Abstract

Arbitrary public announcement logic (APAL) is a logic of change of knowledge with modalities representing quantification over announcements. We present two rather different versions of APAL wherein this quantification is restricted to formulas only containing a subset of all propositional variables: FSAPAL and SCAPAL; and another version quantifying over all announcements implied by or implying a given formula: IPAL. We then determine the relative expressivity of these logics and APAL. The IPAL quantifier promises to provide a novel perspective on substructural implication as dynamic consequence.

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