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222
Automaton Logic
 International Journal of Theoretical Physics
, 1996
"... The experimental logic of Moore and Mealy type automata is investigated. key words: automaton logic; partition logic; comparison to quantum logic; intrinsic measurements 1 ..."
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Cited by 79 (47 self)
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The experimental logic of Moore and Mealy type automata is investigated. key words: automaton logic; partition logic; comparison to quantum logic; intrinsic measurements 1
Foundations of Quantum Physics: a General Realistic and
 Operational Approach, Int. J. Theor. Phys
, 1999
"... We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it ‘changes ’ under the influence of the rest of the universe. Therefore we base our formalism on the following basic notions: (1 ..."
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Cited by 36 (25 self)
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We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it ‘changes ’ under the influence of the rest of the universe. Therefore we base our formalism on the following basic notions: (1) the states of the entity; they describe the modes of being of the entity, (2) the experiments that can be performed on the entity; they describe how we act upon and collect knowledge about the entity, (3) the probabilities; they describe our repeated experiments and the statistics of these repeated experiments, (4) the symmetries; they describe the interactions of the entity with the external world without being experimented upon. Starting from these basic notions we formulate the necessary derived notions: mixed states, mixed experiments and events, an eigen closure structure describing the properties of the entity, an ortho closure structure introducing an orthocomplementation, outcome determination, experiment determination, state determination and atomicity giving rise to some of the topological separation axioms for the closures. We define the notion of sub entity in a general way and identify the morphisms of our structure. We study specific examples in detail in the light of this formalism: a classical deterministic entity and a quantum entity described by the standard quantum mechanical formalism. We present a possible solution to the problem of the description of sub entities within the standard quantum mechanical procedure using the tensor product of the Hilbert spaces, by introducing a new completed quantum mechanics in Hilbert space, were new ‘pure ’ states are introduced, not represented by rays of the Hilbert space.
Information and Its Metric
 Nonlinear Structures in Physical Systems – Pattern Formation, Chaos and Waves
, 1990
"... INTRODUCTION This brief note introduces a measure of distance between information sources. It demonstrates that the space of information sources has much topological structure which heretofore has not been utilized directly in applications of information theory or in the study of complex systems. T ..."
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Cited by 33 (4 self)
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INTRODUCTION This brief note introduces a measure of distance between information sources. It demonstrates that the space of information sources has much topological structure which heretofore has not been utilized directly in applications of information theory or in the study of complex systems. The space of information sources is, in fact, a metric space to which a geometric picture can be ascribed. Furthermore, if one considers the elemental events from the information source to be experimental measurements, then the logic of inference is described by a metric lattice. Although this note is restricted to a presentation of formal details and to their geometric interpretation, a few motivational remarks are in order. There are four aspects of the use of information theory in the physics of complex systems that suggest a need for a better understanding of its formal structure and of the concept of information itself. Briefly, these are the observational theory of chaotic syste
Finite precision measurement nullifies the KochenSpecker theorem
, 1999
"... Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S 2, can be colored so that the contradiction with hidden variable theories provided by KochenSpecker constructions do ..."
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Cited by 32 (1 self)
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Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S 2, can be colored so that the contradiction with hidden variable theories provided by KochenSpecker constructions does not obtain. Thus, in contrast to violation of the Bell inequalities, no quantumoverclassical advantage for information processing can be derived from the KochenSpecker theorem alone.
Weakly complete axiomatization of exogenous quantum propositional logic
 Information and Computation
, 2006
"... A weakly complete finitary axiomatization for EQPL (exogenous quantum propositional logic) is presented. The proof is carried out using a non trivial extension of the FaginHalpernMegiddo technique together with three Henkin style completions. 1 ..."
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Cited by 32 (23 self)
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A weakly complete finitary axiomatization for EQPL (exogenous quantum propositional logic) is presented. The proof is carried out using a non trivial extension of the FaginHalpernMegiddo technique together with three Henkin style completions. 1
Word vectors and quantum logic: Experiments with negation and disjunction
 In Proceedings of the 8th Mathematics of Language Conference
, 2003
"... A calculus which combined the flexible geometric structure of vector models with the crisp efficiency of Boolean logic would be extremely beneficial for modelling natural language. With this goal in mind, we present a formulation for logical connectives in vector spaces based on standard linear alge ..."
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Cited by 25 (3 self)
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A calculus which combined the flexible geometric structure of vector models with the crisp efficiency of Boolean logic would be extremely beneficial for modelling natural language. With this goal in mind, we present a formulation for logical connectives in vector spaces based on standard linear algebra, giving examples of the use of vector negation to discriminate between different senses of ambiguous words. It turns out that the operators developed in this way are precisely the connectives of quantum logic (Birkhoff and von Neumann, 1936), which to our knowledge have not been exploited before in natural language processing. In quantum logic, arbitrary sets are replaced by linear subspaces of a vector space, and set unions, intersections and complements are replaced by vector sum, intersection and orthogonal complements of subspaces. We demonstrate that these logical connectives (particularly the orthogonal complement for negation) are powerful tools for exploring and analysing word meanings and show distinct advantages over Boolean operators in document retrieval experiments. This paper is organised as follows. In Section 0.1 we describe some of the ways vectors have been used to represent the meanings of terms and documents in natural language processing, and describe the way the WORDSPACE used in our later experiments is built automatically from text corpora. In Section 0.2 we define the logical connectives on vector spaces, focussing particularly on negation and disjunction. This introduces the basic material needed to understand the worked
Abstract scalars, loops, and free traced and strongly compact closed categories
 PROCEEDINGS OF CALCO 2005, VOLUME 3629 OF SPRINGER LECTURE NOTES IN COMPUTER SCIENCE
, 2005
"... We study structures which have arisen in recent work by the present author and Bob Coecke on a categorical axiomatics for Quantum Mechanics; in particular, the notion of strongly compact closed category. We explain how these structures support a notion of scalar which allows quantitative aspects of ..."
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Cited by 25 (5 self)
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We study structures which have arisen in recent work by the present author and Bob Coecke on a categorical axiomatics for Quantum Mechanics; in particular, the notion of strongly compact closed category. We explain how these structures support a notion of scalar which allows quantitative aspects of physical theory to be expressed, and how the notion of strong compact closure emerges as a significant refinement of the more classical notion of compact closed category. We then proceed to an extended discussion of free constructions for a sequence of progressively more complex kinds of structured category, culminating in the strongly compact closed case. The simple geometric and combinatorial ideas underlying these constructions are emphasized. We also discuss variations where a prescribed monoid of scalars can be ‘glued in ’ to the free construction.
ORTHOMODULARITY IN INFINITE DIMENSIONS; A THEOREM Of M. Solèr
, 1995
"... Maria Pia Solèr has recently proved that an orthomodular form that has an infinite orthonormal sequence is real, complex, or quaternionic Hilbert space. This paper provides an exposition of her result, and describes its consequences for Baer ∗rings, infinitedimensional projective geometries, ort ..."
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Cited by 23 (0 self)
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Maria Pia Solèr has recently proved that an orthomodular form that has an infinite orthonormal sequence is real, complex, or quaternionic Hilbert space. This paper provides an exposition of her result, and describes its consequences for Baer ∗rings, infinitedimensional projective geometries, orthomodular lattices, and Mackey’s quantum logic.
Delinearizing linearity: projective quantum axiomatics from strong compact closure
 QPL 2005
, 2005
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