Hypothesis formation is known as one of the branches of Artificial Intelligence, The general question of Artificial IntelligencE' ,"Can computers think?" is specified to the question ,"Can computers formulate and justify hypotheses?" Various attempts have been made to answer the latter question positively. The present book is one such attempt. Our aim is not to formalize and mechanize the whole domain of inductive reasoning. Our ultimate question is: Can computers formulate and justify scientific hypotheses? Can they comprehend empirical data and process them rationally, using the apparatus of modern mathematical logic and statistics to try to produce a rational image of the observed empirical world? Theories of hypothesis formation are sometimes called logics of discovery. Plotkin divides a logic of discovery into a logic of induction: studying the notion of justification of a hypothesis, and a logic of suggestion: studying methods of suggesting reasonable hypotheses. We use this division for the organization of the present book: Chapter I is introductory and explains the subject of our logic of discovery. The rest falls into two parts: Part A - a logic of induction, and Part B - a logic of suggestion.
Introduction: What is a Logic of Discovery.- I. Introduction: What is a Logic of Discovery.- I.1 Informal considerations.- I.2 Some mathematical notions.- A. A Logic of Induction.- II. A Formalization of Observational and Theoretical Languages.- II.1 Structures.- II.2 Observational predicate calculi.- II.3 Function calculi.- II.4 Function calculi with state dependent models.- III. The Logic of Observational Functor Calculi.- III.1 Monadic observational predicate calculi.- III.2 Associational and implicational quantifiers.- III.3 Calculi with incomplete information.- III.4 Calculi with qualitative values.- III.5 More on the logic of observational predicate calculi.- IV. Logical Foundations of Computational Statistics.- IV.1 Preliminaries.- IV.2 The concept of statistics.- IV.3 The form of theoretical sentences and inference rules.- IV.4 Observational predicate calculi based on statistical procedures.- IV.5 Some properties of statistically motivated observational function calculi.- V. Rank Calculi.- V.1 Generalized random structures and the hypothesis Ho of d-homogeneity.- V.2 Rank tests of d-homogeneity and independence.- V.3 Function calculi with enumeration models.- V.4 Observational monadic function calculi with rational valued models.- B. A Logic of Suggestion.- VI. Listing of Important Observational Statements and Related Logical Problems.- VI.1 Observational research problems and their solutions.- VI.2 Indirect solutions.- VI.3 Helpful quantifiers in X-predicate calculi.- VI.4 Incompressibility.- VII. A General Guha-Method with Associational Quantifiers.- VII.1 A system of r-problems.- VII.2 Solutions.- VII.3 Remarks on realization and optimization.- VII.4 Some remarks concerning GUHA-methods based on rank calculi.- VIII. Further Statistical Problems of the Logic of Discovery.- VIII.1 Local interpretation.- VIII.2 Global interpretation.- VIII.3 Some questions for statistics.- Postcript: Some Remarks on the History of the Guha Method and its Logic of Discovery.