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Quantified Reflection Calculus with one modality · arXivDesk

2003.13651Mar 30, 2020Submitted to Advances in Modal Logic 2020

Quantified Reflection Calculus with one modality

Ana de Almeida Borges, Joost J. Joosten

Abstract

This paper presents the logic QRC $_1$ , which is a strictly positive fragment of quantified modal logic. The intended reading of the diamond modality is that of consistency of a formal theory. Predicate symbols are interpreted as parametrized axiomatizations. We prove arithmetical soundness of the logic QRC $_1$ with respect to this arithmetical interpretation. Quantified provability logic is known to be undecidable. However, the undecidability proof cannot be performed in our signature and arithmetical reading. We conjecture the logic QRC $_1$

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This paper presents the logic QRC₁, which is a strictly positive fragment of quantified modal logic. The intended reading of the diamond modality is that of consistency of a formal theory.

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The paper addresses: Quantified Reflection Calculus with one modality.
This paper presents the logic QRC₁, which is a strictly positive fragment of quantified modal logic.