On the Role of Postconditions in Dynamic First-Order Epistemic Logic

Dynamic Epistemic Logic (DEL) is a logic that models information change in a multi-agent setting through the use of action models with pre- and post-conditions. In a recent work, DEL has been extended to first-order epistemic logic (DFOEL), with a proof that the resulting Epistemic Planning Problem is decidable, as long as action models pre- and post-conditions are non-modal and the first-order domain is finite. Our contribution highlights the role post-conditions have in DFOEL. We show that the Epistemic Planning Problem with possibly infinite first-order domains is undecidable if the non-modal event post-conditions may contain first-order quantifiers, while, on the contrary, the problem becomes decidable when event post-conditions are quantifier-free. The latter result is non-trivial and makes an extensive use of automatic structures.