligatory markers, which although considered in their own field, are not excluded, but different as to object and method. Predominantly, Justice is exposed as one of the great values of the Law, and main theories in order to offer future lawyers the basis regarding the current Science of Law and its significance. (shrink)

Guarded fragments of first-order logic were recently introduced by Andreka, van Benthem and Nemeti; they consist of relational first-order formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful model-theoretic properties and especially because they are decidable classes that avoid the usual syntactic restrictions (on the arity of relation symbols, the quantifier pattern or the number of variables) of almost all other known decidable (...) fragments of first-order logic. Here, we investigate the computational complexity of these fragments. We prove that the satisfiability problems for the guarded fragment (GF) and the loosely guarded fragment (LGF) of first-order logic are complete for deterministic double exponential time. For the subfragments that have only a bounded number of variables or only relation symbols of bounded arity, satisfiability is EXPTIME-complete. We further establish a tree model property for both the guarded fragment and the loosely guarded fragment, and give a proof of the finite model property of the guarded fragment. It is also shown that some natural, modest extensions of the guarded fragments are undecidable. (shrink)

Goodstein’s principle is arguably the first purely number-theoretic statement known to be independent of Peano arithmetic. It involves sequences of natural numbers which at first appear to diverge, but eventually decrease to zero. These sequences are defined relative to a notation system based on exponentiation for the natural numbers. In this article, we provide a self-contained and modern analysis of Goodstein’s principle, obtaining some variations and improvements. We explore notions of optimality for notation systems and apply them to the classical (...) Goodstein process and to a weaker variant based on multiplication rather than exponentiation. In particular, we introduce the notion of base-change maximality, and show how it leads to far-reaching extensions of Goodstein’s result. We moreover show that by varying the initial base of the Goodstein process, one readily obtains independence results for each of the fragments $\mathsf {I}\Sigma _n$ of Peano arithmetic. (shrink)

According to the implicit commitment thesis, once accepting a mathematical formal system S, one is implicitly committed to additional resources not immediately available in S. Traditionally, this thesis has been understood as entailing that, in accepting S, we are bound to accept reflection principles for S and therefore claims in the language of S that are not derivable in S itself. It has recently become clear, however, that such reading of the implicit commitment thesis cannot be compatible with well-established positions (...) in the foundations of mathematics which consider a specific theory S as self-justifying and doubt the legitimacy of any principle that is not derivable in S: examples are Tait’s finitism and the role played in it by Primitive Recursive Arithmetic, Isaacson’s thesis and Peano Arithmetic, Nelson’s ultrafinitism and sub-exponential arithmetical systems. This casts doubts on the very adequacy of the implicit commitment thesis for arithmetical theories. In the paper we show that such foundational standpoints are nonetheless compatible with the implicit commitment thesis. We also show that they can even be compatible with genuine soundness extensions of S with suitable form of reflection. The analysis we propose is as follows: when accepting a system S, we are bound to accept a fixed set of principles extending S and expressing minimal soundness requirements for S, such as the fact that the non-logical axioms of S are true. We call this invariant component the semantic core of implicit commitment. But there is also a variable component of implicit commitment that crucially depends on the justification given for our acceptance of S in which, for instance, may or may not appear reflection principles for S. We claim that the proposed framework regulates in a natural and uniform way our acceptance of different arithmetical theories. (shrink)

The case for longtermism depends on the vast potential scale of the future. But that same vastness also threatens to undermine the case for longtermism: If the universe as a whole, or the future in particular, contain infinite quantities of value and/or disvalue, then many of the theories of value that support longtermism (e.g., risk-neutral total utilitarianism) seem to imply that none of our available options are better than any other. If so, then even apparently vast effects on the far (...) future cannot in fact make the world morally better. On top of this, some strategies for avoiding this problem of “infinitarian paralysis” (e.g., exponential pure time discounting) yield views that are much less supportive of longtermism. In this chapter, we explore how the potential infinitude of the future affects the case for longtermism. We argue that (i) there are reasonable prospects for extending risk-neutral totalism and similar views to infinite contexts and (ii) many such extension strategies will still support the case for longtermism, since they imply that when we can only effect (or only predictably affect) a finite, bounded part of an infinite universe, we can ignore the unaffectable rest of the universe and reason as if the finite, affectable part were all there is. (shrink)

