Graham Emil Leigh

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Richard Heck in [2] and Volker Halbach in [1] have recently manifested much interest in an unconventional way of constructing (axiomatic) theories of truth, in which syntactic and logical notions concerning the object theory O are formalised in a disjoint theory of syntax S. In the talk, I shall first argue for the proposed alternative. I will then present(More)
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)
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 Π1-cuts corresponds to computing the language of a particular class of regular tree grammars. The present paper expands this connection to the level of Π2-cuts. Given(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 truththeoretic principles as isolated in Leigh and(More)
S. Feferman, Reflecting on incompleteness. Journal of Symbolic Logic vol. 56 no. 1 (1991), pp. 1–49. W.N. Reinhardt, Some remarks on extending and interpreting theories with a partial predicate for truth. Journal of Philosophical Logic vol. 15 no. 2 (1986), pp. 219–251. V. Halbach and L. Horsten, Axiomatizing Kripke’s theory of truth. Journal of Symbolic(More)
This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth. §1. New questions for the Revision Theory of(More)
We present two finitary cut-free sequent calculi for the modal μ-calculus. One is a variant of Kozen's axiomatisation in which cut is replaced by a strengthening of the induction rule for greatest fixed point. The second calculus derives annotated sequents in the style of Stirling's ‘tableau proof system with names’ (2014) and features(More)