Definition. Decision properties [ltp-000X]

A decision property (called strong monitorable by Amjad et al.) is a property for which both confirmation and refutation only require a finite prefix. In other words, decision properties are the intersection of a safety and guarantee property. This makes decision properties the clopen sets in our topology. A simple characterisation from topology is that P is a decision property iff \overline {P}=\underline {P}.