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Prolegomena to a Theory of Mechanized Formal Reasoning

Classics (Collection 2)

This is an informal description of my ideas about using formal logic as a tool for reasoning systems using computers. Introduction The title of this paper contains both the words'mechanized' and'theory'. I want to make the point that the ideas presented here are not only of interest to theoreticians. I believe that any theory of interest to artificial intelligence must be realizable on a computer. I will not present difficult examples.


REASONING ABOUT KNOWLEDGE AND ACTION / 473 REASONING ABOUT KNOWLEDGE AND ACTION

Classics (Collection 2)

The first section discusses the importance of having systems that understand the concept of knowledge, and how knowledge is related to action. Section 2 points out some of the special problems that are involved in reasoning about knowledge, and section $ presents a logic of knowledge based on the idea of possible worlds. Section 4 integrates this with a logic of actions and gives an example of reasoning in the combined system. Section 5 makes some concluding comments. I. Introduction One of the most important concepts an intelligent system needs to understand is the concept of knowledge.


P. J. HAYES

Classics (Collection 2)

Minsky introduced the terminology of'frames' to unify and denote a loose collection of related ideas on knowledge representation: a collection which, since the publication of his paper (Minsky, 1975) has become even looser. It is not at all clear now what frames are, or were ever intended to be. I will assume, below, that frames were put forward as a (set of ideas for the design of a) formal language for expressing knowledge, to be considered as an alternative to, for example, semantic networks or predicate calculus. At least one group have explicitly designed such a language, KRL (Bobrow/ Winograd, 1977a, 19776), based on the frames idea. But it is important to distinguish this from two other possible interpretations of what Minsky was urging, which one might call the metaphysical and the heuristic (following the terminology of (Mc Carthy/Hayes, 1968)).



Relational Programming

Classics (Collection 2)

A programming language needs simple and well defined semantics. The two favoured theoretical bases for languages have been lambda calculus as advocated by Landin and others, and predicate calculus as advocated by Kowalski (see Landin (1966) and Kowalski (1973)). In this paper I adopt an approach based on predicate calculus, but in a manner that differs from the existing PROLOG language (Warren 1975 and Battani & Meloni 1973) in that I adopt a "forward inference" approach -- inferring conclusions from premises, rather than the "backward inference" approach of PROLOG, which starts with a desired conclusion and tries to find ways of inferring it. This difference is reflected in the internal structure of the associated implementations, that of PROLOG being a "backtrack search" kind of implementation, while the most obvious implementation of the system proposed here involves a kind of mass operation on tables of data, reminiscent of APL (Iverson 1962) but in fact identical in many respects with the work of Codd (Codd 1970) on relational data bases. Indeed, from one perspective this paper can be seen as an extension of Codd's work into the realm of general purpose computing.


MI-8-Intro.pdf

Classics (Collection 2)

The eighth volume completes a ten-year span of the Machine Intelligence series. It is appropriate, therefore, to take stock of the main events, and to note certain solid steps and occasional forward leaps. Leaps are normally preceded by some preparatory backtracking. The uniform procedures of heuristic search and resolution theorem-proving which dominated the scene in 1965 cannot of themselves, as we now see, be developed into "the answer" to automatic problem-solving. This realisation has paved the way for machine-aided forays into nontrivial mathematics, as indicated in Bledsoe and Tyson's contribution to this volume.



INTRODUCTION KNOWLEDGE AND MATHEMATICAL REASONING

Classics (Collection 2)

R.B. DAVIS 19 Representing knowledge about mathematics for computer-aided teaching, part II -- the diversity of roles that a computer can play in assisting learning. J. Do RAN 433 22 Chromosome classification and segmentation as exercises in knowing what to expect. D.A. HU FFM AN 493 25 How to see a simple world: an exegesis of some computer programs for scene analysis.


Preface

Classics (Collection 2)

But the point I wish to make is that we can now calculate many thousands of times as fast as we could in 1953 and at least a million times as fast as we could three hundred years ago. Now this change is quite extraordinary, if one compares it for example with the increase in the speed of travel. A satellite orbiting the earth or moving towards the planets is unlikely to go much faster than twenty-five or thirty thousand miles an hour. An ordinary man can usually do two and a half or three, so that the satellite is perhaps ten thousand times as fast as a walking man. The enormous increase in speed of travel has changed our world and our ideas of the potentially possible.


15 Mathematical and Computational Models of Transformational Grammar

Classics (Collection 2)

In this paper we compare three models of transformational grammar: the mathematical model of Ginsburg and Partee (1969) as applied by Salomaa (1971), the mathematical model of Peters and Ritchie (1971 and forthcoming), and the computer model of Friedman et al. (1971). All of these are, of course, based on the work of Chomsky as presented in Aspects of the Theory of Syntax (1965). We were led to this comparison by the observation that the computer model is weaker in three important ways: search depth is not unbounded, structures matching variables cannot be compared, and structures matching variables cannot be moved. All of these are important to the explanatory adequacy of transformational grammar. Both mathematical models allow the first, they each allow some form of the second, one of them allows the third.