Set Theory and Logic

1901 Submissions

[18] viXra:1901.0467 [pdf] submitted on 2019-01-31 09:57:54

Refutation of Spatial Relations and Claims in Distributive Mereotopology

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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate the contact algebra logic of RCC-8 for tangential and non-tangential spatial relations. The respective representations in T0 spaces for four equations to be equivalent. Two only are equivalent, with the iff implication chain as not tautologous. These results refute distributive mereotopology.
Category: Set Theory and Logic

[17] viXra:1901.0460 [pdf] submitted on 2019-01-30 18:24:18

Refutation of De Finettian Logics of Indicative Conditionals

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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate De Finettian logics which specifies four conditionals, as attributed to Aristotle, Boethius, Cooper-Cantwell, Jeffrey, and six axioms. None is tautologous. This refutes their use to justify connexive logic.
Category: Set Theory and Logic

[16] viXra:1901.0458 [pdf] submitted on 2019-01-30 20:30:32

Refutation of the Quantifier Most

Authors: Colin James III
Comments: 1 Page. © 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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate two equivalent semantics for "Most A are B" which while logically equivalent are neither tautologous. Hence the quantifier Most is refuted.
Category: Set Theory and Logic

[15] viXra:1901.0446 [pdf] submitted on 2019-01-29 20:07:52

Refutation of the Interval for Model Checking

Authors: Colin James III
Comments: 1 Page. © 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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate three sub-interval relations named reflexive, proper or irreflexive, and strict. None is tautologous. This refutes those relations and model checking therefrom.
Category: Set Theory and Logic

[14] viXra:1901.0442 [pdf] submitted on 2019-01-29 07:21:53

Refutation of Sabotage Modal Logic (Revisited)

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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate six equations for a definition and properties of sabotage modal logic. The special symbols ■ and ♦ act as functions, so we assign them variable names. Because none is tautologous, sabotage modal logic is refuted.
Category: Set Theory and Logic

[13] viXra:1901.0440 [pdf] submitted on 2019-01-29 08:02:21

Refutation of Poison Modal Logic (PML)

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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate four formulas as validities of poison modal logic (PML). None is tautologous, thereby refuting poison modal logic (PML).
Category: Set Theory and Logic

[12] viXra:1901.0434 [pdf] submitted on 2019-01-28 18:43:38

Refutation of Approximations of Theories

Authors: Colin James III
Comments: 1 Page. © 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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate the definition of T-approximations which is not tautologous, thereby refuting the approximations of theories.
Category: Set Theory and Logic

[11] viXra:1901.0423 [pdf] submitted on 2019-01-28 08:40:52

Refutation of an Epistemic Logic for Knowledge and Probability

Authors: Colin James III
Comments: 1 Page. © 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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate axioms and definitions of an epistemic logic for knowledge and probability. Two equations are not tautologous, hence refuting the proposed epistemic logic.
Category: Set Theory and Logic

[10] viXra:1901.0382 [pdf] submitted on 2019-01-26 12:07:00

Refutation of Dempster-Shafer Belief and Plausibility Theory

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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate Dempster-Shafer belief and plausibility functions. Three definitions are not tautologous. This refutes Dempster-Shafer belief and plausibility theory.
Category: Set Theory and Logic

[9] viXra:1901.0379 [pdf] submitted on 2019-01-25 21:34:32

Refutation of a Modal Logic System for Reasoning About the Degree of Blameworthiness

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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate a modal logic system for the blameable coalition of an outcome if there is a strategy to prevent it and where the degree of blameworthiness is measured by costs of prevention or sacrifice. Of eight axioms, three are not tautologous, hence refuting the approach. We do not consider the claimed technical result of a completeness theorem.
Category: Set Theory and Logic

[8] viXra:1901.0342 [pdf] replaced on 2019-01-24 20:27:58

Refutation of Descriptive Unions in Descriptively Near Sets

Authors: Colin James III
Comments: 3 Pages.

We evaluate an intersection operator named descriptive union for descriptively near sets. From two sources the definition of the operator is not tautologous. A proof of seven properties derived from the second definition contains two trivial tautologies with the rest as not tautologous. This refutes the descriptive intersection operator and descriptively near sets on which it is based. This also casts doubt on the bevy of derived math and physics papers so spawned at arxiv, researchgate, and vixra.
Category: Set Theory and Logic

[7] viXra:1901.0308 [pdf] submitted on 2019-01-21 10:35:28

Refutation of Block Argumentation

Authors: Colin James III
Comments: 3 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 warn troll Mikko at Disqus to read the article four times before hormonal typing.)

We evaluate the approach of block argumentation using the legal example of a popular case. Three scenarios are not tautologous. We attempt to resuscitate the method by substitution of generic block argumentation and also by testing the consequent parts separately. The equations were not tautologous, hence refuting the block argumentation approach as presented.
Category: Set Theory and Logic

[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: Wu Ye TangYin
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] replaced on 2019-01-28 02:47:12

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