Reducing compositional to disquotational truth

Review of Symbolic Logic 2 (4):786-798 (2009)
Disquotational theories of truth, that is, theories of truth based on the T-sentences or similar equivalences as axioms are often thought to be deductively weak. This view is correct if the truth predicate is allowed to apply only to sentences not containing the truth predicate. By taking a slightly more liberal approach toward the paradoxes, I obtain a disquotational theory of truth that is proof theoretically as strong as compositional theories such as the Kripket probe the compositional axioms
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    Andrea Cantini (1989). Notes on Formal Theories of Truth. Zeitshrift für Mathematische Logik Und Grundlagen der Mathematik 35 (1):97--130.
    Solomon Feferman (1991). Reflecting on Incompleteness. Journal of Symbolic Logic 56 (1):1-49.
    Volker Halbach, Axiomatic Theories of Truth. Stanford Encyclopedia of Philosophy.

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