A new lifetime distribution, called exponential doubly Poisson distribution, is proposed with decreasing, increasing, and upside-down bathtub-shaped hazard rates. One of the reasons for introducing the new distribution is that it can describe the failure time of a system connected in the form of a parallel-series structure. Some properties of the proposed distribution are addressed. Four methods of estimation for the involved parameters are considered based on progressively type II censored data. These methods are maximum likelihood, moments, least squares, (...) and weighted least squares estimations. Through an extensive numerical simulation, the performance of the estimation methods is compared based on the average of mean squared errors and the average of absolute relative biases of the estimates. Two real datasets are used to compare the proposed distribution with some other well-known distributions. The comparison indicates that the proposed distribution is better than the other distributions to match the data provided. (shrink)

In this paper we devise some technical tools for dealing with problems connected with the philosophical view usually called mathematical instrumentalism. These tools are interesting in their own right, independently of their philosophical consequences. For example, we show that even though the fragment of Peano's Arithmetic known as IΣ₁ is a conservative extension of the equational theory of Primitive Recursive Arithmetic (PRA). IΣ₁ has a super-exponential speed-up over PRA. On the other hand, theories studied in the Program of (...) Reverse Mathematics that formalize powerful mathematical principles have only polynomial speed-up over IΣ₁. (shrink)

I offer a new cartography of ethical resistance. I argue that there is an uncharted interaction between managerial secrecy and organizational silence, which may exponentially increase the incidence of corruption in ways not yet understood. Current methods used to raise levels of moral conduct in business and government practice appear blind to this powerful duo. Extensive literature reviews of secrecy and silence scholarships form the background for an early stage conceptual layout of the co-production of secrecy and silence.

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss (...) one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo. (shrink)

Resumen: El concepto “womenomics” propone la idea de “comprar la economía femenina” designando con ello la necesidad de Japón de hacer esfuerzos por incluir exponencialmente a la mujer en el mercado laboral e introducir uno de los mecanismos para corregir un futuro de estancamiento y contracción del crecimiento económico. El concepto lo acuñó en 1999 Kathy M. Matsui al frente de la división de investigación en Asia de Economía, Materias primas y Estrategia del grupo de banca y valores más importantes (...) del mundo, Goldman Sachs. En este ensayo se propone estudiar y analizar críticamente el marco político y económico de la estrategia conocida como Abe-Womenomics con el objetivo de conocer un aspecto de la actual política japonesa doméstica, y, por extensión, las implicaciones regionales e internacionales de su adopción y adaptación, para, luego, demostrar si este tipo de medidas buscan un giro hacia la equidad genuina o solamente replican un patrón productivista, resignificando las aspiraciones feministas en beneficio del sistema neoliberal. Palabras clave: Abe-Womenomics, Womenomics, Kathy M. Matsui, Nancy Fraser, resignificación, neoliberalismo. Abstract: The concept "womenomics" proposes the idea of "buying the female economy", thus designating Japan's need to make efforts to exponentially include women in the labor market and introduce one of the mechanisms to correct a future of stagnation and contraction of the economic growth. The concept was coined in 1999 by Kathy M. Matsui at the head of the Asian research division of Economy, Commodities and Strategy of the world's leading banking and investment group, Goldman Sachs. This essay proposes to study and critically analyze the political and economic framework of the strategy known as Abe-Womenomics, with the aim of knowing an aspect of current Japanese domestic policy, and, by extension, the regional and international implications of its adoption and adaptation. Then, the objective is to demonstrate whether this type of measure seeks a turn towards a genuine equity or only replicates a productivist pattern, re-signifying feminist aspirations for the benefit of the neoliberal system. Keywords: Abe-Womenomics, Womenomics, Kathy M. Matsui, Nancy Fraser, resignification, neoliberalism. (shrink)

