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Predicate Logics on Display

Heinrich Wansing
Studia Logica: An International Journal for Symbolic Logic
Vol. 62, No. 1 (Jan., 1999), pp. 49-75
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016028
Page Count: 27
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Predicate Logics on Display
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Abstract

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Benthem's modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap's display logic by introduction rules for the existential and the universal quantifier. These rules for ∀x and ∃x are analogous to the display introduction rules for the modal operators □ and ◇ and do not themselves allow the Barcan formula or its converse to be derived. En route from the minimal 'modal' predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules.

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