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LOGICS OF LOGICS
- Part of
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- Journal:
- The Review of Symbolic Logic , First View
- Published online by Cambridge University Press:
- 22 August 2025, pp. 1-11
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- Article
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We investigate a system of modal semantics in which
$\Box \phi $ is true if and only if 
$\phi $ is entailed by a designated set of formulas by a designated logics. We prove some strong completeness results as well as a natural connection to normal modal logics via an application of some lattice-theoretic fixpoint theorems. We raise a difficult problem that arises naturally in this setting about logics which are identical with their own ‘meta-logic’, and draw a surprising connection to recent work by Andrew Bacon and Kit Fine on McKinsey’s substitutional modal semantics.
