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In Béziau (Log Log Philos 15:99–111, 2006) a logic $$\mathbf {Z}$$ Z was defined with the help of the modal logic $$\mathbf {S5}$$ S5 . In it, the negation operator is understood as meaning ‘it is not necessary that’. The strong soundness–completeness result for $$\mathbf {Z}$$ Z with respect to a version of Kripke semantics was also given there. Following the formulation of $$\mathbf {Z}$$ Z we...
In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar; but only partial results has been obtained also for regular logics (see [8] and [9])...
In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar; but only partial results has been obtained also for regular logics (see [8] and [9])...
Jaśkowski’s discussive logic D2 was formulated with the help of the modal logic S5 as follows (see [7, 8]): $${A \in {D_{2}}}$$ iff $${\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}$$ , where (–)• is a translation of discussive formulae from Ford into the modal language. We say that a modal logic L defines D2 iff $${{\rm D}_{2} = \{A \in {\rm For^{\rm d}} : \ulcorner\diamond{{A}^{\bullet}}\urcorner...
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