Set Theory and Logic

1812 Submissions

[10] viXra:1812.0168 [pdf] submitted on 2018-12-09 10:12:03

Affirmation of the Craig Interpolation Theorem

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 Craig interpolation theorem, find a mistake in a Craig lemma as rendered by Feferman, and affirm the theorem.
Category: Set Theory and Logic

[9] 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

[8] 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

[7] viXra:1812.0153 [pdf] submitted on 2018-12-08 20:02:54

Refutation of Definable Modal Operators on Stable Set Lattices

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 definable modal operators on stable set lattices. None of the definitions or implementations is tautologous, hence refuting the operators.
Category: Set Theory and Logic

[6] 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

[5] viXra:1812.0070 [pdf] replaced on 2018-12-09 16:36:16

Recent Advances in Refutation and Confirmation Using Meth8/VŁ4 Modal Logic Model Checker

Authors: Colin James III
Comments: 512 Pages.

We evaluated 360 artifacts in 1848 assertions to confirm 378 as tautology and 1470 as not (79.5%). We resuscitated the four-valued logic of Łukasiewicz in Meth8/VŁ4 on the 2-tuple {00, 10, 01, 11} as respectively {False for contradiction; Contingent for falsity; Non contingent for truthity; Tautology for proof}. The designated proof value is T for tautology. Meth8 contains recent advances in parsing technology named sliding window.
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