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38
Conceptual integration networks
 Cognitive Science
, 1998
"... Conceptual integration"blending"is a general cognitive operation on a par with analogy, recursion, mental modeling, conceptual categorization, and framing. It serves a variety of cognitive purposes. It is dynamic, supple, and active in the moment of thinking. It yields products that frequently be ..."
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Cited by 112 (8 self)
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Conceptual integration"blending"is a general cognitive operation on a par with analogy, recursion, mental modeling, conceptual categorization, and framing. It serves a variety of cognitive purposes. It is dynamic, supple, and active in the moment of thinking. It yields products that frequently become entrenched in conceptual structure and grammar, and it often performs new work on its previously entrenched products as inputs. Blending is easy to detect in spectacular cases but it is for the most part a routine, workaday process that escapes detection except on technical analysis. It is not resewed for special purposes, and is not costly. In blending, structure from input mental spaces is projected to a separate, "blended " mental space. The proiection is selective. Through completion and elaboration, the blend develops structure not provided by the inputs. Inferences, arguments, and ideas developed in the blend can have effect in cognition, leading us to modify the initial inputs and to change our view of the corresponding situations. Blending operates according to a set of uniform structural and dynamic principles. It additionally observes a set of optimality principles. I. Ih'TRODUCTION Much of the excitement about recent work on language, thought, and action stems from the discovery that the same structural cognitive principles are operating in areas that were once viewed as sharply distinct and technically incommensurable. Under the old view, there were word meanings, syntactic structures, sentence meanings (typically truthconditional), discourse and pragmatic principles, and then, at a higher level, figures of speech like metaphor and metonymy, scripts and scenarios, rhetoric, forms of inductive and deductive rea
Partial realizations of Hilbert’s program
 Journal of Symbolic Logic
, 1988
"... JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JS ..."
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Cited by 38 (8 self)
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JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Association for Symbolic Logic is collaborating with JSTOR to digitize, preserve and extend access to The
Science, Computational Science and Computer Science: At a Crossroads
 Comm. ACM
, 1993
"... We describe computational science as an interdisciplinary approach to doing science on computers. Our purpose is to introduce computational science as a legitimate interest of computer scientists. We present a foundation for computational science based on the need to incorporate computation at the s ..."
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Cited by 25 (2 self)
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We describe computational science as an interdisciplinary approach to doing science on computers. Our purpose is to introduce computational science as a legitimate interest of computer scientists. We present a foundation for computational science based on the need to incorporate computation at the scientific level; i.e., computational aspects must be considered when a model is formulated. We next present some obstacles to computer scientists' participation in computational science, including a cultural bias in computer science that inhibits participation. Finally, we look at some areas of conventional computer science and indicate areas of mutual interest between computational science and computer science. Keywords: education, computational science. 1 What is Computational Science ? In December, 1991, the U. S. Congress passed the High Performance Computing and Communications Act, commonly known as the HPCC . This act focuses on several aspects of computing technology, but two have...
Conceptual Projection and Middle Spaces
, 1994
"... Conceptual projection from one mental space to another always involves projection to "middle" spacesabstract "generic" middle spaces or richer "blended" middle spaces. Projection to a middle space is a general cognitive process, operating uniformly at different levels of abstraction and under sup ..."
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Cited by 13 (1 self)
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Conceptual projection from one mental space to another always involves projection to "middle" spacesabstract "generic" middle spaces or richer "blended" middle spaces. Projection to a middle space is a general cognitive process, operating uniformly at different levels of abstraction and under superficially divergent contextual circumstances. Middle spaces are indispensable sites for central mental and linguistic work. The process of blending is in particular a fundamental and general cognitive process, running over many (conceivably all) cognitive phenomena, including categorization, the making of hypotheses, inference, the origin and combining of grammatical constructions, analogy, metaphor, and narrative. Blending is not secondary to these phenomena but prerequisite, and its operation is not restricted to any one of these phenomena. We give evidence for blending from a wide range of data that includes everyday language, idioms, literary metaphor, nonverbal conceptualization of ac...
Mathematical proofs at a crossroad
 Theory Is Forever, Lectures Notes in Comput. Sci. 3113
, 2004
"... Abstract. For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomaticdeductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimen ..."
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Cited by 7 (7 self)
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Abstract. For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomaticdeductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimental, psychological and social aspects, yesterday only marginal, but now changing radically the very essence of proof. In this paper, we try to organize this evolution, to distinguish its different steps and aspects, and to evaluate its advantages and shortcomings. Axiomaticdeductive proofs are not a posteriori work, a luxury we can marginalize nor are computerassisted proofs bad mathematics. There is hope for integration! 1
ComplexDynamical Extension of the Fractal Paradigm and Its Applications in Life Sciences, in: Fractals in Biology and
, 2005
"... Summary. Complexdynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution to an arbitrary interaction problem. Intrinsic creativity of this extension of usual fractality determines its expon ..."
