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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)
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)
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)
Some remarks on extending and interpreting theories with a partial predicate for truth. Much of the literature on theories of truth can be traced back to Kripke's seminal paper, Outline of a theory of truth. Kripke's aim was to provide an account of self-applicable truth which avoided the inconsistencies highlighted by Tarski's theorem. This involved(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)
In this article we present a number of axiomatic theories of truth which are conservative extensions of arithmetic. We isolate a set of ten natural principles of truth and prove that every consistent permutation of them forms a theory conservative over Peano arithmetic. It seems that each axiomatic theory of truth that occurs in the literature is equipped(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)