 
Summary: From IF to BI
A Tale of Dependence and Separation
Samson Abramsky
Oxford University Computing Laboratory
Jouko Všašanšanen
ILLC Amsterdam
Abstract. We take a fresh look at the logics of informational dependence and
independence of Hintikka and Sandu and Všašanšanen, and their compositional se
mantics due to Hodges. We show how Hodges' semantics can be seen as a special
case of a general construction, which provides a context for a useful completeness
theorem with respect to a wider class of models. We shed some new light on each
aspect of the logic. We show that the natural propositional logic carried by the
semantics is the logic of Bunched Implications due to Pym and O'Hearn, which
combines intuitionistic and multiplicative connectives. This introduces several new
connectives not previously considered in logics of informational dependence, but
which we show play a very natural r^ole, most notably intuitionistic implication. As
regards the quantifiers, we show that their interpretation in the Hodges semantics is
forced, in that they are the image under the general construction of the usual Tarski
semantics; this implies that they are adjoints to substitution, and hence uniquely
determined. As for the dependence predicate, we show that this is definable from a
