Section: New Results

Combinations of classical and intuitionistic logic

Participant : Dale Miller.

Chuck Liang and Miller have been studying the question of how one can mix intuitionistic and classical logic into a single logic. The initial motivation for considering this problem arose from the concerns raised by the ProofCert project of how best to deal with both classical and intuitionistic logic and their associated proof evidence. Will there need to be two different kinds of checkers and two different kinds of libraries for these two different kinds of logics? Will we be able to mix theorems and proofs in one logic with those in the second logic in rich and useful ways?

One way we have considered answering this question is to actually consider a third logic that combines these other two logics. Our work on such combinations is reported in [16] , where a thorough analysis of the semantics and proof theory of such a combination is provides, and in [24] , where significant examples of the computational aspects of proofs are explored in detail.