Graham Emil Leigh

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The first attempt at a systematic approach to axiomatic theories of truth was undertaken by Friedman and Sheard [11]. There twelve principles consisting of axioms, axiom schemata and rules of inference, each embodying a reasonable property of truth were isolated for study. Working with a base theory of truth conservative over PA, Friedman and Sheard raised(More)
This paper explores the interface between principles of self-applicable truth and classical logic. To this end, the proof-theoretic strength of a number of axiomatic theories of truth over intuitionistic logic is determined. The theories considered correspond to the maximal consistent collections of fifteen truth-theoretic principles as isolated in Leigh(More)
Recently a new connection between proof theory and formal language theory was introduced. It was shown that the operation of cut elimination for proofs in first-order predicate logic involving Π 1-cuts corresponds to computing the language of a particular class of regular tree grammars. The present paper expands this connection to the level of Π 2-cuts.(More)
The closure ordinal of a formula of modal µ-calculus µXϕ is the least ordinal κ, if it exists, such that the denotation of the formula and the κ-th iteration of the monotone operator induced by ϕ coincide across all transition systems (finite and infinite). It is known that for every α < ω 2 there is a formula ϕ of modal logic such that µXϕ has closure(More)
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