Previous work has shown that the Complex Conceptual Spaces − Single Observation Mathematical framework is a useful tool for event characterization. This mathematical framework is developed on the basis of Conceptual Spaces and uses integer linear programming to find the needed similarity values. The work of this paper is focused primarily on space event characterization. In particular, the focus is on the ranking of threats for malicious space events such as a kinetic kill. To make the Conceptual Spaces framework work, (...) the similarity values between the contents of observations on the one hand and the properties of the entities observed on the other needs to be found. This paper shows how to exploit Dempster-Shafer theory to implement a statistical approach for finding these similarities values. This approach will allow a user to identify the uncertainty involved in similarity value data, which can later be propagated through the developed mathematical model in order for the user to know the overall uncertainty in the observation-to-concept mappings needed for space event characterization. (shrink)

This paper provides a method for characterizing space events using the framework of conceptual spaces. We focus specifically on estimating and ranking the likelihood of collisions between space objects. The objective is to design an approach for anticipatory decision support for space operators who can take preventive actions on the basis of assessments of relative risk. To make this possible our approach draws on the fusion of both hard and soft data within a single decision support framework. Contextual data is (...) also taken into account, for example data about space weather effects, by drawing on the Space Domain Ontologies, a large system of ontologies designed to support all aspects of space situational awareness. The framework is coupled with a mathematical programming scheme that frames a mathematically optimal approach for decision support, providing a quantitative basis for ranking potential for collision across multiple satellite pairs. The goal is to provide the broadest possible information foundation for critical assessments of collision likelihood. (shrink)

This paper describes an AFOSR-supported basic research program that focuses on developing a new framework for combining hard with soft data in order to improve space situational awareness. The goal is to provide, in an automatic and near real-time fashion, a ranking of possible threats to blue assets (assets trying to be protected) from red assets (assets with hostile intentions). The approach is based on Conceptual Spaces models, which combine features from traditional associative and symbolic cognitive models. While Conceptual Spaces (...) are revolutionary, they lack an underlying mathematical framework. Several such frameworks have attempted to represent Conceptual Spaces, but by far the most robust is the model developed by Holender. His model utilizes integer linear programming in order to obtain an overall similarity value between observations and concepts that support the formation of hypotheses. This paper will describe a method for building Conceptual Spaces models for threats that utilizes ontologies as a means to provide a clear semantic foundation for this inferencing process; in particular threat ontologies and space domain ontologies are developed and employed in this approach. A space situational awareness use-case is presented involving a kinetic kill scenario and results are shown to assess the performance of this fusion-based inferencing framework. (shrink)

Achieving space domain awareness requires the identification, characterization, and tracking of space objects. Storing and leveraging associated space object data for purposes such as hostile threat assessment, object identification, and collision prediction and avoidance present further challenges. Space objects are characterized according to a variety of parameters including their identifiers, design specifications, components, subsystems, capabilities, vulnerabilities, origins, missions, orbital elements, patterns of life, processes, operational statuses, and associated persons, organizations, or nations. The Space Object Ontology provides a consensus-based realist framework (...) for formulating such characterizations in a computable fashion. Space object data are aligned with classes and relations in the Space Object Ontology and stored in a dynamically updated Resource Description Framework triple store, which can be queried to support space domain awareness and the needs of spacecraft operators. This paper presents the core of the Space Object Ontology, discusses its advantages over other approaches to space object classification, and demonstrates its ability to combine diverse sets of data from multiple sources within an expandable framework. Finally, we show how the ontology provides benefits for enhancing and maintaining longterm space domain awareness. (shrink)

This paper addresses the problem of ‘ignorance’ in philosophy and science, particularly with respect to the conceptualization, study and solution of environmental problems. We begin by distinguishing between ‘risk’, ‘uncertainty’ and ‘ignorance’. We then offer a categorization of ignorance, and use these categories to assess the role of science as a means of reducing ignorance. We note that to proceed with science, several 'acts of faith' are necessary. We conclude with a discussion of the importance of an attitude of openness (...) in science and philosophy, especially regarding environmental problems. Throughout, we illustrate our discussion of ignorance, and the problems involved in its reduction, by reference to environmental issues. (shrink)

