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pro vyhledávání: '"Leigh, Graham E."'
We develop the theory of illfounded and cyclic proof systems in the context of the modal $\mu$-calculus. A fine analysis of provability and admissibility bridges the finitary, cyclic and illfounded notions of proof for this logic and re-enforces the
Externí odkaz:
http://arxiv.org/abs/2401.01096
Autor:
Leigh, Graham E., Wehr, Dominik
We consider cyclic proof systems in which derivations are graphs rather than trees. Such systems typically come with a condition that isolates which derivations are admitted as 'proofs', known as a the soundness condition. This soundness condition fr
Externí odkaz:
http://arxiv.org/abs/2301.07544
This paper presents a novel proof of the conservativity of the intuitionistic theory of strictly positive fixpoints, $\widehat{\mathrm{ID}}{}_{1}^{\mathrm{i}}$, over Heyting arithmetic (HA), originally proved in full generality by Arai (2011). The pr
Externí odkaz:
http://arxiv.org/abs/2110.08240
Autor:
Granberg Olsson, Mattias1 (AUTHOR) mattias.granberg.olsson@gu.se, Leigh, Graham E.1 (AUTHOR)
Publikováno v:
Archive for Mathematical Logic. Feb2024, Vol. 63 Issue 1/2, p61-87. 27p.
Autor:
Gorbow, Paul K., Leigh, Graham E.
We develop an untyped framework for the multiverse of set theory. $\mathsf{ZF}$ is extended with semantically motivated axioms utilizing the new symbols $\mathsf{Uni}(\mathcal{U})$ and $\mathsf{Mod}(\mathcal{U, \sigma})$, expressing that $\mathcal{U}
Externí odkaz:
http://arxiv.org/abs/2005.11087
Autor:
Leigh, Graham E., Wehr, Dominik
Publikováno v:
In Annals of Pure and Applied Logic December 2024 175(10)
Publikováno v:
EPTCS 213, 2016, pp. 1-10
We present a structural representation of the Herbrand content of LK-proofs with cuts of complexity prenex Sigma-2/Pi-2. The representation takes the form of a typed non-deterministic tree grammar of order 2 which generates a finite language of first
Externí odkaz:
http://arxiv.org/abs/1606.06384
Akademický článek
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Autor:
Leigh, Graham E.
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
Externí odkaz:
http://arxiv.org/abs/1308.0168
Publikováno v:
Logic Journal of the IGPL; Feb2024, Vol. 32 Issue 1, p1-34, 34p