We present a framework for decision making under uncertainty
where the priorities of the alternatives
can depend on the situation at hand.
We design a logic-programming language, DOP-CLP,
that allows the user to specify the static priority of each
rule and to declare, dynamically, all the alternatives for the
decisions that have to be made. In this paper we focus on a
semantics that reflects all possible
situations in which the decision maker takes the most rational,
possibly probabilistic, decisions given the circumstances.
Our model theory, which is a generalization of classical logic-programming
model theory,
captures uncertainty at the level of total
Herbrand interpretations.
DOP-CLPs can be used to formulate game theoretic concepts.
E.g., we prove that there exists a mapping of strategic games to DOP-CLPs
such that a one-to-one mapping is established between the mixed
strategy Nash equilibria of the former and
the stable models of the latter.