Set Theory and Logic

1901 Submissions

[6] viXra:1901.0192 [pdf] replaced on 2019-01-14 18:02:34

Refutation of Hexagons of Opposition for Statistical Modalities

Authors: Colin James III
Comments: 3 Pages.

Abstract: We evaluate pragmatic hypotheses in the evolution of science as based on probabilistic squares and hexagons of opposition under coherence. Neither conjecture is tautologous, and hence both are refuted.
Category: Set Theory and Logic

[5] viXra:1901.0190 [pdf] submitted on 2019-01-13 20:27:25

An Even Number Greater Than 2 Equals the Sum of Two Prime Numbers.

Authors: 1
Comments: 16 Pages.

On the contrary, if the natural number 2N is not equal to the prime number, On the contrary, prime numbers can only appear in odd numbers.
Category: Set Theory and Logic

[4] viXra:1901.0132 [pdf] submitted on 2019-01-11 05:33:24

Refutation of a Modal Aleatoric Calculus for Probabilistic Reasoning: Extended Version

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only at: info@ersatz-systems dot com. See website ersatz-systems.com . (We instruct troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate a modal aleatoric calculus for probabilistic reasoning using the assumption of probabilistic definitions as P(¬α) = 1−P(α). Five equations in Lemma 1 and its argument are tested. All equations are not tautologous, hence refuting the calculus.
Category: Set Theory and Logic

[3] viXra:1901.0092 [pdf] submitted on 2019-01-07 11:41:57

Denial of the Alleged Łukasiewicz Nightmare in System Ł4

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only at: info@ersatz-systems dot com. See website ersatz-systems.com . (We instruct troll Mikko at Disqus to read the article four times before hormonal typing.)

The alleged Łukasiewicz nightmare of (◇p&◇q)→◇(p&q) is not tautologous in Prover9; however, the equation recast in one variable as (◇p&◇~p)→◇(p&~p) is tautologous. In Meth8/VŁ4, both propositions are tautologous. This speaks for Meth8/VŁ4, based on the corrected modern Square of Opposition as an exact bivalent system, as opposed to Prover9, based on the uncorrected modern Square of Opposition as an inexact probabilistic vector space.
Category: Set Theory and Logic

[2] viXra:1901.0069 [pdf] submitted on 2019-01-05 10:13:15

Monoidal Structures of Logic

Authors: Antoine Balan
Comments: 2 pages, written in french

The tables of truth are relations of a monoid M.
Category: Set Theory and Logic

[1] viXra:1901.0020 [pdf] submitted on 2019-01-02 08:43:08

Relational Structures

Authors: J.A.J. van Leunen
Comments: 3 Pages. This is part of the Hilbert Book Model Project

Lattices form the foundation of important theories. One is classical logic. Another is quantum logic, which is an orthomodular lattice.
Category: Set Theory and Logic