Sequences, Obligations, and the Contrary-to-Duty Paradox

In order to provide an implemented language of deontic concepts on complex actions for the purposes of social simulation, we consider the logical representation of obligations, sequences of actions, and the Contrary to Duty (CTD) Paradox. We show that approaches which follow Standard Deontic Logic (Carmo and Jones (2002)) or Dynamic Deontic Logic (Khosla and Maibaum (1987) and Meyer (1988)) encounter problems with obligations, sequences, and CTDs. In particular, it is crucial to differentiate sequences of obligations from obligations on sequences and to consider contract change over time. Contra Meyer (1988), we argue that the CTD problem cannot be reduced to a a sequence of obligations. Contra Carmo and Jones (2002), the analysis of CTDs needs explicit state change and does not need a concept of ideality. We discuss Pörn’s Criterion, which states that it is critical to a comprehensive theory of deontic reasoning to take dynamic aspects into account (Pörn (1977:ix-x)); in our view, this ought to encompass Contract State Change. In a theory of deontic specifications on actions, we show that articulated, compositional, and productive markers for violation and fulfillment are key to address the problems identified. The theorical arguments inform the Abstract Contract Calculator, a prototype implementation in Haskell of a language for reasoning with and simulating the results of deontically specified actions (Wyner (2006a) and Wyner (2006b)). With the language, one can represent and study the outcomes of multi-agent artificial normative systems as agents execute actions over time.