We examine what happens if we replace ZFC with a localistic/relativistic system, LZFC, whose central new axiom, denoted by Loc(ZFC), says that every set belongs to a transitive model of ZFC. LZFC consists of Loc(ZFC) plus some elementary axioms forming Basic Set Theory (BST). Some theoretical reasons for this shift of view are given. All ${\Pi_2}$ consequences of ZFC are provable in LZFC. LZFC strongly extends Kripke-Platek (KP) set theory minus Δ0-Collection and minus ${\in}$ -induction scheme. ZFC+ “there is (...) an inaccessible cardinal” proves the consistency of LZFC. In LZFC we focus on models rather than cardinals, a transitive model being considered as the analogue of an inaccessible cardinal. Pushing this analogy further we define α-Mahlo models and ${\Pi_1^1}$ -indescribable models, the latter being the analogues of weakly compact cardinals. Also localization axioms of the form ${Loc({\rm ZFC}+\phi)}$ are considered and their global consequences are examined. Finally we introduce the concept of standard compact cardinal (in ZFC) and some standard compactness results are proved. (shrink)

This paper is a sequel to Tzouvaras :571–601, 2010), where a local version of ZFC, LZFC, was introduced and examined and transitive models of ZFC with properties that resemble large cardinal properties, namely Mahlo and Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^1}$$\end{document}-indescribable models, were considered. By analogy we refer to such models as “large models”, and the properties in question as “large model properties”. Continuing here in the same spirit we consider further large model properties, that resemble (...) stronger large cardinals, namely, “elementarily embeddable”, “extendible” and “strongly extendible”, “critical” and “strongly critical”, “self-critical” and “strongly self-critical”, the definitions of which involve elementary embeddings. Each large model property ϕ gives rise to a localization axiom Locϕ saying that every set belongs to a transitive model of ZFC satisfying ϕ. The theories LZFCϕ = LZFC + Locϕ are local analogues of the theories ZFC+“there is a proper class of large cardinals ψ”, where ψ is a large cardinal property. If sext is the property of strong extendibility, it is shown that LZFCsext proves Powerset and Σ1-Collection. In order to refute V = L over LZFC, we combine the existence of strongly critical models with an axiom of different flavor, the Tall Model Axiom. V = L can also be refuted by TMA plus the axiom GC saying that “there is a greatest cardinal”, although it is not known if TMA + GC is consistent over LZFC. Finally Vopěnka’s Principle and its impact on LZFC are examined. It is shown that LZFCsext + V P proves Powerset and Replacement, i.e., ZFC is fully recovered. The same is true for some weaker variants of LZFCsext. Moreover the theories LZFCsext+V P and ZFC+V P are shown to be identical. (shrink)

We investigate the effect of adding a single real on cardinal invariants associated with the continuum. We show:1. adding an eventually different or a localization real adjoins a Luzin set of size continuum and a mad family of size ω1;2. Laver and Mathias forcing collapse the dominating number to ω1, and thus two Laver or Mathias reals added iteratively always force CH;3. Miller's rational perfect set forcing preserves the axiom MA.

A differential manifold (d-manifold, for short) can be defined as a pair (M, C), where M is any set and C is a family of real functions on M which is (i) closed with respect to localization and (ii) closed with respect to superposition with smooth Euclidean functions; one also assumes that (iii) M is locally diffeomorphic to Rn. These axioms have a straightforward physical interpretation. Axioms (i) and (ii) formalize certain “compatibility conditions” which usually are supposed to be (...) assumed tacitly by physicists. Axiom (iii) may be though of as a (nonmetric) version of Einstein's equivalence principle. By dropping axiom (iii), one obtains a more general structure called a differential space (d-space). Every subset of Rn turns out to be a d-space. Nevertheless it is mathematically a workable structure. It might be expected that somewhere in the neighborhood of the Big Bang there is a domain in which space-time is not a d-manifold but still continues to be a d-space. In such a domain we would have a physics without the (usual form of the) equivalence principle. Simple examples of d-spaces which are not d-manifolds elucidate the principal characteristics the resulting physics would manifest. (shrink)

