Expressibility of norms in temporal logic

In this short note we address the issue of expressing norms (such as obligations and prohibitions) in temporal logic. In particular, we address the argument from [1] that norms cannot be expressed in Linear Time Temporal Logic (LTL). Recently, doubts were raised in [1] regarding suitability of LTL and other temporal logics for expressing ‘real life’ norms. We claim that the argument in [1] does not show that LTL is unsuitable for expressing norms. Instead it shows that a translation of deontic notions such as obligations and permissions into temporal logic which interprets ‘obligatory’ as ‘always true’ and ‘permitted’ as ‘eventually true’ does not work, as could be expected. However, [1] is now often cited as an argument against using temporal logic for specifying norms in general. We would like to revisit the example which is considered paradoxical when specified in LTL in [1], and show that it is possible to exactly specify the set of conditions on runs which satisfy the norms from the example using standard LTL. We assume that the reader is familiar with temporal logic, in particular with the syntax and semantics of LTL. We use U for the Until operator, G for always in the future, F for some time in the future. The example is as follows (we compress it slightly without changing the meaning, and use the same variable names for propositions): 1. collection of personal information (A) is forbidden unless authorised by the court (C) 2. The destruction of personal information collected illegally before accessing it (B) excuses the illegal collection 3. collection of medical information (D) is forbidden unless collection of personal information is permitted As pointed out in [1], this classifies possible situations as compliant and noncompliant as follows: