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This essay aims to establish two general recapture theorems that relate various sub-logics to classical logic.

February 19, 2026Asian Journal of Philosophy0 citationsOpen Access

A general recipe for classical recapture

Key Points

This essay aims to establish two general recapture theorems that relate various sub-logics to classical logic.
Proves independence of six inference rules.
Explores possible modifications or extensions of the results.
Compares findings with Jc Beall's previous results from multiple studies.
Establishes that each sub-logic closed under the six rules is equivalent to classical logic.
Demonstrates that the GRT and GRT Dual are more powerful than Beall's approaches.

Abstract

Abstract In this essay, I prove two general recapture theorems (the GRT and the GRTDual GRT Dual). Each of these states that any sub-logic of classical logic that is closed under six rules of inference is equivalent, in the relevant sense, to classical logic. After proving in each case that the six rules in question are independent of one another, and exploring a number of possible modifications or extensions of these results, I compare the results to Jc Beall’s recapture results in Beall (2011), Beall (2013a) and Beall (2013b). The GRT (and GRTDual GRT Dual) are shown to be more powerful and general than Beall’s more piecemeal approach.

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