BACKGROUND -/- The need for detailed description and modeling of cells drives the continuous generation of large and diverse datasets. Unfortunately, there exists no systematic and comprehensive way to organize these datasets and their information. CELDA (Cell: Expression, Localization, Development, Anatomy) is a novel ontology for the association of primary experimental data and derived knowledge to various types of cells of organisms. -/- RESULTS -/- CELDA is a structure that can help to categorize cell types based on species, anatomical (...) localization, subcellular structures, developmental stages and origin. It targets cells in vitro as well as in vivo. Instead of developing a novel ontology from scratch, we carefully designed CELDA in such a way that existing ontologies were integrated as much as possible, and only minimal extensions were performed to cover those classes and areas not present in any existing model. Currently, ten existing ontologies and models are linked to CELDA through the top-level ontology BioTop. Together with 15.439 newly created classes, CELDA contains more than 196.000 classes and 233.670 relationship axioms. CELDA is primarily used as a representational framework for modeling, analyzing and comparing cells within and across species in CellFinder, a web based data repository on cells (http://cellfinder.org). -/- CONCLUSIONS -/- CELDA can semantically link diverse types of information about cell types. It has been integrated within the research platform CellFinder, where it exemplarily relates cell types from liver and kidney during development on the one hand and anatomical locations in humans on the other, integrating information on all spatial and temporal stages. CELDA is available from the CellFinder website: http://cellfinder.org/about/ontology. (shrink)

This paper presents use cases for modular development of ontologies using the OWL imports mechanism. Many of the methods are inspired by work in modular development in software engineering. The approach is aimed at developers of large ontologies covering multiple subdomains that make use of OWL reasoners for inference. Such ontologies are common in biomedical sciences, but nothing in the paper is specific to biomedicine. There are four groups of use cases: (i) organisation and factoring of ontologies; (ii) maintaining stable (...) interfaces and bindings between ontologies and between ontologies and software; (iii) localization of ontologies to the requirements of specific sites and (iv) extension of ontologies and encapsulation of modifications. OWL's axiom-oriented import mechanism has many similarities with import mechanisms in object-oriented software but also important differences – in particular, the effects of OWL imports are global, and the order in which modules are imported is irrelevant. The advantages and disadvantages of OWL's axiom-oriented approach are discussed, and suggestions are made for extensions to allow axioms to be filtered out as well as added – a mechanism that we term “adaptation” to distinguish it from the standard import mechanism. Finally we discuss possible alternatives and practical experience with the approaches presented. (shrink)

An analysis of two heuristic strategies for the development of mechanistic models, illustrated with historical examples from the life sciences. In Discovering Complexity, William Bechtel and Robert Richardson examine two heuristics that guided the development of mechanistic models in the life sciences: decomposition and localization. Drawing on historical cases from disciplines including cell biology, cognitive neuroscience, and genetics, they identify a number of "choice points" that life scientists confront in developing mechanistic explanations and show how different choices result in (...) divergent explanatory models. Describing decomposition as the attempt to differentiate functional and structural components of a system and localization as the assignment of responsibility for specific functions to specific structures, Bechtel and Richardson examine the usefulness of these heuristics as well as their fallibility—the sometimes false assumption underlying them that nature is significantly decomposable and hierarchically organized. When Discovering Complexity was originally published in 1993, few philosophers of science perceived the centrality of seeking mechanisms to explain phenomena in biology, relying instead on the model of nomological explanation advanced by the logical positivists (a model Bechtel and Richardson found to be utterly inapplicable to the examples from the life sciences in their study). Since then, mechanism and mechanistic explanation have become widely discussed. In a substantive new introduction to this MIT Press edition of their book, Bechtel and Richardson examine both philosophical and scientific developments in research on mechanistic models since 1993. (shrink)

This paper describes one style of functional analysis commonly used in the neurosciences called task-bound functional analysis. The concept of function invoked by this style of analysis is distinctive in virtue of the dependence relations it bears to transient environmental properties. It is argued that task-bound functional analysis cannot explain the presence of structural properties in nervous systems. An alternative concept of neural function is introduced that draws on the theoretical neuroscience literature, and an argument is given to show that (...) this alternative concept of may help to overcome the explanatory limitations of task-bound functional analysis. (shrink)

Spontaneous localization theories are a class of quantum theories which solve the so-called measurement problem by non-linearly and stochastically modifying the Schrödinger dynamics. In this paper I briefly explain where these theories are coming from, what their driving ideas and main features are, and how they were historically developed. Also, I discuss their empirical and ontological adequacy, as well as their relativistic extensions and their experimental confirmation.