We investigate the substitution Frege () proof system and its relationship to extended Frege () in the context of modal and superintuitionistic propositional logics. We show that is p-equivalent to tree-like , and we develop a “normal form” for -proofs. We establish connections between for a logic L, and for certain bimodal expansions of L.We then turn attention to specific families of modal and si logics. We prove p-equivalence of and for all extensions of , all tabular logics, all logics (...) of finite depth and width, and typical examples of logics of finite width and infinite depth. In most cases, we actually show an equivalence with the usual system for classical logic with respect to a naturally defined translation.On the other hand, we establish exponential speed-up of over for all modal and si logics of infinite branching, extending recent lower bounds by P. Hrubeš. We develop a model-theoretical characterization of maximal logics of infinite branching to prove this result. (shrink)

The idea of this paper is to approach linear orderings as generalized ordinals and to study how they are made from their initial segments. First we look at how the equality of two linear orderings can be expressed in terms of equality of their initial segments. Then we shall use similar methods to define functions by recursion with respect to the initial segment relation. Our method is based on the use of a game where smaller and smaller initial segments of (...) linear orderings are considered. The length of the game is assumed to exceed that of the descending sequences of elements of the linear orderings considered. By use of such game-theoretical methods we can for example extend the recursive definitions of the operations of sum, product and exponentiation of ordinals in a unique and natural way for arbitrary linear orderings. Extensions coming from direct limits do not satisfy our game-theoretic requirements in general. We also show how our recursive definitions allow very simple constructions for fixed points of functions, giving rise to certain interesting linear orderings. (shrink)

We develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. We demonstrate polynomial-size refutations for hard tautologies like the pigeonhole principle, Tseitin graph tautologies and the clique-coloring tautologies in these proof systems. Using interpolation we establish an exponential-size lower bound on refutations in a certain, considerably strong, fragment of resolution over linear equations, as well as a general polynomial upper bound on (...) interpolants in this fragment.We then apply these results to extend and improve previous results on multilinear proofs , as studied in [Ran Raz, Iddo Tzameret, The strength of multilinear proofs. Comput. Complexity ]. Specifically, we show the following:• Proofs operating with depth-3 multilinear formulas polynomially simulate a certain, considerably strong, fragment of resolution over linear equations.• Proofs operating with depth-3 multilinear formulas admit polynomial-size refutations of the pigeonhole principle and Tseitin graph tautologies. The former improve over a previous result that established small multilinear proofs only for the functional pigeonhole principle. The latter are different from previous proofs, and apply to multilinear proofs of Tseitin mod p graph tautologies over any field of characteristic 0. We conclude by connecting resolution over linear equations with extensions of the cutting planes proof system. (shrink)

The concept of strong admissibility plays an important role in dialectical proof procedures for grounded semantics allowing, as it does, concise proofs that an argument belongs to the grounded extension without having necessarily to construct this extension in full. One consequence of this property is that strong admissibility ceases to be a unique status semantics. In fact it is straightforward to construct examples for which the number of distinct strongly admissible sets is exponential in the number of (...) arguments. We are interested in characterizing properties of collections of strongly admissible sets in the sense that any system describing the strongly admissible sets of an argument framework must satisfy particular criteria. In terms of previous studies, our concern is the signature and with conditions ensuring realizability. The principal result is to demonstrate that a system of sets describes the strongly admissible sets of some framework if and only if that system has the property of being decomposable. (shrink)

The satisfiability problem for the two-variable fragment of first-order logic is investigated over finite and infinite linearly ordered, respectively wellordered domains, as well as over finite and infinite domains in which one or several designated binary predicates are interpreted as arbitrary wellfounded relations. It is shown that FO 2 over ordered, respectively wellordered, domains or in the presence of one well-founded relation, is decidable for satisfiability as well as for finite satisfiability. Actually the complexity of these decision problems is essentially (...) the same as for plain unconstrained FO 2 , namely non-deterministic exponential time. In contrast FO 2 becomes undecidable for satisfiability and for finite satisfiability, if a sufficiently large number of predicates are required to be interpreted as orderings, wellorderings, or as arbitrary wellfounded relations. This undecidability result also entails the undecidability of the natural common extension of FO 2 and computation tree logic CTL. (shrink)

