Knowing that, knowing what, and public communication: public announcement logic with Kv operators

Abstract

In his seminal work [Pla89], Plaza proposed the public announcement logic (PAL), which is considered as the pilot logic in the field of dynamic epistemic logic. In the same paper, Plaza also introduced an interesting “know-value ” op-erator Kv and listed a few valid formulas of PAL+Kv. However, it is unknown that whether these formulas, on top of the axioms for PAL, completely axioma-tize PAL+Kv. In this paper, we first gave a negative answer to this open question. Moreover, we generalize the Kv operator and show that in the setting of PAL, re-placing the Kv operator with its generalized version does not increase the expres-sive power of the resulting logic. This suggests that we can simply use the more flexible generalization instead of the original PAL+Kv. As the main result, we give a complete proof system for PAL plus the generalized operator based on a com-plete axiomatization of epistemic loic with the same operator in the single-agent setting. Key words: public announcement logic, know-value operator, modal logic, multi-agent system 1