The Logic of Deduction and Induction, a New Approach to the Interpretation and Use of Truth Tables
Abstract
Truth tables are interpreted in an existential manner (there exists, all
are). This leads to a method of quantifying induction and deduction
that gives the set of implications for a set of data. The implications
are generated by computer. Currently, a program that can simplify the
expressions (functions) works with fourteen variables. This is equivalent
to a Karnaugh map or the Quine-McCluskey method with fourteen variables,
which is beyond the current state of the art by hand. The procedure utilizes
the XOR to find the irrelevant variables. The result is a set of implications
in simplified form. The method is indefinitely extensible, limited only by
processing time and storage constraints. Currently, it takes about 30
seconds to process fourteen variables in simplified form.
Implications for the profession are an advance in the theory of logic
and in the implementation of induction and deduction in an automated fashion.
The theory is also simpler and more widely applicable than the current theory
of deduction, i.e., applicable to things other than propositions, e.g., sets.