Is Free Choice Permission Admissible in Classical Deontic Logic?

A significant part of the literature in deontic logic revolves around the discussions of puzzles and paradoxes which show that certain logical systems are not acceptable--typically, this happens with deontic KD, i.e., Standard Deontic Logic (SDL)--or which suggest that obligations and permissions should enjoy some desirable properties. One well-known puzzle is the the so-called Free Choice Permission paradox, which was originated by the following remark by von Wright in [23, p. 21]: "On an ordinary understanding of the phrase'it is permitted that', the formula'P(p q)' seems to entail'Pp Pq'. If I say to somebody'you may work or relax' I normally mean that the person addressed has my permission to work and also my permission to relax. It is up to him to choose between the two alternatives." Usually, this intuition is formalised by the following schema: P(p q) (Pp Pq) (FCP) Many problems have been discussed in the literature around FCP: for a comprehensive overview, discussion, and some solutions, see [11, 14, 20]. Three basic difficulties can be identified, among the others [11, p. 43]: - Problem 1: Permission Explosion Problem - "That if anything is permissible, then everything is, and thus it would also be a theorem that nothing is obligatory," [20], for example "If you may order a soup, then it is not true that you ought to pay the bill" [6];