An epistemic logic with hypotheses

• Authors: Levan Uridia;Dirk Walther
• Venue: LORI'11 Proceedings of the Third international conference on Logic, rationality, and interaction
• Year: 2011

We introduce a variant of the standard epistemic logic S5 for reasoning about knowledge under hypotheses or background assumptions. The modal operator of necessity expressing what is known is parameterised with a hypothesis. The operator can be described as relative necessity, a notion already used by Chellas to describe conditionality. In fact, the parameterised box resembles a conditional operator and it turns out that our logic is a variant of Chellas' Conditional Logic. We present an axiomatisation of the logic and show that it bears the same expressivity and computational complexity as S5. Then we consider the extension of our logic with operators for distributed knowledge and show how it can be used to represent knowledge of agents whose epistemic capacity corresponds to any system between S4 and S5.