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Logical Approaches to the Complexity of Search Problems: Proof Complexity, Quantified Propositional Calculus, and Bounded Arithmetic
, 2005
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On the computational complexity of cutreduction
, 2009
"... Using appropriate notation systems for proofs, cutreduction can often be rendered feasible on these notations. Explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all the known results on definable functions of certain such theorie ..."
Abstract

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Using appropriate notation systems for proofs, cutreduction can often be rendered feasible on these notations. Explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all the known results on definable functions of certain such theories can be reobtained in a uniform way. 1 Introduction and Related Work Since Gentzen’s invention of the “Logik Kalkül ” LK and the proof of his “Hauptsatz ” [Gen35a, Gen35b], cutelimination has been studied in many papers on proof theory. Mints ’ invention of continuous normalisation [Min78, KMS75] isolates operational aspects of normalisation, that is, the manipulations on (in
Abstract
, 2006
"... We investigate the relation between intermediate predicate logics based on countable linear Kripke frames with constant domains and Gödel logics. We show that for any such Kripke frame there is a Gödel logic which coincides with the logic defined by this Kripke frame on constant domains and vice ver ..."
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We investigate the relation between intermediate predicate logics based on countable linear Kripke frames with constant domains and Gödel logics. We show that for any such Kripke frame there is a Gödel logic which coincides with the logic defined by this Kripke frame on constant domains and vice versa. This allows us to transfer several recent results on Gödel logics to logics based on countable linear Kripke frames with constant domains: We obtain a complete characterisation of axiomatisability of logics based on countable linear Kripke frames with constant domains. 1 Furthermore, we obtain that the total number of logics defined by countable linear Kripke frames on constant domains is countable. 1