Appendix D - A Logical Basis for Praxeic Reasoning

Summary

The implication that probability theory has a praxeic role to play may appear to be an arbitrary and perhaps dubious appeal to a convenient analogy simply for purposes of posturing for credibility or enhancing intuition. However, the purpose of this appendix is to establish that the praxeic characterization arises from exactly the same kind of assumptions that underly the construction of probability theory for dealing with epistemic issues. We establish the claim that the mathematics of probability theory is the appropriate mechanism with which to characterize preference relationships between members of a multi-agent system. To facilitate this development, we will form praxeic analogies to the various epistemic concepts and present the epistemic concepts in parallel with the praxeic ones.

Probability is based on two-valued logic, i.e., Aristotelian logic. In the epistemic context, this means that an event is either true or false. For any event set A, we will say that A is true if any member of the set is true. If probability theory is to apply to praxeic considerations, it must be based on two-valued logic in that context as well. The praxeic Aristotelian analog to truth is instantiation – an action is either performed or it is not. For any set A of actions, we will say that A is instantiated if any member of the set is instantiated.

The goal of an epistemic inquiry is to ascertain truth. Analogously, the goal of a praxeic endeavour is to ascertain how to act.