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<p>A variable domain model theory with accessibility is developed to interpret the language of second-order propositional modal logic. It is shown that propositionally quantified modal logics S5 and weaker as characterized by the classes of such frames are recursively isomorphic to second-order logic and thus not recursively axiomatizable. The result is then extended to a related class of logics validating a higher-order comprehension principle. While the primary objective of this paper is to explore formal systems, many of the model-theoretic decisions are informed by contingentist views. Given the attention to higher-order formal arguments against contingentism, the results of this paper might be of some interest to those concerned with that debate.</p>

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Expressive Power of Propositionally Quantified Modal Logics on Variable Domain Structures with Accessibility

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Eliya Cohen

摘要

A variable domain model theory with accessibility is developed to interpret the language of second-order propositional modal logic. It is shown that propositionally quantified modal logics S5 and weaker as characterized by the classes of such frames are recursively isomorphic to second-order logic and thus not recursively axiomatizable. The result is then extended to a related class of logics validating a higher-order comprehension principle. While the primary objective of this paper is to explore formal systems, many of the model-theoretic decisions are informed by contingentist views. Given the attention to higher-order formal arguments against contingentism, the results of this paper might be of some interest to those concerned with that debate.