An Introduction to Aristotelian Computer Science
An Introduction to Aristotelian Computer Science
By Thomas Gramstad
This article introduces some of the basic ideas behind a deductive database based on Aristotelian logic. The database was created by Eyal Mozes and is the basis for his doctoral thesis, completed at the Weizmann Institute in Rehovot, Israel.
Aristotelian logic is the area of logic which is concerned with rules for reasoning from general premises to specific conclusions, i.e., deductive logic - an area that was founded and almost singlehandedly developed by Aristotle. Today it is common among philosophers and mathematicians to regard it as a special case of predicate calculus. This view, however, is severely mutilated, if not killed, by the latest gadget from the Aristotelian Philosophy Defense Department.
Why use Aristotelian logic in a database? Aristotelian logic is concerned with actual human thought. This gives the database some unique features: It can give natural-language explanations for its deductions; it can volunteer information, in answer to yes/no questions, if a stronger or weaker version of the "yes" answer can be proven; it can point out likely (but unprovable) possibilities; it can suggest "missing rules" (i.e., new rules that would allow a "yes" answer); and it can even suggest instances in which nondeductive forms of reasoning (e.g., analogy, induction) may be useful.
There is, however, a deeper motivation for the use of Aristotelian logic. In agreement with H.B. Veatch, the author of Intentional Logic (Yale University Press 1952), Eyal Mozes criticizes modern mathematical logic for confusing real relations - the relations among different objects and between objects and their properties - with logical ones. Thus, general facts used in deduction are referred to as "deductive rules" when they are contained in a deductive database. However, stresses Eyal Mozes, they are not rules guiding the deduction - they are premises of the deduction.
Aristotelian logic, created for the purpose of understanding and practically guiding actual human thought, studies the relations of identity on which human knowledge and thought are based, their possible forms, and their use in inference; this study is the theory of the syllogism. ... Previous work on deductive databases was based on mathematical logic, and therefore did not recognize the role of the logical relation of identity as the base of knowledge and of inference; instead, database relations - which represent real relations - were treated as if they are logical relations. That is why general facts about these relations were treated as if they are deduction rules, and the four possible types of general facts were not recognized. One result of this is that the various distinctions and classifications made in Aristotelian logic - such as the classification of syllogisms into figures, and the classification of the fallacies - which are relevant to human thinking and allow implicit reasoning about knowledge, and the resulting capabilities of the user interaction, were not possible. (Mozes, p. 21)
The thesis consists of 9 chapters. The introductory chapter describes the goals of the thesis, the basic features of the database, and projects the historical influence of traditional philosophical logic vs. modern, mathematical logic. The second chapter provides an overview of the structure of the database as seen by the user, and the third chapter describes the deductive procedures; this chapter may serve as a brief introduction to Aristotelian logic. Chapter 4 compares the thesis to other works on deductive databases, and other works on Aristotelian logic. Chapter 5 provides examples of how the database works. Chapter 6 discusses the philosophical motivation behind the database. Chapter 7 considers the use of Aristotelian logic as an extension of the usual procedures of deductive databases, and provides a system of rules for valid inference and a partial formal semantics. Chapter 8 describes the implementation of the prototype system, including its general architecture and the major algorithms. Chapter 9 contains conclusions and suggestions for future research. Finally, an appendix lists the valid moods and figures of the syllogism, and another gives examples of runs with the deductive algorithm.
The database demonstrates the advantages of Aristotelian logic and suggests two broad areas to which it can be applied:
Applications in which interactions with human users are important.
Simulations of human thought, especially AI applications dealing with induction and the suggestion of possibilities.
Eyal Mozes may be contacted at [email protected]. His thesis is available for free from:
Department of Applied Mathematics
Weizmann Institute of Science
[email protected] (Carol Weintraub)
Ask for Technical Report CS87-18
A Deductive Database Based on Aristotelian Logic
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