This book stands at the intersection of two topics: the decidability and computational complexity of hybrid logics, and the deductive systems designed for them. Hybrid logics are here divided into two groups: standard hybrid logics involving nominals as expressions of a separate sort, and non-standard hybrid logics, which do not involve nominals but whose expressive power matches the expressive power of binder-free standard hybrid logics.The original results of this book are split into two parts. This division reflects the division of (...) the book itself. The first type of results concern model-theoretic and complexity properties of hybrid logics. Since hybrid logics which we call standard are quite well investigated, the efforts focused on hybrid logics referred to as non-standard in this book. Non-standard hybrid logics are understood as modal logics with global counting operators ) whose expressive power matches the expressive power of binder-free standard hybrid logics. The relevant results comprise: 1. Establishing a sound and complete axiomatization for the modal logic K with global counting operators ), which can be easily extended onto other frame classes, 2. Establishing tight complexity bounds, namely NExpTime-completeness for the modal logic with global counting operators defined over the classes of arbitrary, reflexive, symmetric, serial and transitive frames ), MT), MD), MB), MK4) with numerical subscripts coded in binary. Establishing the exponential-size model property for this logic defined over the classes of Euclidean and equivalential frames ), MS5).Results of the second type consist of designing concrete deductive systems for standard and non-standard hybrid logics. More precisely, they include: 1. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for a rich class of binder-free standard hybrid logics. An interesting feature of indicated calculi is the nonbranching character of the rule, 2. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for non-standard hybrid logics. The internalization technique applied to a tableau calculus for the modal logic with global counting operators is novel in the literature, 3. Devising the first hybrid algorithm involving an inequality solver for modal logics with global counting operators. Transferring the arithmetical part of reasoning to an inequality solver turned out to be sufficient in ensuring termination.The book is directed to philosophers and logicians working with modal and hybrid logics, as well as to computer scientists interested in deductive systems and decision procedures for logics. Extensive fragments of the first part of the book can also serve as an introduction to hybrid logics for wider audience interested in logic.The content of the book is situated in the areas of formal logic and theoretical computer science with some elements of the theory of computational complexity. (shrink)

Although telepsychiatry consultations have been tried and tested for several years, at least in relatively limited numbers and settings, the current COVID-19 pandemic has caused an exponential increase in their application. Even as lockdown restrictions were lifted and a return to face-to-face consultations was possible, many practitioners and patients decided to uphold teleconsultations for some or a large part of their interactions. This was mostly driven by the exceptional circumstances of the pandemic, as ongoing safety concerns, the need for (...) PPE use and uncertainty around whether face-to-face meetings could go ahead continued to form barriers to usual care practices. Frittgen and Haltaufderheide aptly hypothesise that extensive changes in online communication behaviour will also impact ethical aspects of the therapeutic relationship.1 After considering how the use of technology may affect the therapeutic relationship in video-based consultations, they provide an ethical analysis of this impact along four dimensions: respect for autonomy, lucidity, fidelity and humanity.1 In this commentary I will have a look at the difference between crisis standards of care and usual care, the need to consider specific patient needs in teleconsultation use, the importance of justice understood as equity and access to technology, and a major challenge ahead. Throughout history, crisis situations have often been major catalysts of technological and other progress. Under challenging …. (shrink)

This paper presents a polarized phase semantics, with respect to which the linear fragment of second order polarized linear logic of Laurent [15] is complete. This is done by adding a topological structure to Girard's phase semantics [9]. The topological structure results naturally from the categorical construction developed by Hamano—Scott [12]. The polarity shifting operator ↓ (resp. ↑) is interpreted as an interior (resp. closure) operator in such a manner that positive (resp. negative) formulas correspond to open (resp. closed) facts. (...) By accommodating the exponentials of linear logic, our model is extended to the polarized fragment of the second order linear logic. Strong forms of completeness theorems are given to yield cut-eliminations for the both second order systems. As an application of our semantics, the first order conservativity of linear logic is studied over its polarized fragment of Laurent [16]. Using a counter model construction, the extension of this conservativity is shown to fail into the second order, whose solution is posed as an open problem in [16]. After this negative result, a second order conservativity theorem is proved for an eta expanded fragment of the second order linear logic, which fragment retains a focalized sequent property of [3]. (shrink)