Spontaneous localization theory is a quantum theory proposed by GianCarlo Ghirardi, together with Alberto Rimini and Tullio Weber in 1986. However, soon it became clear to Ghirardi that his work was more than just one theory: he actually developed a framework, a family of theories in which the wavefunction jumps, but where the ontology of the theory is underdetermined. After acknowledging that the wavefunction did not provide a satisfactory ontology, he assumed that matter was described by a continuous matter (...) density field in three-dimensional space, whose evolution is governed by a stochastic wavefunction evolution. Alternatively, Bell assumed that the wavefunction would govern a spatiotemporal event ontology, dubbed ‘flashes.’ However, not much work has been done with the perhaps most obvious possibility, namely that physical objects are made of particles. This paper has two aims. First to explain the reason why people require spontaneous localization theory to be more than just a theory about the wavefunction. This is done by showing how the problem everyone in the foundation of quantum mechanics take to be the fundamental problem of quantum mechanics, namely the measurement problem, is a red herring. Then, the paper explores the possibility of spontaneous localization theories of particles. I argue that this discussion is not a mere exercise, as spontaneous localization theories of particles may be amenable to a relativistic extension which does not require a foliation, and because in general the peculiar type of indeterminism of spontaneous localization theories may help shedding new light on the nature of the tension between quantum theory and relativity. (shrink)

Alzheimer's disease is characterized by amyloid-beta peptide -loaded plaques in the brain. Abeta is a cleavage fragment of amyloid-beta protein precursor and over production of APP may lead to amyloidogenesis. The regulatory region of the APP gene contains consensus sites recognized by the transcription factor, specificity protein 1 , which has been shown to be required for the regulation of APP and Abeta. To understand the role of SP1 in APP biogenesis, herein we have characterized the relative distribution and (...) class='Hi'>localization of SP1, APP, and Abeta in various brain regions of rodent and primate models using immunohistochemistry. We observed that overall distribution and cellular localization of SP1, APP, and Abeta are similar and neuronal in origin. Their distribution is abundant in various layers of neocortex, but restricted to the Purkinje cell layer of the cerebellum, and the pyramidal cell layer of hippocampus. These findings suggest that overproduction of Abeta in vivo may be associated with transcriptional pathways involving SP1 and the APP gene. (shrink)

Case studies in the psychophysics, modeling and localization of human vision are presented as an example of.

Starting from the phase space representation of quantum mechanics we provide an Euclidean system of covariance for the photon. In particular, we consider systems with the Poincaré group as the symmetry group and use a standard procedure in order to build a phase space and a localization observable on the phase space. Then we focus on the massless representations of the Poincaré group that we use to build a space localization observable for the photon.

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive “outside-inwards approach” in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior. -/- Another consequence (...) of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light-sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi–Metzner–Sachs group. This essay is the second part of a partitioned longer paper. (shrink)

This paper is concerned with n-localization property introduced by Newelski and Rosłanowski in [10] and getting it for CS iterations of forcing notions.

The main aim of this work is to relate integrability in QFT with a complete particle interpretation directly to the principle of causal localization, circumventing the standard method of finding sufficiently many conservation laws. Its precise conceptual-mathematical formulation as “modular localization” within the setting of local operator algebras also suggests novel ways of looking at general (non-integrable) QFTs which are not based on quantizing classical field theories.Conformal QFT, which is known to admit no particle interpretation, suggest the presence (...) of a “partial” integrability, referred to as “conformal integrability”. This manifests itself in a “braid-permutation” group structure which contains in particular informations about the anomalous dimensional spectrum. For chiral conformal models this reduces to the braid group as it is represented in Hecke- or Birman-Wenzl-algebras associated to chiral models.Another application of modular localization mentioned in this work is an alternative to the BRST formulation of gauge theories in terms of stringlike vectorpotentials within a Hilbert space setting. (shrink)

In this paper I argue for the following two related claims. First, the science of phoronomy from Kant's Metaphysical Foundations of Natural Science is grounded in the duplication of space. Second, this duplication is made possible through the self-localization of the subject, as Kant shows in the "Gegnden-Schrift". The thesis of this paper is that the self-localization transforms space into an object that can be cinematically moved and that this action sets the ground for a science of phoronomy, (...) which presupposes the existence of at least two spaces. In the end, the other endpoint of the Kantian determination of space is discussed, namely space understood as an idea of reason. (shrink)

Nuclear proteins are synthesized in the cytoplasm and must subsequently enter the nucleus. Recent experiments indicate some similarities and some differences between protein localization to the nucleus and localization to other organelles.

