 
Summary: The Basic Intuitionistic Logic of Proofs
Sergei Artemov Rosalie Iemhoff
City University of New York Institute for Discrete Mathematics and
Graduate Center Geometry E104, Technical University Vienna
365 Fifth Avenue Wiedner Hauptstrasse 810
New York, NY 10016, U.S.A. 1040, Vienna, Austria
SArtemov@gc.cuny.edu iemhoff@logic.at
February 23, 2005
Abstract
The language of the basic logic of proofs extends the usual propositional lan
guage by forming sentences of the sort x is a proof of F for any sentence F. In
this paper a complete axiomatization for the basic logic of proofs in Heyting
Arithmetic HA was found.
1 Introduction.
The classical logic of proofs LP inspired by the works by Kolmogorov [24] and GĻodel
[16, 17] was found in [3, 4] (see also surveys [6, 8, 12]). LP is a natural extension of the
classical propositional logic in a language of proofcarrying formulas. LP axiomatizes
all valid logical principles concerning propositions and proofs with a fixed sufficiently
rich set of operations. Operations of proofs in LP suffice to recover explicit provability
content in the classical modal logic by realizing modalities by appropriate proof terms.