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Cited by 4 (4 self)
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Summary. Complexdynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution to an arbitrary interaction problem. Intrinsic creativity of this extension of usual fractality determines its exponentially high operation efficiency, which underlies many specific functions of living systems, such as autonomous adaptability, “purposeful ” development, intelligence and consciousness (at higher complexity levels). We outline in more detail genetic applications of complexdynamic fractality, demonstrate the dominating role of genome interactions, and show that further progressive development of genetic research, as well as other lifescience applications, should be based on the dynamically fractal structure analysis of interaction processes involved. We finally summarise the obtained extension of mathematical concepts and approaches closely related to their biological applications. 1
Software Engineering Frontiers in Computational Science and Engineering
, 1995
"... In 1991, the US Congress passed the High Performance Computing and Communications bill, commonly known as the HPCC bill, enshrining the Grand Challenges as national priorities. The very nature of these problems require the multidisciplinary teamwork of engineers plus computer, mathematical and physi ..."
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Cited by 3 (3 self)
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In 1991, the US Congress passed the High Performance Computing and Communications bill, commonly known as the HPCC bill, enshrining the Grand Challenges as national priorities. The very nature of these problems require the multidisciplinary teamwork of engineers plus computer, mathematical and physical scientists. But many important scientific and engineering problems are solved daily on workstationsthese were dubbed the "petty challenges". Both classes of problem are demanding computational systems although quite different from nonscientific systems. We review a philosophical background for CSE, using this development to point out how seemingly innocuous decisions made by engineers and scientists can have disastrous results. Hence, software engineers should see CSE as a professional challenge. Our program is based on studying applications, the algorithms to solve problems arising in those applications, and the mapping of those algorithms to architectures. Using Computing Reviews...
A Critique of Inductive Causation
 Proc. 5th European Conf. on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU '99, London), LNAI 1638, 6879
, 1999
"... : In this paper we consider the problem of inducing causal relations from statistical data. Although it is well known that a correlation does not justify the claim of a causal relation between two measures, the question seems not to be settled. Research in the field of Bayesian networks revived an a ..."
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Cited by 2 (1 self)
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: In this paper we consider the problem of inducing causal relations from statistical data. Although it is well known that a correlation does not justify the claim of a causal relation between two measures, the question seems not to be settled. Research in the field of Bayesian networks revived an approach suggested in [16]. It is based on the idea that there are relationships between the causal structure of a domain and its corresponding probability distribution, which could be exploited to infer at least part of the causal structure from a set of dependence and independence statements. This idea was developed into the inductive causation algorithm [14]. We review this algorithm and examine the assumptions underlying it. 1 Introduction If A causes B, an occurrence of A should be accompanied or (closely) followed by an occurrence of B. That causation implies conjunction is the basis of all reasoning about causation in statistics. But is this enough to infer causal relations from stati...
Observations: four assumptions about invariance in perception
 Journal of Experimental Psychology: Human Perception and Performance
, 1983
"... The term invariance has become more central to current views of perception. I take this as a good trend, but the term is rooted in mathematics, and its use in perception brings with it a host of assumptions that have generally been unexamined. The purpose of this article is to state some of these as ..."
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Cited by 2 (0 self)
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The term invariance has become more central to current views of perception. I take this as a good trend, but the term is rooted in mathematics, and its use in perception brings with it a host of assumptions that have generally been unexamined. The purpose of this article is to state some of these assumptions and assess their validity, with the hope that we can continue to find the term useful while acknowledging its limitations. The assumptions discussed are that (a) mathematics is an appropriate descriptive language for perception, (b) mathematical truths are transportable into perception without change of meaning, (c) mathematical imports are useful in explaining perception, and (d) perceptual invariants, like their mathematical counterparts, are absolute and not subject to threshold considerations. If invariants of the energy flux at the receptors of an organism exist, and if these invariants correspond to the permanent properties of the environment, and if they are the basis of the organism's perception of the
Nonlinear Logic (NLL) – Making Sense out of
 Logical SelfReference”, AIAA Paper 20064726, 42 nd Joint Propulsion Conference
"... The fundamental argument against any kind of fasterthanlight (FTL) phenomenon is the issue of temporal paradox. Thanks to Special Relativity, FTL implies time travel and given time travel, the possibility of temporal paradox seems unavoidable. This is an argument from logic, not physics, yet upon ..."
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Cited by 1 (1 self)
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The fundamental argument against any kind of fasterthanlight (FTL) phenomenon is the issue of temporal paradox. Thanks to Special Relativity, FTL implies time travel and given time travel, the possibility of temporal paradox seems unavoidable. This is an argument from logic, not physics, yet upon closer examination it is discovered that our formal systems of logic studiously avoid selfreference in their foundational premises. This is doubly odd once it is realized that selfreference is unavoidable for any logical system of sufficient power, as demonstrated by Gödel’s Incompleteness Theorem. This paper presents a brief overview of the major attempts to construct logical systems with selfreference built into their foundations. It then covers in some detail Nonlinear Logic (NLL) the selfreferential logical system developed by Novatia Labs as part of their research project into the potential for quantum systems to support superluminal communications. Like most formal systems of logic, statements in NLL consist of typographical strings. The major addition to the symbol set is the label operator so that selfreference can be indicated. There is also a symbolic representation of statements in NLL derived from digital circuits that is isomorphic with the typographical representation. The digital circuit formalism is useful for