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<p>This paper gives a formulation of quantum logic in the abstract algebraic setting laid out by Dunn and Hardegree (<CitationRef CitationID="CR8">2001</CitationRef>). On this basis, it provides a comparative analysis of viable quantum logical bivalent semantics and their classical counterparts, thereby showing that the truth-functional status of classical and quantum connectives is not as different as usually thought. Then it points out that bivalent semantics for quantum logic – compatible with realism about quantum mechanics – can be maintained, albeit at the price of truth-functionality. Finally, the paper critically addresses Geoffrey Hellman’s argument (<CitationRef CitationID="CR11">1980</CitationRef>) that this lack of truth-functionality entails a change of meaning between classical and quantum connectives.</p>

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Quantum Logic and Meaning

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年11月11日

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  • Sebastian Horvat,
  • Iulian D. Toader

摘要

This paper gives a formulation of quantum logic in the abstract algebraic setting laid out by Dunn and Hardegree (2001). On this basis, it provides a comparative analysis of viable quantum logical bivalent semantics and their classical counterparts, thereby showing that the truth-functional status of classical and quantum connectives is not as different as usually thought. Then it points out that bivalent semantics for quantum logic – compatible with realism about quantum mechanics – can be maintained, albeit at the price of truth-functionality. Finally, the paper critically addresses Geoffrey Hellman’s argument (1980) that this lack of truth-functionality entails a change of meaning between classical and quantum connectives.