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A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS (fourth edition)
, 2005
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Paraconsistency of Interactive Computation
 In (Ed.), Workshop on Paraconsistent Computational Logic. Denmark Harms, W. (2004). Information and Meaning in Evolutionary Processes
, 2002
"... Abstract. The goal of computational logic is to allow us to model computation as well as to reason about it. We argue that a computational logic must be able to model interactive computation. We show that firstorder logic cannot model interactive computation due to the incompleteness of interaction. ..."
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Abstract. The goal of computational logic is to allow us to model computation as well as to reason about it. We argue that a computational logic must be able to model interactive computation. We show that firstorder logic cannot model interactive computation due to the incompleteness of interaction. We show that interactive computation is necessarily paraconsistent, able to model both a fact and its negation, due to the role of the world (environment) in determining the course of the computation. We conclude that paraconsistency is a necessary property for a logic that can model interactive computation. 1
On the existence of truly autonomic computing systems and the link with quantum computing, arXiv: cs.LO/0411094
"... A theoretical model of truly autonomic computing systems (ACS), with infinitely many constraints, is proposed. An argument similar to Turing’s for the unsolvability of the halting problem, which is permitted in classical logic, shows that such systems cannot exist. Turing’s argument fails in the rec ..."
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A theoretical model of truly autonomic computing systems (ACS), with infinitely many constraints, is proposed. An argument similar to Turing’s for the unsolvability of the halting problem, which is permitted in classical logic, shows that such systems cannot exist. Turing’s argument fails in the recently proposed nonAristotelian finitary logic (NAFL), which permits the existence of ACS. NAFL also justifies quantum superposition and entanglement, which are essential ingredients of quantum algorithms, and resolves the EinsteinPodolskyRosen (EPR) paradox in favour of quantum mechanics and nonlocality. NAFL requires that the autonomic manager (AM) must be conceptually and architecturally distinct from the managed element, in order for the ACS to exist as a nonselfreferential entity. Such a scenario is possible if the AM uses quantum algorithms and is protected from all problems by (unbreakable) quantum encryption, while the managed element remains classical. NAFL supports such a link between autonomic and quantum computing, with the AM existing as a metamathematical entity. NAFL also allows quantum algorithms to access truly random elements and thereby supports nonstandard models of quantum (hyper) computation that permit infinite parallelism. 1.
Comments to Neutrosophy
 University of New Mexico
, 2001
"... Any system based on axioms is incomplete because the axioms cannot be proven from the system, just believed. But one system can be lessincomplete than other. Neutrosophy is lessincomplete than many other systems because it contains them. But this does not mean that it is finished, and it can alway ..."
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Any system based on axioms is incomplete because the axioms cannot be proven from the system, just believed. But one system can be lessincomplete than other. Neutrosophy is lessincomplete than many other systems because it contains them. But this does not mean that it is finished, and it can always be improved. The comments presented here are an attempt to make Neutrosophy even lessincomplete. I argue that lessincomplete ideas are more useful, since we cannot perceive truth or falsity or indeterminacy independently of a context, and are therefore relative. Absolute being and relative being are defined. Also the “silly theorem problem ” is posed, and its partial solution described. The issues arising from the incompleteness of our contexts are presented. We also note the relativity and dependance of logic to a context. We propose “metacontextuality ” as a paradigm for containing as many contexts as we can, in order to be lessincomplete and discuss some possible consequences. 1.
Contextuality: A Philosophical Paradigm, with Applications to Philosophy of Cognitive Science
 in Artificial Life IX
, 2002
"... We develop on the idea that everything is related, inside, and therefore determined by a context. This stance, which at first might seem obvious, has several important consequences. This paper first presents ideas on Contextuality, for then applying them to problems in philosophy of cognitive sci ..."
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We develop on the idea that everything is related, inside, and therefore determined by a context. This stance, which at first might seem obvious, has several important consequences. This paper first presents ideas on Contextuality, for then applying them to problems in philosophy of cognitive science. Because of space limitations, for the second part we will assume that the reader is familiar with the literature of philosophy of cognitive science, but if this is not the case, it would not be a limitation for understanding the main ideas of this paper. We do not argue that Contextuality is a panaceic answer for explaining everything, but we do argue that everything is inside a context. And because this is always, we sometimes ignore it, but we believe that many problems are dissolved with a contextual approach, noticing things we ignore because of their obviousity. We first give a notion of context. We present the idea that errors are just incongruencies inside a context. We also present previous ideas of absolute being, relative being, and lessincompleteness.
