Qualitative decision theory via channel theory
We recast parts of decision theory in terms of channel theory concentrating on qualitative issues. Channel theory allows one to move between model theoretic and language theoretic notions as is necessary for an adequate covering. Doing so clarifies decision theory and presents the opportunity to investigate alternative formulations. As an example, we take some of Savage's notions of decision theory and recast them within channel theory. In place of probabilities, we use a particular logic of preference. We introduce a logic for describing actions separate from the logic of preference over actions. The structures introduced by channel theory that represent the decision problems can be seen to be an abstract framework. This frame work is very accommodating to changing the nature of the decision problems to handle different aspects or theories about decision making.