Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system]

This paper offers a two dimensional variation of Standard Deontic Logic , which we call . Using we can show that we can overcome many of the difficulties that has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so could have been presented already in the 1970s. Better late than never! As a detailed case study illustrating the power of , we examine the system of Deontic Logic of Andrew Jones and Ingmar Pörn offered in 1985 to solve the Chisholm paradox of Contrary to Duties. The critical examination is done using logics and methods available in 1985 and solutions are proposed using what was available in 1985.