Set Theory and Logic

1908 Submissions

[29] viXra:1908.0601 [pdf] submitted on 2019-08-29 19:03:58

Refutation of Bell's Theorem for Temporal Logic

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 evaluate Bell's theorem for temporal logic. It is not tautologous. Hence schematics of a protocol for a violation of Bell's inequalities for temporal order are similarly moot. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[28] viXra:1908.0580 [pdf] submitted on 2019-08-28 09:52:17

Refutation of Extended Truth Definitions to Peano Arithmetic

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 evaluate proof-theoretic analysis by iterated reflection and ordinal analysis of iterated arithmetical comprehension. The former is not tautologous, and the latter is a contradiction. This refutes the extended truth definitions as proffered on Peano arithmetic and forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[27] viXra:1908.0572 [pdf] submitted on 2019-08-28 23:35:30

Refutation of Tannakian Categories Via Profinite Groups of Iwasawa Embedding

Authors: Colin James III
Comments: 1 Page. 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 evaluate the seminal equation to axiomatize profinite groups with the Iwasawa embedding property. It is not tautologous. This taints Tannakian categories and subsequent conjectures to establish model theory of proalgebraic (pro-affine algebraic) groups. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[26] viXra:1908.0554 [pdf] submitted on 2019-08-27 18:38:37

Solution to the Traveling Salesman Problem as a Theorem, Unrelated to P, NP

Authors: Colin James III
Comments: 1 Page. 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 evaluate the traveling salesman problem (TSP) to confirm it as a theorem but with multiple solutions for n = 4 cities. The number of solutions here is also given by n = 4. Our results do not relate to P, NP, or NP-hard. Hence the salesman problem as an outstanding mathematical problem of optimization is refuted, and as such becomes a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[25] viXra:1908.0489 [pdf] replaced on 2019-08-29 05:14:08

The Mathematical Expressions of Quranic Exegeses and the Mathematical Definition of the Quranic Correctness

Authors: Hiroki Tahara
Comments: 4 Pages.

I succeeded to give mathematical expressions to any correct Quranic Exegeses and define the Quranic correctness as the unique existence of Tahara I function. In a precise mathematical sense, the expressions and the definition are ill-defined however they might have meanings to prove the Quranic correctness.
Category: Set Theory and Logic

[24] viXra:1908.0449 [pdf] submitted on 2019-08-21 11:27:58

Refutation of Resolution-Based Decision Procedure for Two Variables with Equality

Authors: Colin James III
Comments: 3 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 evaluate six equations and three conjectures for the decision procedure. None is tautologous. This refutes the procedure for two variables with equality, and forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[23] viXra:1908.0445 [pdf] replaced on 2019-08-23 19:04:22

Availability of Meth8/VŁ4 Demo for 2-Variables (P,q) with Unlimited Sequents

Authors: Colin James III
Comments: 1 Page. 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.

This is free on request from info@ersatz-systems.com. Please state name and organization to receive: Unrestricted m8_executable.exe; Instructions.txt with known anomalies; and Editable sample meth8_input_file.txt. The input file contains the shortest confirmation of McCune's proof of Huntington's equation: (~(~p+q)+~(~p+~q))=p. The input file contains the shortest refutation of paraconsistent logic: ((p>q)&(q>p))&((~p>~q)&(~q>~p)). The input file also contains the refutation for provability logic of the Gödel-Löb axiom GL as, "The necessity of choice, as always implying a choice, implies always a choice": #(#p>p)>#p.
Category: Set Theory and Logic

[22] viXra:1908.0442 [pdf] submitted on 2019-08-21 22:59:52

Refutation of Paraconsistent Logic on One Conjecture

Authors: Colin James III
Comments: 1 Page. 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 evaluate the seminal equivalence and replacement formula of paraconsistent logic, that one formula is equivalent to another in the sense that either can be substituted for the other wherever they appear as a subformula. It is not tautologous, and hence relegates paraconsistent logic to a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[21] viXra:1908.0426 [pdf] submitted on 2019-08-20 14:42:16

Refutation of the Hoop and Pocrim in Heyting Algebras

Authors: Colin James III
Comments: 4 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 evaluate 14 equations for the hoop and pocrim in Heyting algebras as not tautologous. The methodology of using proof assistants Prover9 and Mace8 is also refuted. These artifacts form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[20] viXra:1908.0363 [pdf] replaced on 2019-08-18 09:55:05

Scalability of Meth8/VL4

Authors: Colin James III
Comments: 1 Page.

