From IF to BI: a tale of dependence and separation

We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and V¨a¨an¨anen, and their compositional semantics 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 rˆole, 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 t...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Samson Abramsky, Jouko A. Väänänen
• Keywords: CORR 2011, Education, Intuitionistic Implication, Logics, Semantics