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

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.