Mechanizing Hypothesis Formation Mathematical Foundations for a Gene
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
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P. Hajek T. Havranek
Mechanizing Hypothesis Formation Mathematical Foundations for a General Theory
Springer-Verlag Berlin Heidelberg New York 1978
Petr Hajek Mathematical Institute, Czechoslovak Academy of Sciences Praha, Czechoslovakia TomM Havranek Department of Biomathematics, Czechoslovak Academy of Sciences Praha, Czechoslovakia The authors are members of the Society of Czechoslovak Mathematicians and Physicists
AMS Subject Classification (1970): 02-02, 02 C 05, 68-02, 68 A 20, 68A 45
ISBN-13: 978-3-540-08738-0 001: 10.1007/978-3-642-66943-9
e-ISBN-13: 978-3-642-66943-9
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2141/3140-543210
Serlin Heidelberg 1978
To Marie and Marie
Preface
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. In Part A we define and investigate formal calculi appropriate for formalizing (fragments of) observational and
theoretical languages of scientific theories
based on empirical data. The definitions are motivated by statistical considerations, which seem to be unjustly neglected in contemporary Artificial Intelligence. Our calculi are modified generalized
predicate calculi and are related to calculi
proposed by Suppes. The following are emphasized: ( i) explicit semantics in T arski 's style, (ii) use of generalized quantifiers and abstract truth values,
VIII (iii) relation to effective computability and complexity of computations.
As a result, we obtain Ca) ma
