Studia Logica

, Volume 62, Issue 1, pp 49–75

Predicate Logics on Display

  • Heinrich Wansing

DOI: 10.1023/A:1005125717300

Cite this article as:
Wansing, H. Studia Logica (1999) 62: 49. doi:10.1023/A:1005125717300


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 Behthem'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.

predicate logic quantifiers display logic modal logic 

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Heinrich Wansing

There are no affiliations available

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