Set Theory and Logic

1812 Submissions

[20] viXra:1812.0440 [pdf] submitted on 2018-12-27 14:03:53

Refutation of a Minimal Non-Contingency Logic System

Authors: Colin James III
Comments: 1 Page. © Copyright 2016-2019 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We evaluate a minimal non-contingency logic system based on its unique definition which is not tautologous and hence reject it.
Category: Set Theory and Logic

[19] viXra:1812.0429 [pdf] submitted on 2018-12-26 21:59:10

The New Bivalent, Three-Valued Logic VŁ3

Authors: Colin James III
Comments: 3 Pages. © Copyright 2016-2019 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We build and test a new bivalent three-valued logic named VŁ3. Recent advances are support of the classical tautologies, modal definitions, the law of excluded fourth, and extended contradiction principle.
Category: Set Theory and Logic

[18] viXra:1812.0413 [pdf] replaced on 2019-01-18 16:37:12

A Rational Cover

Authors: Igor Hrnčić
Comments: 3 Pages. Version 2: added 2 figures with clarifications.

This letter demonstrates in an elegant way that Cantor’s postulate that there’s a bijection between any two countable infinite sets is flawed.
Category: Set Theory and Logic

[17] viXra:1812.0371 [pdf] submitted on 2018-12-20 07:18:22

Refutation of Lambda λ-Calculus and Lisp

Authors: Colin James III
Comments: 2 Pages. © Copyright 2016-2019 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We evaluate McCarthy's lambda λ-calculus in six equations. Five of the equations are not tautologous, and one equation is a trivial tautology. McCarthy's three-valued logic is not bivalent on which the LISP programming language is implemented, and hence also flawed.
Category: Set Theory and Logic

[16] viXra:1812.0314 [pdf] submitted on 2018-12-18 19:54:48

Rejection of Trivial Objections to Modal Logic Ł4

Authors: Colin James III
Comments: 2 Pages. © Copyright 2016-2019 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We evaluate objections to the modal logic Ł4 by six equations in contra arguments which we reject as not tautologous. The concluding equation invoked as (((p=p)=(q=q)))=(r=r))=((p=q)=r) is not tautologous. We reject the trivial conclusion that "modal syllogisms with both necessary premises and with mixed premises cannot be distinguished while one is necessary and another assertoric[:] Łukasiewicz’ modal logic is useless for investigating Aristotelian modal syllogistic". Hence we use our VŁ4 to invalidate objections to itself.
Category: Set Theory and Logic

[15] viXra:1812.0275 [pdf] replaced on 2018-12-17 12:21:39

Confirmation of the Łukasiewicz Square of Opposition Via Logic VŁ4

Authors: Colin James III
Comments: 4 Pages. © Copyright 2016-2019 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We evaluate the existential import of the Revised Modern Square of Opposition. We confirm that the Łukasiewicz syllogistic was intended to apply to all terms. What follows is that Aristotle was mistaken in his mapping of vertices, which we correct and show fidelity to Aristotle's intentions. We also evaluate the Cube of Opposition of Seuren. Two final claims are not tautologous, hence refuting the Cube, which also contradict criticism of Seuren that was not based on those claims.
Category: Set Theory and Logic

[14] viXra:1812.0267 [pdf] submitted on 2018-12-15 08:57:19

Refutation of Pure Alethic Modal Logic (Pam)

Authors: Colin James III
Comments: 1 Page. © Copyright 2016-2019 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We evaluate the formula □p → p → ◊p as the backbone of pure alethic modal logic (PAM). Two inconsistent results arise from different orders of precedence: a result of not tautologous, not contradictory; and a tautologous result. That ambiguity refutes PAM.
Category: Set Theory and Logic

[13] viXra:1812.0217 [pdf] submitted on 2018-12-12 13:52:02

Refutation of Graded Modal Logic

Authors: Colin James III
Comments: 2 Pages. © Copyright 2016-2019 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We evaluate definitions of five frame classes and a main theorem of satisfiability. Three of the five frame classes are not tautologous and the designated example for satisfiability is not tautologous. This refutes graded modal logic.
Category: Set Theory and Logic

[12] viXra:1812.0214 [pdf] submitted on 2018-12-12 21:38:39

Refutation of Lyndon Interpolation

Authors: Colin James III
Comments: 2 Pages. © Copyright 2016-2019 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We evaluate the Lyndon interpolation on the logic GL. Each is not tautologous, and the combination is not tautologous, hence rendering both refuted.
Category: Set Theory and Logic

[11] viXra:1812.0209 [pdf] replaced on 2019-02-03 06:50:24

Refutation of the Hahn-Banach Theorem

Authors: Colin James III
Comments: 2 Pages.

