Truth problem in the context of interpretations of quantum logic

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.

💡 Research Summary

The paper tackles the longstanding “truth problem” in quantum logic by proposing a modal‑semantic expansion that treats quantum propositions not merely as true or false but as statements whose status can be possible, impossible, necessary, or contingent. Traditional quantum logic inherits the binary truth‑value system of classical logic, assigning a proposition a value of 1 (true) or 0 (false) depending on the outcome of a measurement. While this captures the Copenhagen view that observation determines truth, it fails to represent the multiplicity of potential outcomes, entanglement, and non‑local correlations that are intrinsic to quantum phenomena.

To overcome these limitations, the author imports tools from modal logic and possible‑worlds semantics. A quantum system is modeled as a set W of possible worlds, each world representing a complete specification of experimental settings and outcomes. An accessibility relation R between worlds encodes physically admissible transformations—such as unitary evolution, measurement collapse, or changes in experimental context. Within this framework a quantum proposition φ is evaluated at a world w by a satisfaction relation ⊨(w, φ). Rather than a Boolean value, the evaluation yields a pair of degrees: a “possibility” degree μₚ(w, φ) and a “necessity” degree μₙ(w, φ), both ranging from 0 to 1. The modal operators ◇ and □ are then defined in the usual way: ◇φ holds at w if there exists an R‑accessible world v where μₚ(v, φ) > 0, while □φ holds at w only if μₙ(v, φ) = 1 for every accessible v.

Mathematically the construction resembles a Kripke frame ⟨W,R⟩ equipped with a valuation function μ: W × Formulas →