The progression of theories suggested for our world, from ego- to geo- to helio-centric models to universe and multiverse theories and beyond, shows one tendency: The size of the described worlds increases, with humans being expelled from their center to ever more remote and random locations. If pushed too far, a potential theory of everything (TOE) is actually more a theories of nothing (TON). Indeed such theories have already been developed. I show that including observer localization into such theories (...) is necessary and sufficient to avoid this problem. I develop a quantitative recipe to identify TOEs and distinguish them from TONs and theories in-between. This precisely shows what the problem is with some recently suggested universal TOEs. (shrink)

Objective: Atypical patterns of language lateralization due to early reorganizational processes constitute a challenge in the pre-surgical evaluation of patients with pharmaco-resistant epilepsy. There is no consensus on an optimal analysis method used for the identification of language dominance in MEG. This study examines the concordance between MEG source localization of beta power desynchronization and fMRI with regard to lateralization and localization of expressive and receptive language areas using a visual verb generation task.Methods: Twenty-five patients with pharmaco-resistant epilepsy, (...) including six patients with atypical language lateralization, and ten right-handed controls obtained MEG and fMRI language assessment. Fourteen patients additionally underwent the Wada test. We analyzed MEG beta power desynchronization in sensor (controls) and source space (patients and controls). Beta power decrease between 13 and 35 Hz was localized applying Dynamic Imaging of Coherent Sources Beamformer technique. Statistical inferences were grounded on cluster-based permutation testing for single subjects.Results: Event-related desynchronization of beta power in MEG was seen within the language-dominant frontal and temporal lobe and within the premotor cortex. Our analysis pipeline consistently yielded left language dominance with high laterality indices in controls. Language lateralization in MEG and Wada test agreed in all 14 patients for inferior frontal, temporal and pari... (shrink)

ABSTRACT This article elaborates a concept of localization through interpreting key arguments in Colombian philosopher Santiago Castro-Gómez’s early works grouped by the author under the name “genealogies of coloniality.” Following the role localization in his genealogies of coloniality reveals what Castro-Gómez calls “heterarchic articulations.” Heterarchic articulations delineate an analytic model of power that traces how multiple technologies and formations of power operating at different levels, from colonial geopolitics to individual “corpopolitics” of desire, converge and configure radically localized processes (...) of subjectivation. Localization understood in these terms, the author argues, allows Castro-Gómez to radicalize, transform, and combine Foucault’s genealogical approach and decolonial theory. The article concludes by showing that, besides radicalizing and combining genealogy and decoloniality, the localization at work in Castro-Gómez’s genealogies of coloniality serves to interpret theorizations and phenomena of contemporary violence by turning to Mexican transfeminist philosopher Sayak Valencia’s analysis of “gore capitalism.”. (shrink)

The principle of set theory known as the Axiom of Choice has been hailed as “probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid's axiom of parallels which was introduced more than two thousand years ago” (Fraenkel, Bar-Hillel & Levy 1973, §II.4). The fulsomeness of this description might lead those unfamiliar with the axiom to expect it to be as startling as, say, the Principle (...) of the Constancy of the Velocity of Light or the Heisenberg Uncertainty Principle. But in fact the Axiom of Choice as it is usually stated appears humdrum, even self-evident. For it amounts to nothing more than the claim that, given any collection of mutually disjoint nonempty sets, it is possible to assemble a new set — a transversal or choice set — containing exactly one element from each member of the given collection. Nevertheless, this seemingly innocuous principle has far-reaching mathematical consequences — many indispensable, some startling — and has come to figure prominently in discussions on the foundations of mathematics. It (or its equivalents) have been employed in countless mathematical papers, and a number of monographs have been exclusively devoted to it. (shrink)

This paper relates to a formal statement of the mechanisms that are thought minimally necessary to underpin consciousness. This is expressed in the form of axioms. We deem this to be useful if there is ever to be clarity in answering questions about whether this or the other organism is or is not conscious. As usual, axioms are ways of making formal statements of intuitive beliefs and looking, again formally, at the consequences of such beliefs. The use of this style (...) of exposition does not entail a claim to provide a mathematically rigorous formal deductive system. Conventional mathematical notation is used to achieve clarity, although this is elaborated with natural language in an attempt to reduce terseness. In our view, making the approach axiomatic is synonymous with building clear usable tests for consciousness and is therefore a central feature of the paper. The extended scope of this approach is to lay down some essential properties that should be considered when designing machines that could be said to be conscious. In the broader discussion about the nature of consciousness and its neurological mechanisms, it may seem to some that axiomatisation is premature and continues to beg many questions. However, the approach is meant to be open- ended so that others can build further axiomatic clarifications that address the very large number of questions which, in the search for a formal basis for consciousness, still remain to be answered. Of course, in discussions about consciousness many will also argue that the subject is not one that may ever be formally addressed by means of axioms. The view taken in this paper is 'let's try to do it and see how far it gets'. (shrink)

