@article {SL87:ProbModLog,
   AUTHOR = {Fattorosi-Barnaba, M. and Amati, G.},
    TITLE = {Modal operators with probabilistic interpretations. {I}},
  JOURNAL = {Studia Logica},
 FJOURNAL = {Polska Akademia Nauk. Instytut Filozofii i Socjologii. Studia
             Logica},
   VOLUME = {46},
     YEAR = {1987},
   NUMBER = {4},
    PAGES = {383--393},
     ISSN = {0039-3215},
ABSTRACT  = {We present a class of normal modal calculi $P_FD$,
                 whose syntax is endowed with operators $M_r$ (and their
                 dual ones, $L_r$), one for each $r\in [0,1]$: if $a$ is
                 a sentence, $M_r a$ is to be read ``the probability
                 that $a$ is true is strictly greater than $r$'' and to
                 be evaluated as true or false in every world of a
                 $F$-restricted probabilistic kripkean model. Every such
                 a model is a kripkean model, enriched by a family of
                 regular probability evaluations with range in a fixed
                 finite subset $F$ of $[0,1]$: there is one such a
                 function for every world $w$, $PF(w,-)$, and this
                 allows to evaluate $M_r a$ as true in the world $w$ iff
                 $PF(w,a)>r$. In particular, $M_0 a$ as true in the
                 world $w$ iff $PF(w,a)>0$ iff $a$ is possible in $w$
                 with respect to the underlying kripkean model. For
                 every fixed $F$ as before, suitable axioms and rules
                 are displayed, so that the resulting system $P_FD$is
                 complete and compact with respect to the class of all
                 the $F$-restricted probabilistic kripkean models.
	     }