Reasoning with limited computational resources (such as time or memory) is an important problem, in particular in cognitive embedded systems. Classical logic is usually considered inappropriate for this purpose as no guarantees regarding deadlines can be made. One of the more interesting approaches to address this problem is built around the concept of active logics. Although a step in the right direction, active logics still do not offer the ultimate solution. Our work is based on the assumption that Labeled Deductive Systems offer appropriate metamathematical methodology to study the problem. As a first step, we have shown that the LDS-based approach is strictly more expressive than active logics. We have also implemented a prototype automatic theorem prover for LDS-based systems.
Despite the egocentric-sounding title, this is not about myself but rather about the concept of self and how it may relate to that of meta, in the context of various considerations, including formal and informal notions of self-reference, reference in general, theories of consciousness, and the active logic approach to commonsense reasoning.
Even an "elementary" intelligence for control of the physical world will require very many kinds of knowledge and ability. Among these are ones related to perception, action, and reasoning about "near space": that region comprising one's body and the portion of space within reach of one's effectors; chief among these are individuation and categorization of objects. These in turn are made useful in part by the additional capacities to estimate category size, change one's beliefs about categories, and form new categories or revise old categories. In this position paper we point out some issues in knowledge representation that can arise with respect to the above capacities, and suggest that the framework of "active logics" (see below) may be marshaled toward solutions. We will conduct our discussion in terms of learning to understand in a semantically explicit way one's own sensorimotor system and its interactions with near-space objects. Implicit in successful grouping (categorizing) of near-space objects are individuating (grounding, numbering, and binding) them and also calibrating one's sensorimotor system. A glossary below offers brief descriptions of some of these terms.
A COMPARISON OF THE COMMONSENSE AND FIXED POINT THEORIES OF NONMONOTONICITY Dr. Frank M. Brown Department of Computer SC ience University of Kansas Lawrence Kansas ABSTRACT The mathematical fixed point theories of nonmonotonic reasoning are examined and compared to a commonsense theory of nonmonotonic reasoning which models our intuitive ability to reason about defaults. It is shown that all of the known problems of the fixed point theories are solved by the commonsense theory. The concepts of this commonsense theory do not involve mathematical fixed points, but instead are explicitly defined in a monotonic modal quantificational logic which captures the modal notion of logical truth. IINTRODUCTION A number of recent papers [McDermott & Doyle, McDermott, Moore, and Reiter] have attempted to formalize the commonsense notion of something being possible with respect to what is assumed. All these papers have been based on the mathematical theory of fixed points.
In the paper(Perlis, Purang, Andersen 1998) we outlined a general approach to automated dialogue, based on a variety of considerations including ideas from cognitive psychology. The resulting thesis there was that meta-dialogue can play a fundamental role in making effective dialogue possible, and that a proper treatment of time in turn plays a fundamental role in making effective meta-dialogue possible. Our work since then has aimed at testing the promise of that approach.