In this paper, we present several extensions of epistemic logic with update operators modelling public information change. Next to the well-known public announcement operators, we also study public substitution operators. We prove many of the results regarding expressivity and completeness using so-called reduction axioms. We develop a general method for using reduction axioms and apply it to the logics at hand.

The purpose of the paper is to present a logical framework that allow to formalize a kind of prima facie duties, defeasible conditional duties, indefeasible conditional duties and actual (indefeasible) duties, as well as to show their logical interconnections.