Reasoning about knowledge of unawareness

Abstract

Awareness has been shown to be a useful addition to standard epistemic logic. However, standard propositional logics for knowledge and awareness cannot express the fact that an agent knows that there are facts of which he is unaware without there being an explicit fact that the agent knows he is unaware of. We extend Fagin and Halpern's logic of general awareness to a logic that allows quantification over variables, so that there is a formula in the language that says "an agent explicitly knows that there exists a fact of which he is unaware." Moreover, that formula can be true without the agent explicitly knowing that he is unaware of any particular formula. We provide a sound and complete axiomatization of the logic. Finally, we show that the validity problem for the logic is recursively enumerable, but not decidable.

On the Interactions of Awareness and Certainty

“…Particularly, this allows an agent to know another agent knows something that the first agent does not. This expressive ability is also considered by Halpern and Rego [9].…”

Semantic Information and the Trivialization of Logic: Floridi on the Scandal of Deduction

“…According to the standard logic of knowledge (epistemic logic) and belief (doxastic logic), as well as to the more recent attempts to axiomatize the "logic of being informed" (information logic), if an agent a knows (or believes, or is informed) that a sentence ϕ is true, and ψ is a logical consequence of ϕ, then a is supposed to know (or believe, or be informed) also that B is true. (For a survey on epistemic and doxastic logic see [32,33]; for information logic, or "the logic of being informed", see [34,35].) This is often described as paradoxical and labelled as "the problem of logical omniscience".…”

Avoiding Shared Clocks in Networks of Timed Automata

“…This is the aim of epistemic logics [HFMV95], which have been extended to real-time in [WL04,Dim09]. Our notion of contextual TTS also resembles the technique of partitioning states based on observation, used in timed games with partial observability [BDMP03,DLLN09].…”