We give resource bounded versions of the Completeness Theorem for propositional and predicate logic. For example, it is well known that every computable consistent propositional theory has a computable complete consistent extension. We show that, when length is measured relative to the binary representation of natural numbers and formulas, every polynomial time decidable propositional theory has an exponential time (EXPTIME) complete consistent extension whereas there is a nondeterministic polynomial time (NP) decidable theory which has no polynomial time (...) complete consistent extension when length is measured relative to the binary representation of natural numbers and formulas. It is well known that a propositional theory is axiomatizable (respectively decidable) if and only if it may be represented as the set of infinite paths through a computable tree (respectively a computable tree with no dead ends). We show that any polynomial time decidable theory may be represented as the set of paths through a polynomial time decidable tree. On the other hand, the statement that every polynomial time decidable, relative to the tally representation of natural numbers and formulas, is equivalent to P = NP. For predicate logic, we develop a complexity theoretic version of the Henkin construction to prove a complexity theoretic version of the Completeness Theorem. Our results imply that that any polynomial space decidable theory △ possesses a polynomial space computable model which is exponential space decidable and thus △ has an exponential space complete consistent extension. Similar results are obtained for other notions of complexity. (shrink)

During balanced growth of cells in culture all extensive properties of the culture — e.g. cell number, total mass, total DNA content — increase exponentially at the same specific growth rate. Therefore, in some average sense, each component of a cell must double between birth and division. For DNA there exists an elaborate mechanism to ensure precise replication of the genetic material and accurate partitioning of identical copies of the genome to the two daughter cells. Do cells possess another mechanism (...) that intentionally relates the timing of cell division to overall increase in cell size, or is the coordination of growth and division an incidental consequence of size‐independent rules for progress through the cell cycle?. (shrink)

Two-player, zero-sum, non-cooperative, blindfold games in extensive form with incomplete information are considered in this paper. Any information about past moves which players played is stored in a database, and each player can access the database. A polynomial game is a game in which, at each step, all players withdraw at most a polynomial amount of previous information from the database. We show resource-bounded determinacy of some kinds of finite, zero-sum, polynomial games whose pay-off sets are computable by non-deterministic polynomial-time (...) function-oracle Turing machines. We call a pay-off set -determined if, for any polynomial game G associated with the given pay-off set, either player has a winning strategy which is in for any subgames of G. We show that there exists an FP-strongly-determined pay-off set which is computed by an exponential-time oracle Turing machine, where FP is the set of polynomial-time computable functions. We also discuss several relationships between the determinacy of polynomial games and recursion-theoretic properties for the classes co-NP and co-NEXP. We show that the polynomial version of the axiom of choice holds under some assumption of polynomial determinacy for a pay-off set which is polynomial-time computable with parallel queries. This principle of choice implies that co-NP has the separation property. (shrink)

Originating from work in operations research the cutting plane refutation systemCP is an extension of resolution, where unsatisfiable propositional logic formulas in conjunctive normal form are recognized by showing the non-existence of boolean solutions to associated families of linear inequalities. Polynomial sizeCP proofs are given for the undirecteds-t connectivity principle. The subsystemsCP q ofCP, forq≥2, are shown to be polynomially equivalent toCP, thus answering problem 19 from the list of open problems of [8]. We present a normal form theorem (...) forCP 2-proofs and thereby for arbitraryCP-proofs. As a corollary, we show that the coefficients and constant terms in arbitrary cutting plane proofs may be exponentially bounded by the number of steps in the proof, at the cost of an at most polynomial increase in the number of steps in the proof. The extensionCPLE +, introduced in [9] and there shown top-simulate Frege systems, is proved to be polynomially equivalent to Frege systems. Lastly, since linear inequalities are related to threshold gates, we introduce a new threshold logic and prove a completeness theorem. (shrink)

The Central American migrant caravans of 2018 are best understood as having been precipitated by entangled multi-scalar geopolitical histories among the United States, Mexico, Guatemala, Honduras, and El Salvador. Unsurprisingly, the migrants traveling north to the United States garnered widespread attention on social media. So much so that the reaction to the caravan accelerated plans to deploy troops to the US southern border and deny Central Americans the opportunity to seek asylum. This example showcases how the digital world can have (...) exponential material effects. While coverage on border security and migration has been extensive, within political geography, such concerns have rarely been paired with social media. In this article, we take as our object of analysis the digitality or “digital life” of the migrant caravan. Mapping the patterns of migrant caravan-related tweeting paired with the exploration of Twitter’s networked dimensions reveals the platform to be a fundamentally spatial technology. Rather than reflect, refract or distort, Twitter produces and is in turn produced through spatial mechanisms. We present multiple cartographic visualizations in support of this claim and highlight the ways in which a contextual knowledge of the subject under study—the migrant caravan—can further inform analyses of Big Data. (shrink)

