Robert Craven

This paper studies some normative relations that hold between actions, their preconditions and their effects, with particular attention to connecting what are often called ‘ought to be’ norms with ‘ought to do’ norms. We use a formal model based on a form of transition system called a ‘coloured labelled transition system’ (coloured LTS) introduced in a series of papers by Sergot and Craven. Those works have variously presented a formalism (an ‘action language’) nC+ for defining and computing with a (coloured) LTS, and another, separate formalism, a modal language interpreted on a (coloured) LTS used to express its properties. We consolidate these two strands. Instead of specifying the obligatory and prohibited states and transitions as part of the construction of a coloured LTS as in nC+, we represent norms in the modal language and use those to construct a coloured LTS from a given regular (uncoloured) one. We also show how connections between norms on states and norms on transitions previously treated as fixed constraints of a coloured LTS can instead be defined within the modal language used for representing norms.

The action language C+ of Giunchiglia, Lee, Lifschitz, McCain and Turner is a high-level, logical formalism for the representation of domains involving action and change. However, one cannot directly express relationships which hold between states more than one time-step distant, or even say that one action determines another at the next time. We present C+timed, a generalization of C+ which removes these limitations. As for C+, translations to the language of causal theories are given. We also define a new kind of transition system called a ‘run system’ to provide a graphical semantics. Finally, we show how domains involving prohibition and permission can be modelled, by incorporating the ideas of another extension of C+