Continuous recordings of brain electrical activity were obtained from a group of 176 patients throughout surgical procedures using general anesthesia. Artifact-free data from the 19 electrodes of the International 10/20 System were subjected to quantitative analysis of the electroencephalogram (QEEG). Induction was variously accomplished with etomidate, propofol or thiopental. Anesthesia was maintained throughout the procedures by isoflurane, desflurane or sevoflurane (N = 68), total intravenous anesthesia using propofol (N = 49), or nitrous oxide plus narcotics (N = 59). A set (...) of QEEG measures were found which reversibly displayed high heterogeneity of variance between four states as follows: (1) during induction; (2) just after loss of consciousness (LOC); (3) just before return of consciousness (ROC); (4) just after ROC. Homogeneity of variance across all agents within states was found. Topographic statistical probability images were compared between states. At LOC, power increased in all frequency bands in the power spectrum with the exception of a decrease in gamma activity, and there was a marked anteriorization of power. Additionally, a significant change occurred in hemispheric relationships, with prefrontal and frontal regions of each hemisphere becoming more closely coupled, and anterior and posterior regions on each hemisphere, as well as homologous regions between the two hemispheres, uncoupling. All of these changes reversed upon ROC. Variable resolution electromagnetic tomography (VARETA) was performed to localize salient features of power anteriorization in three dimensions. A common set of neuroanatomical regions appeared to be the locus of the most probable generators of the observed EEG changes. (shrink)

Achieving space situational awareness requires, at a minimum, the identification, characterization, and tracking of space objects. Leveraging the resultant space object data for purposes such as hostile threat assessment, object identification, and conjunction assessment presents major challenges. This is in part because in characterizing space objects we reference a variety of identifiers, components, subsystems, capabilities, vulnerabilities, origins, missions, orbital elements, patterns of life, operational processes, operational statuses, and so forth, which tend to be defined in highly heterogeneous and sometimes inconsistent (...) ways. The Space Domain Ontologies are designed to provide a consensus-based realist framework for formulating such characterizations in a way that is both consistent and computable. Space object data are aligned with classes and relations in a suite of ontologies built around the existing Space Object Ontology. They are stored in a dynamically updated Resource Description Framework triple store, which can be queried to support space situational awareness and the needs of spacecraft operators and analysts. This paper provides an overview of the Space Domain Ontologies and their development and use. It presents the motivation for and advantages of the Space Domain Ontologies, including the benefits they provide for enhancing and maintaining long-term space situational awareness. (shrink)

We show that the first order theory of the lattice $\mathscr{L}^{ (S) of finite dimensional closed subsets of any nontrivial infinite dimensional Steinitz Exhange System S has logical complexity at least that of first order number theory and that the first order theory of the lattice L(S ∞ ) of computably enumerable closed subsets of any nontrivial infinite dimensional computable Steinitz Exchange System S ∞ has logical complexity exactly that of first order number theory. Thus, for example, the lattice of (...) finite dimensional subspaces of a standard copy of $\bigoplus_\omega$ Q interprets first order arithmetic and is therefore as complicated as possible. In particular, our results show that the first order theories of the lattice L(V ∞ ) of c.e. subspaces of a fully effective ℵ 0 -dimensional vector space V∞ and the lattice of c.e. algebraically closed subfields of a fully effective algebraically closed field F ∞ of countably infinite transcendence degree each have logical complexity that of first order number theory. (shrink)