We introduce a class of models of the bounded arithmetic theoryPV n . These models, which are generated by their tally part, have a curious feature: they have end-extensions or satisfyB∑ n b only in case they are closed under exponentiation. As an application, we show that if then the polynomial hierarchy does not collapse.

The number of scientific publications is growing exponentially. Research articles cite other work for various reasons and, therefore, have been studied extensively to associate documents. It is argued that not all references carry the same level of importance. It is essential to understand the reason for citation, called citation intent or function. Text information can contribute well if new natural language processing techniques are applied to capture the context of text data. In this paper, we have used contextualized word embedding (...) to find the numerical representation of text features. We further investigated the performance of various machine-learning techniques on the numerical representation of text. The performance of each of the classifiers was evaluated on two state-of-the-art datasets containing the text features. In the case of the unbalanced dataset, we observed that the linear Support Vector Machine achieved 86% accuracy for the “background” class, where the training was extensive. For the rest of the classes, including “motivation,” “extension,” and “future,” the machine was trained on less than 100 records; therefore, the accuracy was only 57 to 64%. In the case of a balanced dataset, each of the classes has the same accuracy as trained on the same size of training data. Overall, SVM performed best on both of the datasets, followed by the stochastic gradient descent classifier; therefore, SVM can produce good results as text classification on top of contextual word embedding. (shrink)

Although ‘glue semantics’ is the most extensively developed theory of semantic composition for LFG, it is not very well integrated into the LFG projection architecture, due to the absence of a simple and well-explained correspondence between glue-proofs and f-structures. In this paper I will show that we can improve this situation with two steps: (1) Replace the current quantificational formulations of glue (either Girard’s system F, or first order linear logic) with strictly propositional linear logic (the quantifier, unit and (...) class='Hi'>exponential free version of either MILL or ILL, depending on whether or not tensors are used). (2) Reverse the direction of the standard σ-projection from f-structure to meaning, giving one going from the (atomic nodes of) the glue-proof to the f-structure, rather than from the f-structure to a ‘semantic projection’ which is itself somehow related to the glue-proof. As a side effect, the standard semantic projection of LFG glue semantics can be dispensed with. A result is that LFG sentence structures acquire a level composed of strictly binary trees, constructed out of nodes representing function application and lambda abstraction, with a significant resemblance to external and internal merge in the Minimalist Program. This increased resemblance between frameworks might assist in making useful comparisons. (shrink)

As familiar as the form of the mathematical equation is to us, the ostensibly simple act of equating unlike things was an achievement many centuries in the making, and one that would ultimately redefine European mathematical enquiry such that its bias toward geometry and the concrete would be displaced by a bias toward algebraic abstraction. The moment of that displacement was the nineteenth century, and its broader significance is on particularly striking display in the British context, where the implications of (...) algebraic abstraction were the object of sustained enquiry among mathematicians, logicians, and economists. This article argues that the ascendance of the algebraic equation, and the transformation in the conception of number on which it was premised, were not simply the product of evolutionary pressures internal to mathematics; the Victorian embrace of algebra was also a response to the practical and cognitive demands of Victorian economic life, which was increasingly reliant on attenuated exchange relations and merely nominal forms of ownership. This was an economy organized around the global extension of trade and characterized by the exponential growth of financial intermediation, of what Walter Bagehot called “number abstracted from reference.” Victorian economic practices thus modeled an abstraction that helped to justify the abstractions of mathematics, and that mathematics in turn was used by economic theorists to argue for the necessity and objectivity of their models. This mutually sustaining dialogue is particularly visible in the writings of William Stanley Jevons, who applied the principles of algebra to philosophy and economic theory so as to reconceive the logic of cognitive and social life in terms of equations. This logic, for which he was merely a spokesman, continues to shape our faith in the special value of abstract, theoretical knowledge. (shrink)