Step-logic: reasoning situated in time

Title of Dissertation: Step-logic: Reasoning Situated in Time Author: Jennifer J. Elgot-Drapkin, Doctor of Philosophy, 1988 Dissertation directed by: Donald Perlis, Associate Professor, Department of Computer Science The world in which a commonsense reasoning agent reasons, that is, the everyday world, is continually changing. These changes occur as the agent proceeds, and must be taken into account as the agent reasons. An often overlooked, but extremely important, change that occurs is simply the passage of time as the agent reasons. A commonsense reasoner is frequently limited in the amount of time it has to reason. Conclusions that may be logically (or otherwise) entailed by the agent’s information take time to be derived. But time spent in such derivations is concurrent with changes in the world. This limitation must be recognized by the reasoner himself; that is, the agent should be able to reason about its ongoing reasoning efforts themselves. To do this, the agent’s reasoning must be ‘‘situated’’ in a temporal environment. The problem that I address is that of defining a formalism in which the on-going process of deduction itself is part of that very same reasoning. This involves focusing on individual deductive steps, rather than the collection of all conclusions ever reached. This has led to the formulation of step (or situated) logic, an approach to reasoning in which the formalism has a kind of real-time self-reference that affects the course of deduction itself. Such a notion of logic deviates in a crucial way from traditional formal deductive mechanisms, for the proof process becomes part of the available information used in forming proofs. A precise characterization of step-logic is given, with details of two particular step-logics. Two commonsense reasoning problems, the Brother problem and the Three-wise-men problem, are modelled using step-logic, providing real-time formal solutions to these commonsense reasoning problems. These solutions were then implemented on an IBM PC-AT. It appears that step-logic is a promising formalism for modelling the fact that reasoning takes time. Contradictions can arise and be subsequently resolved within the logic itself, permitting a genuinely computational solution to certain types of default reasoning. STEP-LOGIC: Reasoning Situated in Time by Jennifer J. Elgot-Drapkin Dissertation submitted to the Faculty of the Graduate School of the University of Maryland in partial fulfillment of the requirements for the degree of Doctor of Philosophy 1988