Recent scholarship has inquired into the socio-historical, discursive genesis of trauma. Trauma and the Ontology of the Modern Subject, however, seeks what has not been actualized in trauma studies - that is, how the necessity and unassailable intensity of trauma is fastened to its historical emergence. We must ask not only what trauma means for the individual person's biography, but also what it means to be the historical subject of trauma. In other words, how does being human in this current (...) period of history implicate one's lived possibilities that are threatened, and perhaps framed, through trauma? Foucauldian sensibilities inform a critical and structural analysis that is hermeneutically grounded. Drawing on the history of ideas and on Lacan's work in particular, John L. Roberts argues that what we mean by trauma has developed over time, and that it is intimately tied with an ontology of the subject; that is to say, what it is to be, and means to be human. He argues that modern subjectivity - as articulated by Heidegger, Levinas, and Lacan - is structurally traumatic, founded in its finitude as self-withdrawal in time, its temporal self-absence becoming the very conditions for agency, truth and knowledge. The book also argues that this fractured temporal horizon - as an effect of an interrupting Otherness or alterity - is obscured through the discourses and technologies of the psy-disciplines (psychiatry, psychology, and psychotherapy). Consideration is given to social, political, and economic consequences of this concealment. Trauma and the Ontology of the Modern Subject will be of enduring interest to psychoanalysts and psychotherapists as well as scholars of philosophy and cultural studies. (shrink)

Hastings Center Report, Volume 52, Issue 2, Page 14-20, March‐April 2022.

The overall goal of the approach developed in this paper is to estimate the likelihood of a given kinetic kill scenario between hostile spacebased adversaries using the mathematical framework of Complex Conceptual Spaces Single Observation. Conceptual spaces are a cognitive model that provide a method for systematically and automatically mimicking human decision making. For accurate decisions to be made, the fusion of both hard and soft data into a single decision framework is required. This presents several challenges to this data (...) fusion framework. The first is the challenge involved in handling multiple complex terminologies, which is addressed by drawing on a set of Space Domain Ontologies. Another challenge is the complex combinatorics involved when considering all possible feature combinations. This can be mitigated by using integer linear programming optimization that is outlined by the Complex Conceptual Spaces Single Observation mathematical model framework. A third challenge is the complicated physics that is involved in a spacecraft collision that must be addressed to obtain a better understanding of threat assessment. Overcoming these various challenges allows for a quantitative ranking for the potential of a kinetic kill collision across multiple spacecraft pairs. In addition to overcoming these challenges this paper will break down threat assessment into four domains and identify a ranking of threat both for each individual domain and for the four domains combined. Simulation results are shown to verify the developed concepts. (shrink)

This article argues that we could improve the design of research protocols by developing an awareness of and a responsiveness to the social contexts of all the actors in the research enterprise, including subjects, investigators, sponsors, and members of the community in which the research will be conducted. ?Social context? refers to the settings in which the actors are situated, including, but not limited to, their social, economic, political, cultural, and technological features. The utility of thinking about social contexts is (...) introduced and exemplified by the presentation of a hypothetical case in which one central issue is limitation of the probability of injury to subjects by selection of individuals who are not expected to live long enough for the known risks of the study to become manifest as harms. Benefits of such considerations may include enhanced subject satisfaction and cooperation, community acceptance, and improved data quality, among other desirable consequences. (shrink)

This article argues that we could improve the design of research protocols by developing an awareness of and a responsiveness to the social contexts of all the actors in the research enterprise, including subjects, investigators, sponsors, and members of the community in which the research will be conducted. “Social context” refers to the settings in which the actors are situated, including, but not limited to, their social, economic, political, cultural, and technological features. The utility of thinking about social contexts is (...) introduced and exemplified by the presentation of a hypothetical case in which one central issue is limitation of the probability of injury to subjects by selection of individuals who are not expected to live long enough for the known risks of the study to become manifest as harms. Benefits of such considerations may include enhanced subject satisfaction and cooperation, community acceptance, and improved data quality, among other desirable consequences. (shrink)

In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q& R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability (...) calculus for prob(P/Q& R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q& R) 1 A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability—nomic probability—there are principles of "probable probabilities" that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r, s, a) such that if prob(P/Q) = r, prob(P/R) = s, andprob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&R) = Y(r, s, a). Numerous other defeasible inferences are licensed by similar principles of probable probabilities. This has the potential to greatly enhance the usefulness of probabilities in practical application. (shrink)