We evaluate the Hahn-Banach theorem. Without or with the universal quantifiers, the equations are not tautologous. This refutes the Hahn-Banach theorem.
Category: Set Theory and Logic

[10] viXra:1812.0205 [pdf] submitted on 2018-12-11 22:27:00

Refutation of Agm Postulates and Levi and Harper Bridging Principles

Authors: Colin James III
Comments: 2 Pages. © Copyright 2016-2018 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We evaluate the AGM logic system in eight postulates and two bridging principles. The postulates named success, inclusion, vacuity, and inconsistency and the Levi and Harper bridging principles are not tautologous, hence refuting the AGM logic system.
Category: Set Theory and Logic

[9] viXra:1812.0204 [pdf] submitted on 2018-12-11 22:28:46

Resolution of Moore's Paradox as a Theorem

Authors: Colin James III
Comments: 1 Page. © Copyright 2016-2018 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We evaluate Moore's paradox, as touted by Wittgenstein, with Hintikka's omissive or commissive logical forms as "P and NOT(belief in P)" or "P and belief in NOT-P". The former as antecedent (contradictory) and the latter as consequent (neither contradictory nor tautologous) imply tautology, a theorem.
Category: Set Theory and Logic

[8] viXra:1812.0168 [pdf] replaced on 2019-03-28 17:38:13

Refutation of the Constructive Craig Interpolation Theorem by Feferman

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

We evaluate the Craig constructive interpolation theorem, find a mistake in a Craig lemma as rendered by Feferman, and refute the theorem as not constructive.
Category: Set Theory and Logic

[7] viXra:1812.0165 [pdf] submitted on 2018-12-09 16:20:16

Refutation of the modal logic GL2

Authors: Colin James III
Comments: 2 Pages. © Copyright 2016-2018 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We evaluate the modal logic GL2 in two axioms and for satisfiability. One of the two axioms is not tautologous, and the five formulas for PSpace complete satisfiability are not tautologous. Hence GL2 is refuted.
Category: Set Theory and Logic

[6] viXra:1812.0161 [pdf] submitted on 2018-12-10 04:29:36

An Application for Medical Decision Making with the Fuzzy Soft Sets

Authors: Murat Kirisci
Comments: 6 Pages.

In the present study, for the medical decision making problem, the proposed technique related to the fuzzy soft set by Celik-Yamak through Sanchez’s method was used. The real dataset which is called Cleveland heart disease dataset applied in this problem.
Category: Set Theory and Logic

[5] viXra:1812.0152 [pdf] submitted on 2018-12-08 20:08:04

Refutation of the Definition of Sacchetti's Modal Logics of Provability

Authors: Colin James III
Comments: 1 Page. © Copyright 2016-2018 by Colin James III All rights reserved. Updated abstract at ersatz-systems.com . Respond to the author by email at: info@ersatz-systems dot com.

We evaluate the definition of Sacchetti's modal logics of provability. It is not tautologous. Therefore it is a mistake to use it as a basis for constructing fixed point procedures.
Category: Set Theory and Logic

[4] viXra:1812.0047 [pdf] replaced on 2018-12-04 11:12:13

Refutation of the Lonely Runner Conjecture with Three Runners

Authors: Colin James III
Comments: 2 Pages. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

We evaluate the conjecture of the lonely runner with three runners. We do not assume a runner may be stationary as a no-go contestant. The result is that the conjecture diverges from tautology by one logical value and hence is refuted. We then assume a runner can be stationary with result of the same truth table also to refute the conjecture.
Category: Set Theory and Logic

[3] viXra:1812.0038 [pdf] submitted on 2018-12-02 08:48:13

Refutation of a Modal Logic for Partial Awareness from Published Example

Authors: Colin James III
Comments: 3 Pages. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

We evaluate a modal logic for partial awareness from a published example. The definitions and conjectures are not tautologous. We show how to exclude a priori logical clauses to promote a perhaps unintended tautology for the example. However, our evaluation does not rely on modal operators, suggesting that the system as proffered should be renamed to a logic for awareness, without the word modal.
Category: Set Theory and Logic

[2] viXra:1812.0016 [pdf] replaced on 2018-12-03 12:51:54

Refutation of the Frauchiger-Renner Thought Paradox as a Quantum Model

Authors: Colin James III
Comments: 4 Pages.

We use modal logic to evaluate a quantum model of the Frauchiger-Renner thought experiment as not a contradiction (paradox) and not a tautology (theorem). The example misapplies the Born rule which we refute elsewhere.
Category: Set Theory and Logic

[1] viXra:1812.0007 [pdf] submitted on 2018-12-01 03:10:43

Refutation of Modal Forms on Vietoris Space

Authors: Colin James III
Comments: 1 Page. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

We use modal logic to evaluate the defined modal forms on Vietoris space to find them not tautologous.
Category: Set Theory and Logic