We offer two more packages in Meth8 to process increasing numbers of propositional variables.
Category: Set Theory and Logic

[19] viXra:1908.0293 [pdf] submitted on 2019-08-15 07:59:10

The Problem P=NP

Authors: Thierry DELORT
Comments: 6 Pages.

In this article, we are going to solve the problem P=NP for a particular kind of problems called basic problems of numerical determination. Nonetheless, this solution can be generalized to all problems belonging to class P or NP. We are going to propose 3 fundamental Axioms permitting to solve the problem P=NP, but those Axioms can also be considered as pure logical assertions, intuitively evident and never contradicted, permitting to understand the solution of the problem P=NP. Indeed, we will see that the conclusion of this article solves the considered problem.
Category: Set Theory and Logic

[18] viXra:1908.0274 [pdf] replaced on 2019-08-14 10:40:22

Refutation of the Paradox of Hempel’s Raven

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 evaluate the hypothesis which is not tautologous and hence not a paradox. It forms a non tautologous fragment of the universal logic VL4.
Category: Set Theory and Logic

[17] viXra:1908.0273 [pdf] replaced on 2019-08-14 10:41:21

Refutation of Differential Reasoning

Authors: Colin James III
Comments: 1 Page. 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 refute Hempel’s raven paradox elsewhere, hence refuting differential reasoning which forms a non tautologous fragment of the universal logic VL4.
Category: Set Theory and Logic

[16] viXra:1908.0221 [pdf] submitted on 2019-08-12 06:13:45

Refutation of Perfect and Strong Functions in Fuzzy Logic

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.

For fuzzy logic, we evaluate the definition of the residuated lattice operator as not tautologous. We evaluate the perfect fuzzy function and strong (surjective) fuzzy function as not tautologous, but logical equivalents. This refutes the fuzzy functions and distinctions. These form a non tautologous fragment of the universal logic VL4.
Category: Set Theory and Logic

[15] viXra:1908.0220 [pdf] submitted on 2019-08-12 06:15:51

Refutation of Zadeh's Swedes and Italians Challenge as a Logic Problem

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.

Abstract: For Zadeh's Swedes and Italians challenge problem, we evaluate the linguistic weighted average (LWA) for the conjecture that Swedes are on average taller than Italians. None is tautologous, refuting the challenge as a logic problem. These form a non tautologous fragment of the universal logic VL4.
Category: Set Theory and Logic

[14] viXra:1908.0219 [pdf] submitted on 2019-08-12 06:16:53

Refutation of Shared Variables in Cross Axiom Models of Alternating Turing Machines

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 evaluate shared variables for the reduction of alternating Turing machines (ATMs) to subset space logic (SSL). The purpose of shared variables is to use binary counters for mapping cross-axiom models. None is tautologous, to refute cross-axiom models in the completeness conjectures. These form non tautologous fragment of the universal logic VL4.
Category: Set Theory and Logic

[13] viXra:1908.0211 [pdf] submitted on 2019-08-11 10:48:58

Refutation of the Hrushovski Construction, to Confirm Lachlan and Zil'ber

Authors: Colin James III
Comments: Pages.

A condition for the Hrushovski construction is not tautologous, refuting it. This also denies alleged refutations using it, namely, to confirm the Lachlan conjecture and Zil'ber conjecture. The construction forms a non tautologous fragment of the universal logic VL4.
Category: Set Theory and Logic

[12] viXra:1908.0163 [pdf] submitted on 2019-08-09 18:11:53

Refutation of Abductive Repair in Ontology Engineering

Authors: Colin James III
Comments: 3 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 evaluate the stated example of complete-debug problem (CDP) in formulas framing the definitions, oracles, and repairs. None is tautologous. This forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[11] viXra:1908.0146 [pdf] submitted on 2019-08-08 08:03:40

Refutation of Leibniz' Identity of Indiscernibles and Leo-III Theorem Prover

Authors: Colin James III
Comments: Pages.

