This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL 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 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study (...) illustrating the power of 2SDL, we examine the system DL 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. (shrink)

We introduce reactive Kripke models for intuitionistic logic and show that the reactive semantics is stronger than the ordinary semantics. We develop Beth tableaux for the reactive semantics.

This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL 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 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study (...) illustrating the power of 2SDL, we examine the system DL 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. (shrink)