The Development of Models of Computation with Advances in Technology and Natural Sciences
"... Abstract. The development of models of computation induces the development of technology and natural sciences and vice versa. Current state of the art of technology and sciences, especially networks of concurrent processes such as Internet or biological and sociological systems, calls for new comput ..."
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Abstract. The development of models of computation induces the development of technology and natural sciences and vice versa. Current state of the art of technology and sciences, especially networks of concurrent processes such as Internet or biological and sociological systems, calls for new computational models. It is necessary to extend classical Turing machine model towards physical / natural computation. Important aspects are openness and interactivity of computational systems, as well as concurrency of computational processes. The development proceeds in two directions – as a search for new mathematical structures beyond algorithms as well as a search for different modes of physical computation that are not equivalent to actions of human executing an algorithm, but appear in physical systems in which concurrent interactive information processing takes place. The article presents the framework of infocomputationalism as applied on computing nature, where nature is an informational structure and its dynamics (information processing) is understood as computation. In natural computing, new developments in both understanding of natural systems and in their computational modelling are needed, and those two converge and enhance each other. 1 INTRODUCTION: WHAT IS COMPUTING
unknown title
"... Inconsistency in Deception for Defense The use of deception is one of many defensive techniques being explored today. In the past, defenders of systems have used deception haphazardly, but now researchers are developing systematic methods of deception. The cornerstone of these methods is internal co ..."
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Inconsistency in Deception for Defense The use of deception is one of many defensive techniques being explored today. In the past, defenders of systems have used deception haphazardly, but now researchers are developing systematic methods of deception. The cornerstone of these methods is internal consistency: projecting a “false reality”, or “fiction”, that the attacker is to accept as reality. We challenge the necessity of this cornerstone, and explore the nature and possible uses of inconsistency in deception as a defense.
JANUSZ CIUCIURA
"... In the logical literature, Discursive (or Discussive) Logic introduced by Stanis̷law Ja´skowski is seen as one of the earliest examples of the socalled paraconsistent logic. There is some confusion over what is actually discursive logic nevertheless. One of the possible sources of the confusion is ..."
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In the logical literature, Discursive (or Discussive) Logic introduced by Stanis̷law Ja´skowski is seen as one of the earliest examples of the socalled paraconsistent logic. There is some confusion over what is actually discursive logic nevertheless. One of the possible sources of the confusion is easy to discern; it comes from the fact that Ja´skowski published his two papers in Polish and their English translations appeared many years later. 2 Up till 1999, no one but a Polish reader was able to read Ja´skowski‘s paper on the discursive conjunction and consequently some authors took discursive logic to be a foremost example of a nonadjunctive logic. 3 The situation became even more complicated when da Costa, Dubikajtis and Kotas presented an axiomatization with discursive connectives as primitive symbols. It turned out that a connective of the discursive conjunction they considered did not coincide with any connective presented by Ja´skowski. Moreover, their axiomatization contained some axiom schemata that were not generally valid in Ja´skowski‘s logic. 4 The purpose of this paper is to clarify the confusion surrounding the discursive logic. We will present a new (direct) semantics and axiomatization of Ja´skowski‘s adjunctive discursive logic and show how to define and axiomatize two additional connectives of negation.
THE NATURE OF CONTEMPORARY CORE MATHEMATICS
, 2010
"... Abstract. The goal of this essay is a description of modern mathematical practice, with emphasis on differences between this and practices in the nineteenth century. I explain how and why these differences greatly increased the effectiveness of mathematical methods and enabled sweeping developments ..."
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Abstract. The goal of this essay is a description of modern mathematical practice, with emphasis on differences between this and practices in the nineteenth century. I explain how and why these differences greatly increased the effectiveness of mathematical methods and enabled sweeping developments in the twentieth century. A particular concern is the significance for mathematics education: elementary education remains modeled on the mathematics of the nineteenth century and before, and use of modern methodologies might give advantages similar to those seen in mathematics. This draft is about 90 % complete, and comments are welcome. 1.