The paper defends the thesis that analysis of truth problem in the context of interpretations of quantum logic allows to reveal the prospect of elicitation of specifics of the relations between quantum mechanics and quantum logic in a context of modal expansions of quantum logic. It is found the way for solution of the problem of detection of features of creation of quantum-mechanical researches as a single case of semantics of "the possible worlds". Studies in the field of logic foundation of quantum physics receive the status of "possible quantum mechanics". Therefore they can be presented not simply as "truth" and "false" distinction within judgments about the physical phenomena but also as display logically possible and (or) impossible, necessary and (or) casual constructions of physical sciences.The paper defends the thesis that analysis of truth problem in the context of interpretations of quantum logic allows to reveal the prospect of elicitation of specifics of the relations between quantum mechanics and quantum logic in a context of modal expansions of quantum logic. It is found the way for solution of the problem of detection of features of creation of quantum-mechanical researches as a single case of semantics of "the possible worlds". Studies in the field of logic foundation of quantum physics receive the status of "possible quantum mechanics". Therefore they can be presented not simply as "truth" and "false" distinction within judgments about the physical phenomena but also as display logically possible and (or) impossible, necessary and (or) casual constructions of physical sciences.

arXiv:1407.2858Jul 10, 20140 citations

Quantum Logic in Historical and Philosophical Perspective

Christian DE RONDE, Graciela Domenech, Héctor Freytes

Jan 1, 201438 citations

Records, chance, and determination: a three-layer semantics for quantum measurement and future contingents

Murat Kelikli

Abstract This paper reconstructs a “logic of the future” for indeterministic settings by separating three semantic roles that are often conflated when future-tense truth is identified with probability. First, we introduce an external bivalent semantics in which truth is evaluated along branching histories and settlement is defined relative to admissible continuations. Second, we distinguish an internal probabilistic layer: a measure over admissible histories representing objective chance or assertibility rather than truth. Third, and most importantly, we add a minimal record–determination layer, expressed by the operators $\boldsymbol {\mathsf Rec}$ and $\boldsymbol {\mathsf Det}$ , which explains when classical reasoning is locally licensed within an otherwise open and indeterministic future. We show that under $\boldsymbol {\mathsf Rec}+\boldsymbol {\mathsf Det}$ classical inference is recovered exactly at those points where records determine outcomes, without entailing global determinism. The main technical results, including the Domino Lemma and the Record-to-Outcome Theorem , formalize the idea that once a fact is recorded and dynamically linked to a future outcome, that outcome becomes settled for purposes of truth-evaluation and reasoning. The framework is semantic and interpretation-neutral: rather than adjudicating between quantum interpretations, it provides a principled semantic criterion for when classical reasoning is locally licensed within an indeterministic setting. In this way it preserves Aristotle’s anti-fatalist insight from De Interpretatione 9, retains Sudbery’s probabilistic machinery for quantum chance, and provides a principled criterion for the local return of classical logic.Abstract This paper reconstructs a “logic of the future” for indeterministic settings by separating three semantic roles that are often conflated when future-tense truth is identified with probability. First, we introduce an external bivalent semantics in which truth is evaluated along branching histories and settlement is defined relative to admissible continuations. Second, we distinguish an internal probabilistic layer: a measure over admissible histories representing objective chance or assertibility rather than truth. Third, and most importantly, we add a minimal record–determination layer, expressed by the operators $$\boldsymbol {\mathsf Rec}$$ and $$\boldsymbol {\mathsf Det}$$ , which explains when classical reasoning is locally licensed within an otherwise open and indeterministic future. We show that under $$\boldsymbol {\mathsf Rec}+\boldsymbol {\mathsf Det}$$ classical inference is recovered exactly at those points where records determine outcomes, without entailing global determinism. The main technical results, including the Domino Lemma and the Record-to-Outcome Theorem , formalize the idea that once a fact is recorded and dynamically linked to a future outcome, that outcome becomes settled for purposes of truth-evaluation and reasoning. The framework is semantic and interpretation-neutral: rather than adjudicating between quantum interpretations, it provides a principled semantic criterion for when classical reasoning is locally licensed within an indeterministic setting. In this way it preserves Aristotle’s anti-fatalist insight from De Interpretatione 9, retains Sudbery’s probabilistic machinery for quantum chance, and provides a principled criterion for the local return of classical logic.

SyntheseMay 18, 20260 citations

The History of Quantum Logic

María Luisa Dalla Chiara, Roberto Giuntini, Miklós Rédei

Handbook of the history of logicJan 1, 20077 citations

Quantum Theory and Logic

M. Strauss

Springer eBooksJan 1, 19720 citations

\boldsymbol {\mathsf Rec}

and

\boldsymbol {\mathsf Det}

, which explains when classical reasoning is locally licensed within an otherwise open and indeterministic future. We show that under

\boldsymbol {\mathsf Rec}+\boldsymbol {\mathsf Det}

classical inference is recovered exactly at those points where records determine outcomes, without entailing global determinism. The main technical results, including the Domino Lemma and the Record-to-Outcome Theorem , formalize the idea that once a fact is recorded and dynamically linked to a future outcome, that outcome becomes settled for purposes of truth-evaluation and reasoning. The framework is semantic and interpretation-neutral: rather than adjudicating between quantum interpretations, it provides a principled semantic criterion for when classical reasoning is locally licensed within an indeterministic setting. In this way it preserves Aristotle’s anti-fatalist insight from De Interpretatione 9, retains Sudbery’s probabilistic machinery for quantum chance, and provides a principled criterion for the local return of classical logic.