Generalizing Problem Reduction: A Logical Analysis

Abstract

Froblcm reduction is the name given to the problem-solving paradigm in which the problem solver manages a network of representing its intentions, repeatedly reducing tasks to subtasks and coordinating their execution. This idea needs a lot of generalization for it to be able to handle a realistic range of problems. Even after the model of time is made more realistic (to handle continuity and branching), issues remain regarding what it means to have a task or a subtask, how a task can succeed or fail, whether a task is feasible. A profitable way to study these issues is to attempt to add axioms about tasks to a first-order temporal logic. The result sheds light on what sorts of generalizations of task networks are needed.