Product ?ukasiewicz?Quantum Logic |
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| Authors: | Cesarino Bertini and Roberto Leporini |
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| Institution: | (1) Dipartimento di Filosofia, Universit? di Firenze, via Bolognese 52, I-50139 Firenze, Italy;(2) Dipartimento di Scienze Pedagogiche e Filosofiche, Universit? di Cagliari, via Is Mirrionis 1, I-09123 Cagliari, Italy;(3) Dipartimento di Matematica, Statistica, Informatica e Applicazioni, Universit? di Bergamo, via dei Caniana 2, I-24127 Bergamo, Italy |
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| Abstract: | The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a density operator (called qumix). In this framework, any sentence α of the language gives rise to a quantum circuit that transforms the qumix associated to the atomic subformulas of α into the qumix associated to α. In this paper we enrich the language by adding a new connective which expresses truncated sum. |
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