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A CONSTRUCTIVE INTERPRETATION OF THE LOGICAL CONSTANTS

Part of: Proof theory and constructive mathematics

Published online by Cambridge University Press:  02 October 2025

MOHAMMAD ARDESHIR  and
WIM RUITENBURG
MOHAMMAD ARDESHIR
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES SHARIF UNIVERSITY OF TECHNOLOGY P.O. BOX 11365-9415 TEHRAN, IRAN E-mail: mardeshir@sharif.edu
WIM RUITENBURG*
Affiliation:
DEPARTMENT OF MATHEMATICAL AND STATISTICAL SCIENCES MARQUETTE UNIVERSITY P.O. BOX 1881 MILWAUKEE, WI 53201 USA
*
E-mail: wim.ruitenburg@marquette.edu
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Abstract

Heyting’s intuitionistic predicate logic describes very general regularities observed in constructive mathematics. The intended meaning of the logical constants is clarified through Heyting’s proof interpretation. A re-evaluation of proof interpretation and predicate logic leads to the new constructive Basic logic properly contained in intuitionistic logic. We develop logic and interpretation simultaneously by an axiomatic approach. Basic logic appears to be complete. A brief historical overview shows that our insights are not all new.

Keywords

constructive logicproof interpretationintuitionistic logic

MSC classification

Primary: 03F03: Proof theory, general 03F55: Intuitionistic mathematics 03F65: Other constructive mathematics

Information

Type
Article
Information
Bulletin of Symbolic Logic , Volume 31 , Issue 2 , June 2025 , pp. 288 - 318
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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