Axiomatization of an Orthologic of Indeterminacy
Recently, we ( Synthese, 199 (5–6):13247–13281, 2021 ) proposed Kripke-like semantics for two quantum logics of interderminacy. These logics expand the vocabulary of standard Birkhoff-von Neumann propositional quantum logic with a pair of modal operators interpreted as “it is (in)determinate that”,...
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Veröffentlicht in: | Journal of philosophical logic 2024-12, Vol.53 (6), p.1441-1462 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Recently, we (
Synthese, 199
(5–6):13247–13281,
2021
) proposed Kripke-like semantics for two quantum logics of interderminacy. These logics expand the vocabulary of standard Birkhoff-von Neumann propositional quantum logic with a pair of modal operators interpreted as “it is (in)determinate that”, allowing them to express in the object language statements such as “it is indeterminate that system S is spin-up in the x-direction”, as well as statements of any logical complexity involving ascriptions of (in)determinacy. We present an axiomatization of a logic closely related to one of these quantum logics of indeterminacy and prove that this axiomatization is sound and complete with respect to the Kripke-like semantics. We then prove that this logic is decidable. |
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ISSN: | 0022-3611 1573-0433 |
DOI: | 10.1007/s10992-024-09756-5 |