A Further Note on Inductive Generalization

In this paper, we develop the algorithm, given in Plotkin (1970), for finding the least generalization of two clauses, into a theory of inductive generalization.. The types of hypothesis which can be formed are very simple. They all have the form: (x)PX=:l Qx.. We have been guided by ideas from the philosophy of science, following Buchanan (1966). There is' no search for infallible methods of .generating true hypotheses. Instead we define (in terms of first-order predicate calculus) the notions of data and evidence for the data. Next, some formal criteria are set up for a sentence to be a descriptive hypothesis which is a goodexplanation of the data, given the evidence. We can then look for the best such hypothesis. Although this problem is insoluble in general, some soluble subcases can be distinguished. We programmed one of these and tried some examples.

[1]  Jaakko Hintikka,et al.  Knowledge, Acceptance, and Inductive Logic , 1966 .

[2]  Penelope Maddy,et al.  The logical structure of the world , 2007 .

[3]  R. Kowalski.  Studies in the completeness and efficiency of theorem-proving by resolution , 1970 .

[4]  C. W. Tate.  Solve it. , 2005, Nursing standard (Royal College of Nursing (Great Britain) : 1987).

[5]  M. Kendall,et al.  The Logic of Scientific Discovery. , 1959 .

[6]  John G. Kemeny,et al.  The Use of Simplicity in Induction , 1953 .

[7]  H. Putnam.  Mathematics, Matter and Method: ‘Degree of confirmation’ and inductive logic , 1979 .

[8]  G. Kreisel.  Informal Rigour and Completeness Proofs , 1967 .

[9]  Charisma Lee.  A completeness theorem and a computer program for finding theorems derivable from given axioms , 1967 .

[10]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[11]  Gordon Plotkin,et al.  A Note on Inductive Generalization , 2008 .

[12]  Philip J. Stone,et al.  Experiments in induction , 1966 .

[13]  Willard Van Orman Quine,et al.  A Way to Simplify Truth Functions , 1955 .

[14]  Gary James Jason,et al.  The Logic of Scientific Discovery , 1988 .

[15]  Jaakko Hintikka,et al.  Towards a Theory of Inductive Generalization , 1970 .

[16]  H. Kyburg,et al.  Logical foundations of probability , 1951 .

[17]  G. Kreisel,et al.  Hilbert's programme and the search for automatic proof procedures , 1970 .

[18]  Atocha Aliseda,et al.  Logics in Scientific Discovery , 2004 .