Set Theory and Logic

1909 Submissions

[14] viXra:1909.0431 [pdf] submitted on 2019-09-20 19:11:30

Refutation of Interpretability Logic, and Vaught and Adjunctive Set Theory

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 axioms and inference rules of interpretability logics ILM and TOL with none tautologous, making doubtful the claimed completeness. We then turn to Vaught and adjunctive set theory with neither tautologous. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[13] viXra:1909.0411 [pdf] submitted on 2019-09-19 13:22:46

Refutation of a Modal Logic for Supervised Learning

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 ten conjectures which are not tautologous, and with four as contradictory. This refutes the approach and models of modal logic for supervised learning as a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[12] viXra:1909.0369 [pdf] submitted on 2019-09-17 14:33:15

Resolution in Classical Modal Logic of a Security Barrier Model

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 three states of a security barrier example. For the security barrier as equivalent to the road width, the two cases are staying on the road, or staying on the road or going off of the road. Staying on the road is not a theorem. However staying on the road or going off road is a theorem. For the security barrier as larger than the road width, then staying on the road is effectively enforced as a theorem. This evaluation concludes that casting a problem to substructural epistemic resource logic is an unneeded effort for model resolution. The resolution in classical model logic of a security barrier model relegates the authors’ conjectures to non tautologous fragments of the universal logic VŁ4.
Category: Set Theory and Logic

[11] viXra:1909.0367 [pdf] submitted on 2019-09-17 15:15:52

Recent Advances in the Modal Model Checker Meth8 with the VŁ4 Universal Logic

Authors: Colin James III
Comments: 34 Pages. Copyright 2016-2019 by Colin James III All rights reserved.

We use the Meth8/VŁ4 modal logic model checker to evaluate 629 artifacts in 3274 assertions to refute 2726 as non tautologous (83.3%). This is the abstract, table of results, and table of contents. The current document in 1045-pages includes the availability of Meth8/VŁ4 and is requestable from info@ersatz-systems.com.
Category: Set Theory and Logic

[10] viXra:1909.0365 [pdf] submitted on 2019-09-17 21:57:03

Refutation of Axiomatizing Logics of Fuzzy Preferences Using Graded Modalities

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 fuzzy preference relation of the assumed ∧-transitivity theorem as not tautologous, relegating it, along with the subsequent minimal modal logics of a finite residuated lattice and the Bulldozed method, as non tautologous fragments of the universal logic VŁ4.
Category: Set Theory and Logic

[9] viXra:1909.0335 [pdf] submitted on 2019-09-17 01:14:44

Refutation of Modal Operators on Rings of Continuous Functions

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 five expressions for a definition (2), two remarks (2), and a lemma proof (1). None is tautologous. This refutes the titled conjecture which drags in the Hausdorff and Stone topologies, Kripke frames, and dualities of Gelfand-Naimark-Stone and Esakia-Goldblatt. These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[8] viXra:1909.0293 [pdf] replaced on 2019-09-17 07:00:17

Showing the Real Numbers are Denumerable Using Binary Digit Ratios

Authors: James Edwin Rock
Comments: 2 Pages.

Cantor’s diagonal argument starts with an invalid premise. Using binary decimals, we calculate the ratio of ones to the total number of digits for decimals in the closed interval [0, 1]. We use these ratios to show that the real numbers are denumerable. The reals numbers have the same cardinality as the power set of the natural numbers. There is no hierarchy of infinities in Level Set Theory.
Category: Set Theory and Logic

[7] viXra:1909.0284 [pdf] submitted on 2019-09-13 19:42:35

Refutation of Predicate Transformer Semantics for Hybrid Systems

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 steps of the approach to verify hybrid systems in the style of dynamic logic. Top tier input assumes modal Kleene algebras which are not bivalent. Middle tier processing invokes binary relations (which we do not test). Bottom tier output produces Lipschitz continuous vector fields as verification of hybrid store dynamics, which are not bivalent. This refutes the Isabelle framework for hybrid systems verification, and forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[6] viXra:1909.0256 [pdf] submitted on 2019-09-11 11:50:18

Square of Opposition as Meth8 Corrected

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 modern revision of the square of opposition is not tautologous and forms a non tautologous fragment of the universal logic VŁ4. Consequently we redefine the square so that it is validated as tautologous. Instead of definientia using implication for universal terms or conjunction for existential terms, we adopt the equivalent connective for all terms. The modal modifiers necessity and possibility map quantifiers as applying to the entire terms rather than to the antecedent within the terms.
Category: Set Theory and Logic

[5] viXra:1909.0240 [pdf] submitted on 2019-09-10 16:35:12

Refutation of Bitstring and Question-Answer Semantics

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 bitstring semantics and its follow-on by partition. Its ordered set of exhaustive predicates is not bivalent but a probabilistic vector space. Its calculus of relations is not tautologous. Hence its broader framework of question-answer semantics (QAS) is not tautologous. The conjecture of “generalizing the Aristotelian square within one common gathering” is denied. What is affirmed is the Meth8 corrected, modern, revised square of opposition is a square, to mean the following conjectures are probabilistic vector spaces: collapsed number line of opposition; non-standard quadrilateral of oppositions; and colored square of oppositions. Bitstring semantics and the extended QAS form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[4] viXra:1909.0237 [pdf] submitted on 2019-09-10 20:36:44

Refutation of Cook-Reckhow Definition

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 Cook-Reckhow definition as represented for conjectures of a polynomial equation and integer linear inequalities with both as not tautologous. Hence we do not evaluate the conjecture of a relational form on which the paper subsequently relies. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[3] viXra:1909.0081 [pdf] submitted on 2019-09-04 19:09:54

Refutation of Automorphism and Borel Dynamics

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 definition of automorphism as not tautologous, hence refuting conjectures of Borel dynamics, and forming non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[2] viXra:1909.0079 [pdf] submitted on 2019-09-04 23:26:42

Refutation of Skolem Witness and Counter-Example Functions

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 Skolem witness function and counter-example function. The functions are not tautologous and not counter-exemplary. This refutes the conjecture of a witness function as opposite a counter-example function and forms a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic

[1] viXra:1909.0058 [pdf] submitted on 2019-09-03 23:11:03

Refutation of the Russell-Prawitz 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 Russell-Prawitz embedding as not tautologous. Hence atomization of universal instantiation does not follow (nor does proof reduction, weakening of dinaturality conversion, or strict simulation). These conjectures form a non tautologous fragment of the universal logic VŁ4.
Category: Set Theory and Logic