Introducing Some Classical Elements of Modal Logic to the Propositional Logics of Qualitative Probabilities
Dimitar Gelev

Abstract:
Introducing Some Classical Elements of Modal Logic to the Propositional
  Logics of Qualitative Probabilities
Dimitar P. Gelev

This paper presents the construction of canonical models for a number of 
logics of qualitative probabilities by introducing a conservative infinitary 
rule into their axiomatizations. These logics include the minimal logic of 
qualitative probabilities and a new multioperator propositional logic, that 
contains qualitative probabilistic analogons of operations essential to 
propositional dynamic logic. These operations capture some basic laws for 
stochastic processes into this new logic's semantics and are given a complete
axiomatization.
The paper also presents qualitative probabilistic versions of the modal logic 
techniques of unravelling and filtration.
All the constructs and arguments in this paper are suitable to be combined 
with their counterparts for other propositional, e.g. modal logics, and can 
possibly be incorporated in proofs of completeness and decidability of logics
containing both qualitative probabilistic and other propositional operators 
for application purposes.