Hierarchical Meta-Logics - Some Proof Theoretical Results

Hierarchical meta-logics for beliefs and prov-ability: how we can do without modal logics. REFERENCES 70 Artiicial Intelligence. As argued in GS93], MR systems closely resemble the current (implementational) practice in meta-theoretic theorem proving and in the representation of propositional attitudes. In this paper we have studied the proof theoretic properties of MR systems and also their relationship with normal modal logics. Acknowledgements The research described in this paper owes a lot to the openess and sharing of ideas which exists in the Mechanized Reasoning groups in Trento and in Genoa. Alex Simpson and Vanni Criscuolo have provided useful feedback on many of the topics described in this paper. The discussions with Alessandro Cimatti, Enrico Giunchiglia, Paolo Traverso, have provided useful insights. We also thank Alessandro Agostini for his reading of earlier versions of this paper and Toby Walsh for his comments about style.