Forgetting complex propositions

Abstract

This paper uses possible-world semantics to model the changes that may occur in an agent's knowledge as she loses information. This builds on previous work in which the agent may forget the truth-value of an atomic proposition, to a more general case where she may forget the truth-value of a propositional formula. The generalization poses some challenges, since in order to forget whether a complex proposition π is the case, the agent must also lose information about the propositional atoms that appear in it, and there is no unambiguous way to go about this.We resolve this situation by considering expressions of the form [ ‡π]ϕ, which quantify over all possible (but 'minimal') ways of forgetting whether π. Propositional atoms are modified non-deterministically, although uniformly, in all possible worlds. We then represent this within action model logic in order to give a sound and complete axiomatization for a logic with knowledge and forgetting. Finally, some variants are discussed, such as when an agent forgets π (rather than forgets whether π) and when the modification of atomic facts is done non-uniformly throughout the model.

C2PDLS: A Combination of Combinatory and Converse PDL with Substitutions

“…This approach is generalized by van Ditmarsch et al [23]. In a different direction, Fernandez-Duque et al [13] introduced an epistemic logic allowing to forget information. These logics target some particular classes of graphs which limit their use for graph transformations in general.…”