Knowledge without modality: A simplified framework for chronological ignorance

Abstract

Shoham's logic of chronological ignorance (CI) provides a formal approach for representing and reasoning about causal relationships. The utility of the formalism comes from imposing a partial order on Kripke interpretations for theories in a modal logic of temporal knowledge. In this paper we show that the use of modal logic in this context is unnecessary and that the same result can be achieved using classical logic. While semantically simpler, the classical approach is somewhat unwieldy. To overcome this problem we suggest an alternative underlying language, called asserted logic. The logic allows the convenient representation found in Shoham's approach without sacrificing the truth functional semantics and proof theory of classical logic. We demonstrate the utility of the logic by providing an equivalent nonmodal CI framework for causal theories.