Set Theory and Logic

1911 Submissions

[21] viXra:1911.0488 [pdf] submitted on 2019-11-29 06:32:40

Logic Cila (Da Costa’s C1) Confirmed as Algebraizable, Refuting Paraconsistent Set Theory

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.

For logic Cila, we evaluate the implication connective truth table from 2001 which is not tautologous. This means the implication connective is algebraizable and refuted, and further refutes paraconsistent logic, and the derived conjecture of paraconsistent set theory as based thereon from 2019. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[20] viXra:1911.0464 [pdf] submitted on 2019-11-27 13:35:40

Refutation of Leibniz’ Indiscernibility of Identicals and Identity of Indiscernibles as Equivalent

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 Leibniz’ law(s) of indiscernibility of identicals and identity of indiscernibles which are not equivalents, and the latter is not tautologous. This contradicts Leibniz’ 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

[19] viXra:1911.0461 [pdf] submitted on 2019-11-26 19:28:46

Refutation of More Axioms: Tarski’s; ax-Groth; Grothpw; Limitation of Size; and Class of All Sets

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 Tarski’s axiom, ax-groth, grothpw, the axiom of the limitation of size, and the class of all sets as not tautologous. This further refutes the Tarski–Grothendieck set theory. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[18] viXra:1911.0434 [pdf] submitted on 2019-11-25 10:11:25

Refutation of Recursive Enumerability and Elementary Frame Definability in Predicate Modal Logic

Authors: Colin James III
Comments: 4 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 equations as not tautologous to show the standard translation of a predicate model into a logic language fails. We evaluate five equations as not tautologous, with the last result as contradictory, to show a class defined to contain frames fails to satisfy a classical first-order formula or to claim logic system equivalency. The conjecture of recursive enumerability and elementary frame definability in predicate modal logic is refuted. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[17] viXra:1911.0416 [pdf] submitted on 2019-11-24 17:03:44

Confirmation of Modus Inversus as a bi-Valent Connective (And Denial of Its Refutation)

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 modus inversus, confirming it as a bi-valent connective. This denies its anonymous refutation to form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[16] viXra:1911.0411 [pdf] submitted on 2019-11-23 22:57:47

Refutation of Brouwer’s Dense Linear Orderings (Dlo)

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 three axioms of Brouwer’s dense linear orderings (DLO) as not tautologous, hence that as a basis for refuting equality and equivalence, intuitionistically. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[15] viXra:1911.0390 [pdf] submitted on 2019-11-23 06:58:00

Number Theory Beyond Frege on the Necessity of Open Arity

Authors: Hannes Hutzelmeyer
Comments: 13 Pages.

A closer look at mathematical proofs led Gottlob Frege to realize that Aristotle's syllogism logic was not sufficient for many theorems. He developped what today is called first-order predicate logic. It is usually thought that predicate logic is sufficient for the theory of natural numbers. However, this first step of modern logic development again is not sufficient. One needs another step, especially to allow for so-called open arity of arrays. This second step cannot be done in general in object-language based on predicate logic but only by metalanguage. Therefore one needs something like the FUME-method (put forward by the author) which allows for a precise treatment of both language levels. Dot-dot-dot … is not admissible in predicate logics as it needs some kind of recursion. In metalanguage, however, one has to introduce some basic recursion right from the setup (but it is much weaker than primitive recursion). For natural numbers two examples are given, one for a concrete version of Robinson arithmetic and one for recursive arithmetic. Without the second step to metalanguage one cannot express some of the most important so-called theorems of number theory in a direct fashion, leave alone prove them. Actually some are not theorems but metatheorems. The examples comprise Chinese remainders, Gödel's beta-function, little Gauss's summing up of numbers, Euclid's unlimited primes and the canonical representation of a natural number (fundamental theorem of natural arithmetic). After one has included the second step which allows one to talk about open arities in metalanguage one can tackle the problem of talking about number-arrays in object language. One can do this to a certain extent by coding number-arrays by (usually) two numbers. This can be done even in Robinson arithmetic using 'Gödel's beta-function'. But one has to make use of the second step before one can return to object-language. Of course, the introduction of two tiers, i.e. object-language and metalanguage, is necessary for many other areas of mathematics, if not to say, most of them.
Category: Set Theory and Logic

[14] viXra:1911.0375 [pdf] submitted on 2019-11-22 02:36:08

Непригодность общепринятых стереотипных тавтологий классической математики для доказательства теорем при классическом подходе к доказательству теорем

Authors: Viktoria Kondratenko
Comments: 9 Pages.

Оторванность гипотетических теорий от реалий живой материи стала причиной проникновения мистики в научные теории. При мистическом мышлении идея применения аналитического метода решения задач познания в голову не приходит. Диалектическая логика в отличие от мистики утверждает обратное: любые проблемные задачи познания жизнедеятельности процессов и явлений мироздания разрешимы исключительно аналитическим путѐм, при этом единственным методом. Автором создана универсальная и формальная теория решения интеллектуальных (т.е. не имеющих заранее известных алгоритмов решения) задач, связанных с познанием жизнедеятельности естественных и рукотворных процессов в любых явлениях мироздания – метод аксиоматического моделирования Кондратенко, эффективность которого достигается путѐм корректной постановки задачи и еѐ решения чисто формальным методом. Корректность постановки задачи означает, прежде всего, признание несостоятельности всех гипотетических (не подтверждѐнных результатами натурного экспериментирования с предметом познания) теорий. В качестве примера в статье рассматривается парадокс при классическом подходе к доказательству теорем, состоящий в непригодности общепринятых стереотипных тавтологий классической математики для доказательства теорем.
Category: Set Theory and Logic

[13] viXra:1911.0374 [pdf] submitted on 2019-11-22 02:39:06

Формальная модель диалектической логики управления жизнеобеспечивающими функциями психики человека

Authors: Viktoria Kondratenko
Comments: 9 Pages.

Диалектическая логика управления любыми функциональными системами организма человека вытекает из концептуальных знаний о жизнедеятельности этих функциональных систем, добытых исключительно путём натурного экспериментирования с ними. Поэтому концептуальные знания о жизнедеятельности каждой исследуемой функциональной системы человека должны предшествовать описанию сущности логики управления ею. Психика человека является одной из важнейших функциональных систем организма человека. В статье представлены основополагающие концепты жизнедеятельности этой системы, которые позволяют выявить сущность диалектической логики управления её жизнеобеспечивающими функциями, и формальная модель диалектической логики управления функциональной системой психики человека
Category: Set Theory and Logic

[12] viXra:1911.0350 [pdf] submitted on 2019-11-20 09:59:46

Refutation of Premise Rule in Intuitionistic Set Theories

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 seminal equation of the conjecture which is not tautologous, hence refuting the premise rule in intuitionistic set theories. This forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[11] viXra:1911.0334 [pdf] submitted on 2019-11-18 23:21:45

Refutation of Justification Based Reasoning for Dynamic Conflict Resolution

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 first evaluate the last of seven examples, which is not tautologous. This refutes the conjecture of justification based reasoning for dynamic conflict resolution, to form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[10] viXra:1911.0320 [pdf] submitted on 2019-11-18 08:50:16

A Refutation Of Ilija Barukˇci ́c’s Modus Inversus AndConclusions Following From It

Authors: Nhef Luminati
Comments: 6 Pages.

In this paper the general validity of the methodological approach of frequent vixra.org contributor Ilija Barukčić are examined and refuted.
Category: Set Theory and Logic

[9] 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

[8] 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

[7] 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

[6] 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

[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