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arXiv:2107.10817 · Bulletin of Symbolic Logic

TEAM SEMANTICS AND INDEPENDENCE NOTIONS IN QUANTUM PHYSICS

Samson Abramsky, Joni Puljujärvi, Jouko Väänánen

Published Aug 15, 2025• 4 citations
arXivHTMLPDF

Abstract

Abstract We study dependence and independence concepts found in quantum physics, especially those related to hidden variables and non-locality, through the lens of team semantics and probabilistic team semantics, adapting a relational framework introduced in [1]. This also leads to new developments in independence logic and probabilistic independence logic.

DOI
10.1017/bsl.2025.10089

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Abstract We study dependence and independence concepts found in quantum physics, especially those related to hidden variables and non-locality, through the lens of team semantics and probabilistic team semantics, adapting a relational framework introduced in [1]. This also leads to new developments in independence logic and probabilistic independence logic.
In a recent note, Hance and Hossenfelder (arXiv:2211.01331) recall that "locally causal completions of quantum mechanics are possible, if they violate the assumption [called statistical independence or measurement independence] that the hidden variables do not in any way depend on measurement settings" and that, consequently, the experimental violations of Bell inequalities "show that maintaining local causality requires violating statistical independence". However, Hance and Hossenfelder also argue that "we should (...) look for independent experimental evidence that can distinguish the two different options: non-locality and statistical independence, or locality and violations of statistical independence" and that "the unwillingness to consider theories without statistical independence may be the reason we do not yet have a locally causal theory for the foundations of physics that is consistent with general relativity". Here, we recall that there is a third option, namely, rejecting that measurement outcomes are governed in any way by hidden variables. Moreover, we argue that some recent results in the search for principles singling out the sets of quantum correlations for Bell and Kochen-Specker contextuality scenarios point out that this third option is scientifically more plausible and answers the question of why and how nature produces quantum nonlocality.
Abstract A logical approach to Bell’s Inequalities of quantum mechanics has been introduced by Abramsky and Hardy (Abramsky & Hardy, 2012). We point out that the logical Bell’s Inequalities of Abramsky & Hardy (2012) are provable in the probability logic of Fagin, Halpern and Megiddo (Fagin et al., 1990). Since it is now considered empirically established that quantum mechanics violates Bell’s Inequalities, we introduce a modified probability logic, that we call quantum team logic, in which Bell’s Inequalities are not provable, and prove a Completeness theorem for this logic. For this end we generalise the team semantics of dependence logic (Väänänen, 2007) first to probabilistic team semantics, and then to what we call quantum team semantics.
Cognitional Mechanics (CM) provides a formal, axiomatic framework for modeling intelligence as a system of non-commutative operations over semantic manifolds. Unlike quantum computation, which relies on physical qubits, entanglement, and probabilistic evolution, CM abstracts computational processes into deterministic, substrate-independent structures. Relativistic Cognitional Mechanics (RCM) further extends this framework to multi-agent and social contexts, representing individuals, groups, and interactions as points, submanifolds, and tensors on semantic manifolds. The structural similarities between CM and quantum mechanics—particularly non-commutativity and phase-like control—invite exploration of computational parallels. This paper examines whether CM-based computation can achieve the advantages typically attributed to quantum systems, including parallel evaluation, phase-sensitive state selection, and complex non-commutative logic, without invoking physical quantum effects. By formalizing operator sequences and semantic state evolution in classical implementations, we establish a theoretical bridge connecting abstract intelligence mechanics with practical computational architectures. This work positions CM as an independent, low-cost paradigm for high-performance reasoning, structured exploration, and semantic computation, highlighting both its potential and its limitations relative to conventional quantum computation.