Qualitative probability as an intensional logic (original) (raw)

The main aim of this paper is to study the logic of a binary sentential operator 'z=', with the intended meaning 'is at least as probable as'. The object language will be simple; to an ordinary language for truth-functional connectives we add '&' as the only intensional operator. Our choice of axioms is heavily dependent of a theorem due to Kraft et al. [8], which states necessary and sufficient conditions for an ordering of the elements of a finite subset algebra to be compatible with some probability measure. Following a construction due to Segerberg [ 121, we show that these conditions can be translated into our language.