Multi-modal systems of restricted depth (2008)
They are presented as extensions of the classical propositional calculus, the hierarchy of deductive systems SMM – n with n> 1. SMM – n is the multi – modal system of depth – n. The SMM – 1 system is the classic propositional calculation. The SMM– (n + 1) system can be seen as the result of applying the rule of need, associated with reasoners with sufficient reasoning ability, once to the SMM – n system theorems. The SMM system results from the meeting of the hierarchy systems, and can be seen as the multi-modal Km system of logic with restrictions. SMM-n systems are characterized with a Kripke-style semantics, in which the length of the possible world chains is restricted.