This study aims to assess the localization of Schema.org for manuscript description in the Iranian-Islamic information context using documentary and qualitative content analysis. The schema.org introduces schemas for different Web content objects so as to generate structured data. Given that the structure of Schema.org is ontological, the inheritance of the manuscript types from the properties of their parent types, as well as the localization and description of the specific properties of the manuscripts in the Iranian-Islamic information context were (...) investigated in order to improve their indexability and semantic visibility in the Web search engines. The proposed properties specific to the manuscript type and the six proposed properties to be added to the “CreativeWork” type are found to be consistent with other schema properties. In turn, these properties lead to the localization of the existing schema for the manuscript type compatibility with the Iranian-Islamic information context. This schema is also applicable to centers with published records on the Web, and if markup with these properties, their indexability and semantic visibility in Web search engines increases accordingly. The generation of structured data in the Web environment through this schema is deemed to promote the concept of the Semantic Web, and make data and knowledge retrieval easier. (shrink)

In the general relativity theory gravitational energy-momentum density is usually described by a pseudo-tensor with strange transformation properties so that one does not have localization of gravitational energy. It is proposed to set up a gravitational energy-momentum density tensor having a unique form in a given coordinate system by making use of a bimetric formalism. Two versions are considered: (1) a bimetric theory with a flat-space background metric which retains the physics of the general relativity theory and (2) one (...) with a background corresponding to a space of constant curvature which introduces modifications into general relativity under certain conditions. The gravitational energy density in the case of the Schwarzschild solution is obtained. (shrink)

We show how trajectories can be reintroduced in quantum mechanics provided that its spatial continuum is modelled by a variable real number (qr-number) continuum. Such a continuum can be constructed using only standard Hilbert space entities. In this approach, the geometry of atoms and subatomic objects differs from that of classical objects. The systems that are non-local when measured in the classical space-time continuum may be localized in the quantum continuum. We compare trajectories in this new description of space-time with (...) the corresponding Bohmian picture. (shrink)

Functional localization is a central aim of cognitive neuroscience. But the nature and extent of functional localization in the human brain have been subjects of fierce theoretical debate since the 19th Century. In this essay, I first examine how concepts of functional localization have changed over time. I then analyze contemporary challenges to functional localization drawing from research on neural reuse, neural degeneracy, and the context-dependence of neural functions. I explore the consequences of these challenges for (...) topics in philosophy of science and philosophy of mind including localizationist versus anti-localizationist approaches to cognitive neuroscience, multiple realizability, reverse inference in functional neuroimaging, and the modularity of mind. (shrink)

In epistemic logic, some axioms dealing with the notion of knowledge are rather convoluted and difficult to interpret intuitively, even though some of them, such as the axioms.2 and.3, are considered to be key axioms by some epistemic logicians. We show that they can be characterized in terms of understandable interaction axioms relating knowledge and belief or knowledge and conditional belief. In order to show it, we first sketch a theory dealing with the characterization of axioms in terms of interaction (...) axioms in modal logic. We then apply the main results and methods of this theory to obtain specific results related to epistemic and doxastic logics. (shrink)

The concept of event provides the essential bridge from the realm of virtuality of the quantum state to real phenomena in space and time. We ask how much we can gather from existing theory about the localization of an event and point out that decoherence and coarse graining—though important—do not suffice for a consistent interpretation without the additional principle of random realization.

A weak form of intuitionistic set theory WST lacking the axiom of extensionality is introduced. While WST is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up WST with moderate extensionality principles or quotient sets enables the derivation to go through.

Axiom weakening is a technique that allows for a fine-grained repair of inconsistent ontologies. Its main advantage is that it repairs on- tologies by making axioms less restrictive rather than by deleting them, employing the use of refinement operators. In this paper, we build on pre- viously introduced axiom weakening for ALC, and make it much more irresistible by extending its definitions to deal with SROIQ, the expressive and decidable description logic underlying OWL 2 DL. We extend the (...) definitions of refinement operator to deal with SROIQ constructs, in particular with role hierarchies, cardinality constraints and nominals, and illustrate its application. Finally, we discuss the problem of termi- nation of an iterated weakening procedure. (shrink)

What are the relationships between an entity and the space at which it is located? And between a region of space and the events that take place there? What is the metaphysical structure of localization? What its modal status? This paper addresses some of these questions in an attempt to work out at least the main coordinates of the logical structure of localization. Our task is mostly taxonomic. But we also highlight some of the underlying structural features and (...) we single out the interactions between the notion of localization and nearby notions, such as the notions of part and whole, or of necessity and possibility. A theory of localization—we argue—is needed in order to account for the basic relations between objects and space, and runs afoul a pure part-whole theory. We also provide an axiomatization of the relation of localization and examine cases of localization involving entities different from material objects. (shrink)