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- Graham Emil Leigh, Carlo Nicolai
- Rew. Symb. Logic
- 2013

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)

- Graham Emil Leigh, Michael Rathjen
- Arch. Math. Log.
- 2010

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)

- Bahareh Afshari, Stefan Hetzl, Graham Emil Leigh
- TLCA
- 2015

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)

- Graham Emil Leigh
- J. Symb. Log.
- 2015

We present a cut elimination argument that witnesses the conservativity of the compositional axioms for truth (without the extended induction axiom) over any theory interpreting a weak subsystem of arithmetic. In doing so we also fix a critical error in Halbach’s original presentation. Our methods show that the admission of these axioms determines a… (More)

- Graham Emil Leigh, Michael Rathjen
- J. Symb. Log.
- 2012

This paper compares the roles classical and intuitionistic logic play in restricting the free use of truth principles in arithmetic. We consider fifteen of the most commonly used axiomatic principles of truth and classify every subset of them as either consistent or inconsistent over a weak purely intuitionistic theory of truth.

- Graham Emil Leigh
- Ann. Pure Appl. Logic
- 2013

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)

- Leon Horsten, Graham Emil Leigh, Hannes Leitgeb, Philip D. Welch
- Rew. Symb. Logic
- 2012

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)

- Bahareh Afshari, Graham Emil Leigh
- CSL
- 2013

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 there is a formula φ of modal logic such that μXφ has closure… (More)

- Bahareh Afshari, Graham Emil Leigh
- 2017 32nd Annual ACM/IEEE Symposium on Logic in…
- 2017

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)