Adaptation to right-shifting prisms improves left neglect for mental number line bisection. This study examined whether adaptation affects the mental number line in normal participants. Thirty-six participants completed a mental number line task before and after adaptation to either: left-shifting prisms, right-shifting prisms or control spectacles that did not shift the visual scene. Participants viewed number triplets (e.g. 16, 36, 55) and determined whether the numerical distance was greater on the left or right side of the inner number. Participants demonstrated (...) a leftward bias (i.e. overestimated the length occupied by numbers located on the left side of the number line) that was consistent with the effect of pseudoneglect. The leftward bias was corrected by a short period of visuomotor adaptation to left-shifting prisms, but remained unaffected by adaptation to right-shifting prisms and control spectacles. The findings demonstrate that a simple visuomotor task alters the representation of space on the mental number line in normal participants. (shrink)

Probability plays an essential role in many branches of AI, where it is typically assumed that we have a complete probability distribution when addressing a problem. But this is unrealistic for problems of real-world complexity. Statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q&R), and (...) we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability calculus for prob(P/Q&R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q&R)? A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability — nomic probability — there are principles of “probable probabilities” that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r,s:a) such that if prob(P/Q) = r, prob(P/R) = s, and prob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&R) = Y(r,s:a).. (shrink)

ABSTRACT: It is characteristic of a continuum that it be “all of one piece”, in the sense of being inseparable into two (or more) disjoint nonempty parts. By taking “part” to mean open (or closed) subset of the space, one obtains the usual topological concept of connectedness . Thus a space S is defined to be connected if it cannot be partitioned into two disjoint nonempty open (or closed) subsets – or equivalently, given any partition of S into two open (...) (or closed) subsets, one of the members of the partition must be empty. This holds, for example, for the space R of real numbers and for all of its open or closed intervals. Now a truly radical condition results from taking the idea of being “all of one piece” literally, that is, if it is taken to mean inseparability into any disjoint nonempty parts, or subsets, whatsoever . A space S satisfying this condition is called cohesive or indecomposable. While the law of excluded middle of classical logic reduces indecomposable spaces to the trivial empty space and one-point spaces, the use of intuitionistic logic makes it possible not only for nontrivial cohesive spaces to exist, but for every connected space to be cohesive.In this paper I describe the philosophical background to cohesiveness as well as some of the ways in which the idea is modelled in contemporary mathematics. (shrink)

Axioms for the continuum, or smooth real line R. These include the usual axioms for a commutative ring with unit expressed in terms of two operations + and i , and two distinguished elements 0 ≠ 1. In addition we stipulate that R is a local ring, i.e., the following axiom: ∃y x i y = 1 ∨ ∃y (1 – x) i y = 1. Axioms for the strict order relation < on R. These are: 1. a < b (...) and b < c implies a < c. 2. ¬(a < a) 3. a < b implies a + c < b + c for any c. ≤ 4. a < b and 0 < c implies acbc.. (shrink)

At the 1969 annual meeting of the American Association for the Ad vancement ofScience, held in Boston on December 27-29, a sequence of symposia on the philosophical foundations of science was organized jointly by Section L of the Association and the Boston Colloquium for the Philosophy of Science. Section L is devoted to the history, philos ophy, logic and sociology of science, with broad connotations extended both to 'science' and to 'philosophy'. With collaboration generously extended by other and more specialized (...) Sections of the AAAS, the Section L program took an unusually rich range of topics, and indeed the audiences were large, and the discussions lively. This book, regrettably delayed in publication, contains the major papers from those symposia of 1969. In addition, it contains the distin guished George Sarton Memorial Lecture of that meeting, 'Boltzmann, Monocycles and Mechanical Explanation' by Martin J. Klein. Some additions and omissions should be noted: In Part 1, dedicated to the 450th anniversary of the birth of Leonardo da Vinci, we have been una bie to include a contrihution by Elmer Belt who was prevented by storms from participating. In Part II, on physics and the explanation of life, we were unable to persuade Isaac Asimov to overcome his modesty about the historical remarks he made under the title 'Arrhenius Revisited'. (shrink)

This book is a collection of secondary essays on America's most important philosophic thinkers—statesmen, judges, writers, educators, and activists—from the colonial period to the present. Each essay is a comprehensive introduction to the thought of a noted American on the fundamental meaning of the American regime.