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174
Belief, awareness, and limited reasoning
 ARTIFICIAL INTELLIGENCE
, 1988
"... Several new logics for belief and knowledge are introduced and studied, all of which have the property that agents are not logically omniscient. In particular, in these logics, the set of beliefs of an agent does not necessarily contain all valid formulas. Thus, these logics are more suitable than t ..."
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Cited by 144 (13 self)
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Several new logics for belief and knowledge are introduced and studied, all of which have the property that agents are not logically omniscient. In particular, in these logics, the set of beliefs of an agent does not necessarily contain all valid formulas. Thus, these logics are more suitable than traditional logics for modelling beliefs of humans (or machines) with limited reasoning capabilities. Our first logic is essentially an extension of Levesque's logic of implicit and explicit belief, where we extend to allow multiple agents and higherlevel belief (i.e., beliefs about beliefs). Our second logic deals explicitly with "awareness," where, roughly speaking, it is necessary to be aware of a concept before one can have beliefs about it. Our third logic gives a model of "local reasoning," where an agent is viewed as a "society of minds," each with its own cluster of beliefs, which may contradict each other.
Partial realizations of Hilbert’s program
 JOURNAL OF SYMBOLIC LOGIC
, 1988
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Learning as Extraction of LowDimensional Representations
 Mechanisms of Perceptual Learning
, 1996
"... Psychophysical findings accumulated over the past several decades indicate that perceptual tasks such as similarity judgment tend to be performed on a lowdimensional representation of the sensory data. Low dimensionality is especially important for learning, as the number of examples required for a ..."
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Cited by 35 (8 self)
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Psychophysical findings accumulated over the past several decades indicate that perceptual tasks such as similarity judgment tend to be performed on a lowdimensional representation of the sensory data. Low dimensionality is especially important for learning, as the number of examples required for attaining a given level of performance grows exponentially with the dimensionality of the underlying representation space. In this chapter, we argue that, whereas many perceptual problems are tractable precisely because their intrinsic dimensionality is low, the raw dimensionality of the sensory data is normally high, and must be reduced by a nontrivial computational process, which, in itself, may involve learning. Following a survey of computational techniques for dimensionality reduction, we show that it is possible to learn a lowdimensional representation that captures the intrinsic lowdimensional nature of certain classes of visual objects, thereby facilitating further learning of tasks...
Machines, logic and quantum physics
 BULLETIN OF SYMBOLIC LOGIC
, 1999
"... Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of th ..."
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Cited by 18 (0 self)
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Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned.
Mass and 3metrics of nonnegative scalar curvature
 Proc. Int. Cong. Math., Vol
, 2002
"... Physicists believe, with some justification, that there should be a correspondence between familiar properties of Newtonian gravity and properties of solutions of the Einstein equations. The Positive Mass Theorem (PMT), first proved over twenty years ago [45, 53], is a remarkable testament to this f ..."
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Cited by 15 (1 self)
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Physicists believe, with some justification, that there should be a correspondence between familiar properties of Newtonian gravity and properties of solutions of the Einstein equations. The Positive Mass Theorem (PMT), first proved over twenty years ago [45, 53], is a remarkable testament to this faith. However, fundamental mathematical questions concerning mass in general relativity remain, associated with the definition and properties of quasilocal mass. Central themes are the structure of metrics with nonnegative scalar curvature, and the role played by minimal area 2spheres (black holes).
Computational universes
 Chaos, Solitons & Fractals
, 2006
"... Suspicions that the world might be some sort of a machine or algorithm existing “in the mind ” of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science h ..."
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Cited by 15 (5 self)
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Suspicions that the world might be some sort of a machine or algorithm existing “in the mind ” of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science have lent support to the thesis, but empirical evidence is needed before it can begin to replace our contemporary world view.
Another look at generic groups
 Advances in Mathematics of Communications
, 2006
"... (Communicated by Andreas Stein) Abstract. Starting with Shoup’s seminal paper [24], the generic group model has been an important tool in reductionist security arguments. After an informal explanation of this model and Shoup’s theorem, we discuss the danger of flaws in proofs. We next describe an on ..."
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Cited by 12 (4 self)
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(Communicated by Andreas Stein) Abstract. Starting with Shoup’s seminal paper [24], the generic group model has been an important tool in reductionist security arguments. After an informal explanation of this model and Shoup’s theorem, we discuss the danger of flaws in proofs. We next describe an ontological difference between the generic group assumption and the random oracle model for hash functions. We then examine some criticisms that have been leveled at the generic group model and raise some questions of our own. 1.
Formal versus Material Ontologies for information Systems interoperation
 in the Semantic Web. The Computer Journal
, 2006
"... Work performed partly while visiting LADSEBCNR; Corso Stati Uniti, 4; Padova, Italia, Information systems ontology is intended to facilitate interoperability among the many applications which are now becoming available on the Internet. In particular, it is intended to facilitate the development of ..."
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Cited by 10 (1 self)
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Work performed partly while visiting LADSEBCNR; Corso Stati Uniti, 4; Padova, Italia, Information systems ontology is intended to facilitate interoperability among the many applications which are now becoming available on the Internet. In particular, it is intended to facilitate the development of intelligent agents which can automate a large part of the task of a user achieving some end employing multiple autonomous applications. A large number of ontologies exist supporting specific kinds of interoperation among selected, generally mutually description of what there is in the world, in an applicationindependent form, which can be used both to help build specific ontologies and to help in finding common ground among them. This paper argues that for the purposes of information systems interoperation and the semantic web there is a distinction in upper ontologies between formal and material ontologies, based on analogies with concepts in Kant’s synthetic a priori, and that formal ontologies whose focus is on how we see the world are more likely to be successfully developed in the absence of applications than are material ontologies, which attempt to catalog the world a priori. 2
K.P.: Scouting contextsensitive components
 In: The Third NASA/DoD Workshop on Evolvable Hardware—EH2001. (2001) 14–20
"... Nature’s gadgets are implemented without being planned and therefore can utilize contextsensitive components. Thus functionality that would require extensive networks of contextfree components can be elicited from a minimum of material. Proteins can serve as contextsensitive components for patte ..."
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Nature’s gadgets are implemented without being planned and therefore can utilize contextsensitive components. Thus functionality that would require extensive networks of contextfree components can be elicited from a minimum of material. Proteins can serve as contextsensitive components for pattern processing applications. We here describe an evolutionary search strategy currently under investigation for its potential use in conjunction with computer controlled f luidics to evaluate the computational capabilities of proteins. Our algorithm employs evolutionary search not to seek an optimum, but to seek surprises. It directs experiments and incrementally constructs an empirical model from their outcome. Reward is given for discovering conditions that exhibit a discrepancy between the prediction of the current model and the experimental result. As unexpected observations are incorporated into the model, the reward associated with them vanishes. Results obtained so far indicate that evolutionary search is a useful paradigm for characterizing the phenomenology of contextsensitive components. 1.