New Upper Bounds for Satissability in Modal Logics { the Case-study of Modal K
نویسندگان
چکیده
Traditional results in modal logics state that, if a formula ' is satissable in K (K-satissable), then it has a Kripke model M s.t. jjM jj 2 j'j , jjM jj being the number of states of M and j'j the number of subformulas of '. A further result states a bound of jjM jj j'j d , d being the modal depth of '. In more recent papers, a decision procedure has been proposed which branches on the truth values of the distinct \atoms" { i.e., subformulas which cannot be decomposed propositionally. Following this approach, we propose here two new bounds based on the number of distinct atoms jjAtoms(')jj: rst, a K-satissable formula ' has a Kripke model T s.t. jjT jj jjAtoms(')jj d ; second, the K-satissability of ' can be checked in O(j'j 2 jjAtoms(')jj) time and O(j'j) writable memory. Notice that jjAtoms(')jj j'j and j'j is up to 2 O(jjAtoms(')jj) .
منابع مشابه
Istituto per La Ricerca Scientifica E Tecnologica New Upper Bounds for Satisfiability in Modal Logics { the Case-study of Modal K New Upper Bounds for Satissability in Modal Logics { the Case-study of Modal K
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