A computer program capable of acting intelligently in the world must have a general representation of the world in terms of which its inputs are interpreted. Designing such a program requires commitments about what knowledge is and how it is obtained. Thus, some of the major traditional problems of philosophy arise in artificial intelligence. More specifically, we want a computer program that decides what to do by inferring in a formal language that a certain strategy will achieve its assigned goal. This requires formalizing concepts of causality, ability, and knowledge. Such formalisms are also considered in philosophical logic. The first part of the paper begins with a philosophical point of view that seems to arise naturally once we take seriously the idea of actually making an intelligent machine. We go on to the notions of metaphysically and epistemo-logically adequate representations of the world and then to an explanation of can, causes, and knows in terms of a representation of the world by a system of interacting automata. A proposed resolution of the problem of freewill in a deterministic universe and of counterfactual conditional sentences is presented. The second part is mainly concerned with formalisms within which it can be proved that a strategy will achieve a goal. Concepts of situation, fluent, future operator, action, strategy, result of a strategy and knowledge are formalized. A method is given of constructing a sentence of first-order logic which will be true in all models of certain axioms if and only if a certain strategy will achieve a certain goal. The formalism of this paper represents an advance over McCarthy (1963) and Green (1969) in that it permits proof of the correctness of strategies that contain loops and strategies that involve the acquisition of knowledge; and it is also somewhat more concise. The third part discusses open problems in extending the formalism of part 2. The fourth part is a review of work in philosophical logic in relation to problems of artificial intelligence and a discussion of previous efforts to program ‘general intelligence’ from the point of view of this paper.

/pdf/some-philosophical-problems-from-the-standpoint-of-6oprg9bbyt.pdf

Some philosophical problems from the standpoint of artificial intelligence

Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truths which aresynthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill-founded. One effect of abandoning them is, as we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism.

Two Dogmas of Empiricism

The logical theory which is called the calculus of (binary) relations, and which will constitute the subject of this paper, has had a strange and rather capricious line of historical development. Although some scattered remarks regarding the concept of relations are to be found already in the writings of medieval logicians, it is only within the last hundred years that this topic has become the subject of systematic investigation. The first beginnings of the contemporary theory of relations are to be found in the writings of A. De Morgan, who carried out extensive investigations in this domain in the fifties of the Nineteenth Century. De Morgan clearly realized the inadequacy of traditional logic for the expression and justification, not merely of the more intricate arguments of mathematics and the sciences, but even of simple arguments occurring in every-day life; witness his famous aphorism, that all the logic of Aristotle does not permit us, from the fact that a horse is an animal, to conclude that the head of a horse is the head of an animal. In his effort to break the bonds of traditional logic and to expand the limits of logical inquiry, he directed his attention to the general concept of relations and fully recognized its significance. Nevertheless, De Morgan cannot be regarded as the creator of the modern theory of relations, since he did not possess an adequate apparatus for treating the subject in which he was interested, and was apparently unable to create such an apparatus. His investigations on relations show a lack of clarity and rigor which perhaps accounts for the neglect into which they fell in the following years.

/pdf/on-the-calculus-of-relations-soz0roobt6.pdf

On the Calculus of Relations

Role structures in small populations are given operational meaning as algebras generated from the sociometric blockmodels of Part I by Boolean multiplication (matrix multiplication employing binary arithmetic). Many different sociometric structures can yield the same algebraic multiplication table, which captures a different level of social structure. Elements of the algebras are interpreted concretely as compound roles, and interlock among these roles is studied through investigation of their algebraic properties (equations and inclusions). Similarities and differences among algebras from six case studies are explored by means of homomorphisms as well as by multidimensional scaling on a derivative numerical distance measure. Results for particular populations, including reliability and stability tests, are summarized through simple target tables reporting aggregations of more complicated role structures.

/pdf/social-structure-from-multiple-networks-ii-role-structures-3wyx0d5xxx.pdf

Social Structure from Multiple Networks. II. Role Structures

Introduction. Recent developments of symbolic logic have considerable importance for mathematics both with respect to its philosophy and practice. That mathematicians generally are oblivious to the importance of this work of Gödel, Church, Turing, Kleene, Rosser and others as it affects the subject of their own interest is in part due to the forbidding, diverse and alien formalisms in which this work is embodied. Yet, without such formalism, this pioneering work would lose most of its cogency. But apart from the question of importance, these formalisms bring to mathematics a new and precise mathematical concept, that of the general recursive function of Hërbrand-GödelKleene, or its proved equivalents in the developments of Church and Turing. It is the purpose of this lecture to demonstrate by example that this concept admits of development into a mathematical theory much as the group concept has been developed into a theory of groups. Moreover, that stripped of its formalism, such a theory admits of an intuitive development which can be followed, if not indeed pursued, by a mathematician, layman though he be in this formal field. It is this intuitive development of a very limited portion of a sub-theory of the hoped for general theory that we present in this lecture. We must emphasize that, with a few exceptions explicitly so noted, we have obtained formal proofs of all the consequently mathematical theorems here developed informally. Yet the real mathematics involved must lie in the informal development. For in every instance the informal "proof" was first obtained; and once gotten, transforming it into the formal proof turned out to be a routine chore. We shall not here reproduce the formal definition of recursive function of positive integers. A simple example of such a function is an

https://www.ams.org/bull/1944-50-05/S0002-9904-1944-08111-1/S0002-9904-1944-08111-1.pdf

Recursively enumerable sets of positive integers and their decision problems

Modern interest in modal logic began with this seminal work by the American C.I. Lewis. As well as developing a theory of strict implication based on criticism of Russell and Whitebread's concept of implication, it contains historical information on the history and application of algebra to developments in symbolic logic.

Henry M. Sheffer

Papers

A Survey of Symbolic Logic.