Set Theory and Logic

1910 Submissions

[9] viXra:1910.0238 [pdf] submitted on 2019-10-14 17:15:29

Refutation of Basic Logic (BL)

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.

Using classical logic we establish the definition of the new connective tensor ⊗ as a theorem. (This is not supposed to be possible from within classical logic as a subset of the conjecture.) Six rules for formation and reflection are not tautologous. This refutes Basic Logic (bL), forming a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[8] viXra:1910.0229 [pdf] submitted on 2019-10-14 07:57:16

Shorter Refutation of Craig’s Interpolation and Derived Conjectures

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 formula for Craig’s interpolation as not tautologous. This means it is refuted, along with nine conjectures in the following cascade: proving Beth definability; verifying the division of larger problems into smaller problems; representing knowledge by suppression of information; proving intuitionistic and bi-intuitionistic logics, converse modality, tense logic, and extensions with path axioms; and ; and an orthogonality condition for defining duality between interpolates. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[7] viXra:1910.0220 [pdf] submitted on 2019-10-13 23:05:48

Refutation of the Ranked Pentagon Lattice

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 the attribute of ranking lattices of ρ(r) ≥ r which is not tautologous. This refutes the conjecture of ranking lattices for extensions of cofinal and mixed (neither end or cofinal). This further disallows theorems derived therefrom in the pentagon lattice, to form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[6] viXra:1910.0145 [pdf] submitted on 2019-10-09 22:15:21

Refutation of Condensable Models of Set Theory by Satisfaction Classes

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 the first axiom for satisfaction of classes which is not tautologous. That, as one of four axioms for a conjunction, in turn refutes a Tarski theorem as the basis of satisfaction classes. That in turn refutes the conjecture of condensable models of set theory. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[5] viXra:1910.0119 [pdf] submitted on 2019-10-08 00:59:49

Refutation of Pythagorean Triples

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 Pythagorean triples as not tautologous. This invalidates its subsequent use with Ramsey colorings and the computerized proof using the inference of induction as based thereon. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[4] viXra:1910.0033 [pdf] submitted on 2019-10-05 13:39:51

Refutation of Clausal Language (CL)

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.

Three definitions of pairing in natural numbers are evaluated as not tautologous. Refutation of these seminal definitions as a basis of the causal language (CL) also refute extraction proofs of recursive programs. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[3] viXra:1910.0032 [pdf] submitted on 2019-10-05 13:42:39

Refutation of French Smart Building Code Compliance Checking Based on Semantic Rules

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 model of Fig. 1 reducing room classification to regulations ontology as not tautologous. This refutes the conjecture of French smart building code compliance checking based on semantic rules. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[2] viXra:1910.0031 [pdf] submitted on 2019-10-05 13:44:17

Refutation of Complete Intuitionistic Temporal Logics in Topological Dynamics

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 intuitionistic temporal logic (ITL) from its last axiom φ→∀φ which is not tautologous and refutes the seminal basis of intuitionistic temporal logics in topological dynamics. Therefore the claim that ITL is proved decidable and complete is not supported. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[1] viXra:1910.0020 [pdf] submitted on 2019-10-01 18:48:11

Refutation of Induction by Numerical Identity of (-1≤C≤1) = (C≤1)

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 numerical identity of (-1≤C≤1) = (C≤1). It is confirmed by induction in 1MM iterations not to have a counter example. However, the numerical identity as a logical equation is not tautologous. When mapped as an implication (-1≤C≤1) → (C≤1), it is tautologous. This experiment speaks to the fact that induction when defined as an implication is not tautologous not deduction when defined as an implication is tautologous. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic