Reasoned Assumptions and Rational Psychology

Logical epistemology unduly sways theories of thinking that formulate problems of nonmonotonic reasoning as issues of nondeductive operations on logically phrased beliefs, because the fundamental concepts underlying such reasoning have little to do with logic or belief. These formulations make the resulting theories inappropriately special and hide the characteristic structures of nonmonotonic reasoning amid many unrelated structures. We present a more direct mathematical development of nonmonotonic reasoning free of extraneous logical and epistemological assumptions, and argue that the insights gained in this way exemplify the benefits obtained by approaching psychology as a subject for mathematical investigation through the discipline of rational psychology. For Joseph A. Schatz, teacher and friend 1. Reasoning, logic, and psychology Nonmonotonic reasoning, the study of making and revising assumptions in a reasoned or principled way, needs little introduction in artificial intelligence today thanks to years of extensive exposition, analysis, and application. In spite of an admirable history of progress, however, the subject stands in need of some rethinking and redirection as the strengths and limitations of the accepted theories become clearer. This paper seeks to further this rethinking and redirection by presenting the foundations of nonmonotonic reasoning through a mathematical and philosophical approach closer to the concepts and methods of modern physics and rational mechanics than to the standard formulations of artificial intelligence. I believe these concepts and methods, which seek to find the most appropriate means for describing and understanding psychological structure and behavior, will prove productive for rethinking other parts of artificial intelligence as well. This introduction thus attempts to set out some of the motivations for this rethinking and to motivate the methods underlying the formal treatment. This paper celebrates the twentieth volume of Fundamenta Informaticae. The year of its writing (1993) also marks the twentieth anniversary of my involvement in the field of artificial intelligence; the fifteenth anniversary of the appearance of the original nonmonotonic logic (McDermott & Doyle, 1980); and the tenth and fifth anniversaries (respectively) of the appearance of my mathematical monograph (Doyle, 1983c) and my foundational monograph (Doyle, 1988), from which the present paper derives and upon which it improves, and looking back from these anniversaries has led me to include some personal interpretations of their history in this introduction. 1.1 Nonmonotonic reasoning Though the reader will likely find the notion familiar, a few words about the term “nonmonotonic reasoning” should aid in understanding the discussion to follow.