After a brief orientation to logic-based (computational) cognitive modeling, the necessary preliminaries are discussed in this chapter (e.g., what a logic is, and what it is for one to “capture" human cognition are explained). Three “microworlds" or domains that all readers should be comfortably familiar with (natural numbers and arithmetic; everyday vehicles; and residential schools, e.g., colleges and universities) are introduced, in order to facilitate exposition in the chapter. Then the ever-expanding universe U of formal logics, with an emphasis on three categories therein, is given: deductive logics having no provision for directly modeling cognitive states; nondeductive logics suitable for modeling rational belief through time without machinery to directly model cognitive states such as believes and knows; and finally, nondeductive logics that enable the kind of direct modeling of cognitive states absent from the first two types of logic. Then, there follows a focus spcifically on two important aspects of human-level cognition to be modeled in logic-based fashion: the processing of quantification, and defeasible (or nonmonotonic) reasoning. Finally, a brief evaluation of logic-based cognitive modeling is provided, together with some comparison to other approaches to cognitive modeling, and the future of the discipline is considered. The chapter presupposes nothing more than high-school mathematics of the standard sort on the part of the reader.

What is Knowledge Representation and Reasoning?

What is knowledge representation and reasoning (KR&R)? Alas, a thorough account would require a book, or at least a dedicated, full-length paper, but here we shall have to make do with something simpler. Since most readers are likely to have an intuitive grasp of the essence of KR&R, our simple account should suffice. The interesting thing is that this simple account itself makes reference to some of the foundational distinctions in the field of philosophy. These distinctions also play a central role in artificial intelligence (AI) and computer science.

To begin with, the first distinction in KR&R is that we identify knowledge with knowledge that such-and-such holds (possibly to a degree), rather than knowing how. If you ask an expert tennis player how he manages to serve a ball at 130 miles per hour on his first serve, and then serve a safer, topspin serve on his second should the first be out, you may well receive a confession that, if truth be told, this athlete can't really tell you. He just does it; he does something he has been doing since his youth. Yet, there is no denying that he knows how to serve. In contrast, the knowledge in KR&R must be expressible in declarative statements. For example, our tennis player knows that if his first serve lands outside the service box, it's not in play. He thus knows a proposition, conditional in form.

Introduction

This paper introduces an approach to, rather than the final results of, sustained research and development in the area of roboethics described herein. Encapsulated, the approach is to engineer ethically correct robots by giving them the capacity to reason over, rather than merely in, logical systems (where logical systems are used to formalize such things as ethical codes of conduct for warfighting robots). This is to be accomplished by taking seriously Piaget's position that sophisticated human thinking exceeds even abstract processes carried out in a logical system, and by exploiting category theory to render in rigorous form, suitable for mechanization, structure-preserving mappings that Bringsjord, an avowed Piagetian, sees to be central in rigorous and rational human ethical decision making.

We assume our readers to be at least somewhat familiar with elementary classical logic, but we review basic category theory and categorical treatment of deductive systems. Introductory coverage of the former subject can be found in Barwise and Etchemendy [1] and Ebbinghaus, Flum, and Thomas [2]; deeper coverage of the latter, offered from a suitably computational perspective, is provided in Barr and Wells [3]. Additional references are of course provided in the course of this paper.

Preliminaries

A category consists of a collection of objects and a collection of arrows, or morphisms. Associated with each arrow f are a domain (or source), denoted dom f, and a codomain (or target), denoted cod f.