Leibniz' identity of indiscernibles as ∀x∀y[∀F(Fx↔Fy)→x=y] is not tautologous. Consequently the Leo-III theorem prover for higher-order paramodulated extensional logic is also refuted. These form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[10] viXra:1908.0137 [pdf] submitted on 2019-08-07 11:08:28

Refutation of Completeness of Temporal Logics Over Infinite Intervals

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 evaluate three pairs of equations for interval temporal logics [ITL]. None is tautologous, refuting completeness of temporal logics for finite and infinite intervals. These form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[9] viXra:1908.0136 [pdf] submitted on 2019-08-07 11:10:21

Refutation of the Variety of Distributive Bilattices

Authors: Colin James III
Comments: 1 Page. 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.

The example stated of a distributive bilattice is not tautologous. This refutes that variety and forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[8] viXra:1908.0135 [pdf] submitted on 2019-08-07 11:11:24

Refutation of Varieties of Positive 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: info@cec-services dot com. See updated abstract at ersatz-systems.com.

Four definitions of positive modal logic (PML) are not tautologous. This refutes positive modal algebra (PML) on the bounded distributive lattice and forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[7] viXra:1908.0125 [pdf] submitted on 2019-08-07 21:45:28

Refutation of Saturated Free Algebras (Revisited) and Almost Indiscernible Theories

Authors: Colin James III
Comments: 1 Page. 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 evaluate two papers as probabilistic vector spaces with no bivalent basis, non existence, and no meaning. This refutes saturated free algebras and "almost indiscernible theory", forming a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[6] viXra:1908.0079 [pdf] submitted on 2019-08-04 11:28:10

Refutation of the Term Rewriting Approach to Automated Theorem Proving

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.

Using three group axioms, two examples for an original and rewritten proofs are not tautologous. This refutes the term rewriting approach for automated theorem proving to form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[5] viXra:1908.0071 [pdf] submitted on 2019-08-05 04:49:12

Refutation of Symmetry Breaking, Boolean Skeletons, Ensemble Technique, and SMT Solver

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.

The SMT problem as stated is not a theorem, and the derivation of Boolean skeletons, while equivalent, are not the SMT problem. This refutes the symmetry breaking technique and also the attendant ensemble technique. What follows is the SMT solver is refuted, forming a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[4] viXra:1908.0067 [pdf] submitted on 2019-08-05 06:04:40

Refutation of Classification of Finitary, Algebraizable Logics as Undecidable in Hilbert Calculi

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.

Two axioms as tested are not tautologous, to refute the Hilbert calculus as claimed. This refutes the conjecture of classification of finitary, algebraizable logic as undecidable in Hilbert calculi. That also disallows a follow-on article. These form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[3] viXra:1908.0042 [pdf] submitted on 2019-08-02 10:00:13

Refutation of Löwner (Loewner) Order and Quantum Temporal Logic

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 evaluate the Löwner order ⊑ for positive definite as the basis for quantum temporal logic (QTL). The operator is not tautologous. We also evaluate the semantics for QTL in three operators, also not tautologous. These form non tautologous fragments for both in the universal logic VŁ4.
Category: Set Theory and Logic

[2] viXra:1908.0039 [pdf] submitted on 2019-08-02 18:44:05

Refutation of the Wellfoundedness of the Multiset Order

Authors: Colin James III
Comments: 1 Page. 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.

The two equations for an inductive proof of the wellfoundedness of the multiset order are not tautologous, and form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[1] viXra:1908.0038 [pdf] submitted on 2019-08-02 19:35:42

Refutation of the Church-Rosser Theorem

Authors: Colin James III
Comments: 1 Page. 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.

The Church-Rosser theorem evaluates as not tautologous, hence forming a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic