Abstract
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.
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Uridia, L., Walther, D. (2011). An Epistemic Logic with Hypotheses. In: van Ditmarsch, H., Lang, J., Ju, S. (eds) Logic, Rationality, and Interaction. LORI 2011. Lecture Notes in Computer Science(), vol 6953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24130-7_21
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DOI: https://doi.org/10.1007/978-3-642-24130-7_21
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