Set Theory and Logic

1911 Submissions

[10] viXra:1911.0244 [pdf] submitted on 2019-11-13 23:51:00

Refutation of Bunch Theory with Derivations

Authors: Colin James III
Comments: 3 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

We evaluate bunch theory in ten equations which are not tautologous. This refutes the conjecture of bunch theory along with its derivations of: improper bunch theory; wholistic functions; fixed point theory; and formal grammars. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[9] viXra:1911.0215 [pdf] submitted on 2019-11-12 05:59:15

Refutation of Reduction of Provability Logics

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

We evaluate definitions for “Lob” and the “completeness principle” also the necessitation rule. None is tautologous. Hence reduction of provability logics is not confirmed. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[8] viXra:1911.0204 [pdf] submitted on 2019-11-11 20:09:57

Refutation of H-Inductive Sentences and Positive Logic

Authors: Colin James III
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

We evaluate h-universal sentences which are not tautologous. This refutes h-inductive sentences and positive logic. These form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[7] viXra:1911.0183 [pdf] submitted on 2019-11-10 10:39:24

Refutation of Tense Logic and Display to Labelled Proofs Back Again for Tense Logics

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

We evaluate tense logic (Kt) as an extension of K. The equation for A→□A is not tautologous, hence refuting Kt. What follows is that the conjecture of display to labelled proofs and back again for tense logic is not confirmed. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[6] viXra:1911.0117 [pdf] replaced on 2019-11-07 18:44:43

Refutation of Leibnitz’ Indiscernibility of Identicals and Identity of Indiscernibles

Authors: Colin James III
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

We evaluate Leibnitz’ law(s) of indiscernibility of identicals and identity of indiscernibles which are not equivalents, and the latter is not tautologous. The contradicts Leibnitz’ law of identity of indiscernibles. We also note that second-order expressions are expressible as first-order expressions because of the equivalence of respective quantifiers and modal operators in VŁ4. The results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[5] viXra:1911.0068 [pdf] submitted on 2019-11-04 16:22:34

Refutation of Multi-Valued Concurrent Dynamic Logic

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

We evaluate two operators for parallel and sequential composition which are not tautologous. The conjecture of multi-valued, concurrent, propositional, dynamic logics fails. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[4] viXra:1911.0030 [pdf] submitted on 2019-11-02 07:11:49

Refutation of Cohen’s First Model and Derivations as the Method of Forcing

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

We evaluate the definition of Cohen’s first model as not tautologous, hence refuting it and impugning derived conjectures such as forcing. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[3] viXra:1911.0022 [pdf] submitted on 2019-11-01 13:19:50

Refutation of a Common Expression for Law of Trichotomy, Replaced by Shortest Known Proof

Authors: Colin James III
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

We show a common formal logic expression for the law of trichotomy is not tautologous, and replace it with the shortest known proof. The first results forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[2] viXra:1911.0021 [pdf] replaced on 2019-11-02 04:12:14

Refutaton of Frege’s Inference Rule of Generalization

Authors: Colin James III
Comments: 1 Page. © Copyright 2016-2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Updated abstract at ersatz-systems.com.

We evaluate Frege’s inference rule of generalization which is not tautologous. This result forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[1] viXra:1911.0015 [pdf] submitted on 2019-11-01 02:10:03

Refutation of Differential Hoare Logics with Isabelle/hol

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

e evaluate the ordering of K essential to Kleene algebra with test (KAT). It is not tautologous, but the basis for other conjectures: differential dynamic logic (dL); differential Hoare logic; Morgan-style differential refinement calculus; “reasoning with evolution”; and verification conjectures formalized in Isabelle/HOL. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic