Can Many-Valued Logic Help to Comprehend Quantum Phenomena?

Abstract

Following Lukasiewicz, we argue that future non-certain events should be described with the use of many-valued, not 2-valued logic. The Greenberger -Horne -Zeilinger 'paradox' is shown to be an artifact caused by unjustified use of 2-valued logic while considering results of future non-certain events. Description of properties of quantum objects before they are measured should be performed with the use of propositional functions that form a particular model of ∞-valued Lukasiewicz logic. This model is distinguished by specific operations of negation, conjunction, and disjunction that are used in it.

Understanding quantum mechanics: a review and synthesis in precise language

“…3. Specific logical frameworks and analyses can -highlight features of the formalism [548], -contribute to understanding how that formalism relates to independent reality [481,549], and -assess whether or not quantum mechanics necessarily requires new notions of truth [550][551][552][553][554].…”

Hardy’s paradox according to non-classical semantics

“…where the function v P assigning the truth value to the projection operatorP ⋄ in the state |Ψ is determined by the probability P [[[ ⋄]] v = 1] = Ψ|P ⋄ |Ψ . According to [12,13], the value v P represents the degree to which the proposition ⋄ is true before its verification. As Ψ|P ⋄ |Ψ ∈ {x ∈ R : 0 < x < 1}, a semantics defined by the set of the bivaluations (11) and the valuations (35) is infinite-valued.…”

Romanian Studies in Philosophy of Science

“…In the quasi-sets program the indistinguishability of quantum particles is build-in right from the start in the concept of quasi-set. Other approaches include paraconsistent logic (da Costa and de Ronde, 2013), many-valued logic (Pykacz, 2014) and sheaves (Abramsky and Brandenburger, 2011).…”

“…The problem is still open, notwithstanding several attempts like quantum logic (Birkhoff and von Neumann, 1936), topos theory (Doering and Isham, 2011), quasisets (French and Krause, 2010), sheaves (Abramsky and Brandenburger, 2011), paraconsistent logic (da Costa and de Ronde, 2013) and many-valued logic (Pykacz, 2014). Quantum logic has been around for more than 70 years, but it yielded few results.…”