[FOM] Combining classical and intuitionistic features in one logic

[mail@sakharov.net]

Dear FOM Members,
I has been curious about combining the 'best' of classical and intuitionistic logics in one intermediate logic. On one hand, it would be nice to have classical models based on truth tables for the propositional fragment. On the other hand, it would be nice to have the disjunction and existence properties holding for at least some other syntactically-defined fragment. Unfortunately, I was not able (even after checking with few colleagues) to find any work aiming at blending classical and intuitionistic features in one logic. I ended up with my own investigation:
http://www.mathpreprints.com/math/Preprint/asakharov/20040206/3/
but the question remains.

Perhaps, somebody can point to some works of the kind, or have an argument why this combination should not be attempted, or have an argument that some other features should be considered instead.
Alex Sakharov

PS In case someone reads my investigation, I believe I have a proof for the completeness conjecture now.