Propositional logics of dependence (Q278765)

The paper studies propositional downward closed team logic (\(\mathsf{PT}_0\)), propositional dependence logic (\(\mathsf{PD}\)), propositional dependence logic with intuitionistic disjunction (\(\mathsf{PD}^\lor\)), propositional intuitionistic dependence logic (\(\mathsf{PID}\)), and propositional inquisitive logic (\(\mathsf{InqL}\)) are studied.NEWLINENEWLINE\(\mathsf{PD}\) and \(\mathsf{PID}\) are the propositional counterparts of known first-order logics of dependence. The sound and strongly complete deductive systems for logics \(\mathsf{PD}\), \(\mathsf{PD}^\lor\) and \(\mathsf{PID}\) have been constructed.NEWLINENEWLINEIt is proven that all of the logics \(\mathsf{PT}_0\), \(\mathsf{PD}\), \(\mathsf{PD}^\lor\), \(\mathsf{InqL}\) and \(\mathsf{PID}\) are expressively complete, expressively equivalent and compact.