Palavras-chave
Como Citar
Resumo
A teoria quˆantica e a computa¸c˜ao quˆantica d˜ao origem a algumas situa¸c˜oes semˆanticas de caracter´ıstica hol´ıstica, onde o significado de um todo determina o significado de suas partes (e n˜ao reciprocamente, como acontece na semˆantica da maioria das l´ogicas tradicionais). L´ogicas quˆanticas computacionais s˜ao novas formas de l´ogica que tˆem sido sugeridas pela teoria das portas l´ogicas quˆanticas na computa¸c˜ao quˆantica. Na semˆantica padr˜ao dessas l´ogicas, as senten¸cas denotam quantidades de informa¸c˜ao quˆantica (sistemas de qubits ou, mais geralmente, misturas de sistemas de qubits), onde os conectivos l´ogicos s˜ao interpretados como portas l´ogicas quˆanticas especiais (as quais tˆem uma caracter´ıstica revers´ıvel e um comportamento dinˆamico). Um vers˜ao abstrata dessa semˆantica pode ser usada naturalmente para analisar diferentes tipos de fenˆomenos semˆanticos onde padr˜oes hol´ıısticos, contextuais e amb´ıguos desempenham papel essencial. Neste escopo, analisamos algumas caracter´ısticas das linguagens musicais.
Abstract:
Quantum theory and quantum computation give rise to some characteristic holistic semantic situations, where the meaning of a whole determines the meanings of its parts (and not the other way around, as happens in the semantics of most traditional logics). Quantum computational logics are new forms of quantum logic that have been suggested by the theory of quantum logical gates in quantum computation. In the standard semantics of these logics, sentences denote quantum information quantities (systems of qubits, or, more generally, mixtures of systems of qubits), while logical connectives are interpreted as special quantum logical gates (which have a characteristic reversible and dynamic behavior). An abstract version of this semantics can be naturally used to analyze different kinds of semantic phenomena where holistic, contextual and ambiguous patterns play an essential role. In this framework we analyze some characteristic features of musical languages.
Keywords: Quantum computation. Music.
Referências
DALLA CHIARA, M. L., GIUNTINI, R. and LEPORINI, R., “Quantum Computational Logics. A Survey”, in V. Hendricks and J. Malinowski (eds.), Trends in Logic. 50 Years of Studia Logica, Kluwer, 2003, 229–271.
DALLA CHIARA, M. L., GIUNTINI, R. and LEPORINI, R., “Logics from quantum computation”, International Journal of Quantum Information, 3 (2005), 293–337.
DALLA CHIARA, M. L. and GIUNTINI, R., “A formal analysis of musical scores”, Mathematica Slovaca, 56 (2006), 591–609.
DALLA CHIARA, M. L., GIUNTINI, R. and LEPORINI, R., “Compositional and holistic quantum computational semantics”, Natural Computing, 6 (2007), 113–132.
DALLA CHIARA, M. L., GIUNTINI, R. and GREECHIE, R., Reasoning in Quantum Theory, Kluwer, Dordrecht, 2004.
DALLA CHIARA, M. L., GIUNTINI, R. and NEGRI, E., “From quantum mechanics to music”, Advanced Science Letters 1 (2008), 169–178.
DALLA CHIARA, M. L., GIUNTINI, R., and TORALDO DI FRANCIA, G., “Holistic quantum computational semantics and Gestaltthinking”, in A. Bassi, D. D¨urr, T. Weber, N. Zangh`ı (eds.), Quantum Mechanics. Are there quantum jumps? On the present status of quantum mechanics, AIP, 2006, Melville, New York, 86–100.
DALLA CHIARA, M. L., GIUNTINI, R., LEPORINI, R. and TORALDO DI FRANCIA, G., “Quantum computational logics and possible applications”, International Journal of Theoretical Physics, 47 (2008), 44–60.
KITAEV, A. Yu., SHEN, A. H. and VYALYI, M. N., Classical and Quantum Computation, American Mathematical Society, Providence, 2002.
Downloads
