Set Theory and Logic

1910 Submissions

[2] viXra:1910.0559 [pdf] submitted on 2019-10-27 07:25:40

Instruction Set Completeness Theorem: Concept, Relevance, Proof, and Example for Processor Architecture

Authors: William F. Gilreath
Comments: 22 Pages. Published in the General Science Journal

The Instruction Set Completeness Theorem is first formally defined and discussed in the seminal work on one-instruction set computing—the book Computer Architecture: A Minimalist Perspective. Yet the original formalism of the Instruction Set Completeness Theorem did not provide a definitive, explicit mathematical proof of completeness, analyze both singular and plural instruction sets that were either complete or incomplete, nor examine the significance of the theorem to computer architecture instruction sets. A mathematical proof of correctness shows the equivalence of the Instruction Set Completeness Theorem to a Turing machine, a hypothetical model of computation, and thereby establishes the mathematical truth of the Instruction Set Completeness Theorem. With a more detailed examination of the Instruction Set Completeness Theorem develops several surprising conclusions for both the instruction set completeness theorem, and the instruction sets for a computer architecture.
Category: Set Theory and Logic

[1] viXra:1910.0556 [pdf] replaced on 2019-10-28 01:53:49

Modus Inversus – if (Premise is False) Then (Conclusion is False)

Authors: Ilija Barukčić
Comments: 9 Pages.

Objective: When theorems or theories are falsified by a formal prove or by observations et cetera, authors respond many times by different and sometimes inappropriate counter-measures. Even if the pressure by which we are forced to believe in different theories although there are already predictively superior rivals to turn to may be very high, a clear scientific methodology should be able to help us to assure the demarcation between science and pseudoscience. Methods: Karl Popper’s (1902-1994) falsificationist methodology is one of the many approaches to the problem of the demarcation between scientific and non-scientific theories but relies as such too much only on modus tollens and is in fact purely one-eyed. Results: Modus inversus is illustrated in more detail in order to identify non-scientific claims as soon as possible and to help authors not to hide to long behind a lot of self-contradictory and sometimes highly abstract, even mathematical stuff. Conclusions: Modus inversus prevents us from accepting seemingly contradictory theorems or rules in science. Keywords: Science, non-science, modus inversus. E-Mail: Barukcic@t-online.de
Category: Set Theory and Logic