Quantified modal logics of positive rational numbers and some related systems.
Giovanna Corsi · Notre Dame Journal of Formal Logic · 1993
The quantified modal logics QK4.3.D.X and QS4.3 are shown to be characterized by the Kripke models based on the extended frames with nested domains >, respectively, i.e., the set of positive rational numbers ordered by the numerical relation 'less than' ('less than or equal to').Moreover, for each n > 1, the logics C Π .QK4.3.D.X (C Π .QS4.3) are shown to be characterized by the Kripke models based on (reflexive) towers of rank at most n and with nested domains.Other quantified extensions of QK4.3 are considered and proved Kripke complete as well. / The logics QK4.3, QK4.3.D.X and QS4.3Let £ be a first-order modal language, _L G ±.QK4.3 is the quantified modal calculus obtained by adding to the normal propositional modal logic K the following axioms and rules: 4 Dα->DDα 3 D(Dα Λα->j3)vD(Dj3Λj3->cO