Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 

Saved Queries

Sign in to use this feature.

Search Filter Reset All

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Subjects Reset
Select Subjects

Journals

remove_circle_outline
remove_circle_outline
Add Journals Reset
Select Journals

Article Types

remove_circle_outline
remove_circle_outline
Add Article Types Reset
Select Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
Add Countries / Regions Reset
Select Countries / Regions
Update Search
share announcement

Search Results (3)

Search Parameters:
Keywords = law of the excluded middle

Order results
Result details
Results per page
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
14 pages, 4030 KB  
Article
Understanding the Axioms and Assumptions of Logical Mathematical Systems through Raster Images: Application to the Construction of a Likert Scale
by Queralt Viladevall, Salvador Linares-Mustarós, Maria Antonia Huertas and Joan-Carles Ferrer-Comalat
Axioms 2023, 12(12), 1064; https://doi.org/10.3390/axioms12121064 - 21 Nov 2023
Viewed by 1849
Abstract
This article presents different artistic raster images as a resource for correcting misconceptions about different laws and assumptions that underlie the propositional systems of binary logic, Łukasiewicz’s trivalent logic, Peirce’s trivalent logic, Post’s n-valent logic, and Black and Zadeh’s infinite-valent logic. Recognizing similarities [...] Read more.
This article presents different artistic raster images as a resource for correcting misconceptions about different laws and assumptions that underlie the propositional systems of binary logic, Łukasiewicz’s trivalent logic, Peirce’s trivalent logic, Post’s n-valent logic, and Black and Zadeh’s infinite-valent logic. Recognizing similarities and differences in how images are constructed allows us to deepen, through comparison, the laws of bivalence, non-contradiction, and excluded middle, as well as understanding other multivalent logic assumptions from another perspective, such as their number of truth values. Consequently, the first goal of this article is to illustrate how the use of visualization can be a powerful tool for better understanding some logic systems. To demonstrate the utility of this objective, we illustrate how a deeper understanding of logic systems helps us appreciate the necessity of employing Likert scales based on the logic of Post or Zadeh, which is the second goal of the article. Full article
(This article belongs to the Special Issue Swarm Intelligence with Mathematical Fuzzy Logic for Computer Science in Real-World Applications)
►▼ Show Figures

Figure 1

11 pages, 272 KB  
Article
Algorithms for Quantum Computation: The Derivatives of Discontinuous Functions
by Ed Gerck
Mathematics 2023, 11(1), 68; https://doi.org/10.3390/math11010068 - 25 Dec 2022
Viewed by 4456
Abstract
We hope this work allows one to calculate large prime numbers directly, not by trial-and-error, but following a physical law. We report—contrary to conventional assumptions—that differentiation of discontinuous functions (DDF) exists in the set Q, which becomes central to algorithms for quantum computation. [...] Read more.
We hope this work allows one to calculate large prime numbers directly, not by trial-and-error, but following a physical law. We report—contrary to conventional assumptions—that differentiation of discontinuous functions (DDF) exists in the set Q, which becomes central to algorithms for quantum computation. DDF have been thought to exist not in the classical sense, but using distributions. However, DDF using distributions still is defined in terms of mathematical real-numbers (MRN), and do not address the Problem of Closure, here investigated. These facts lead to contradictions using MRN, solved by this work, providing a new unbounded class of physical solutions using physical numbers in quantum mechanics (QM), that were always there (just hidden), allowing DDF without distributions, or MRN. It is worthwhile to see this only in mathematics, to avoid the prejudices found in physics, as this reforms both general relativity and QM. This confirms the opinions of Nicolas Gisin that MRN are non-computable with probability 1, and Niels Bohr that physics is not reality, it is a fitting story about reality. Mathematics can get closer to reality, surprisingly. We just have to base mathematics on nature, not on how it defines nature. Full article
(This article belongs to the Topic Evolutionary Differential Equations, Dynamic Systems, Computation and Optimization)
►▼ Show Figures

Figure 1

4 pages, 133 KB  
Concept Paper
The Three Laws of Thought, Plus One: The Law of Comparisons
by Thomas L. Saaty
Axioms 2014, 3(1), 46-49; https://doi.org/10.3390/axioms3010046 - 10 Feb 2014
Cited by 2 | Viewed by 56762
Abstract
The rules of logic are nearly 2500 years old and date back to Plato and Aristotle who set down the three laws of thought: identity, non-contradiction, and excluded middle. The use of language and logic has been adequate for us to develop mathematics, [...] Read more.
The rules of logic are nearly 2500 years old and date back to Plato and Aristotle who set down the three laws of thought: identity, non-contradiction, and excluded middle. The use of language and logic has been adequate for us to develop mathematics, prove theorems, and create scientific knowledge. However, the laws of thought are incomplete. We need to extend our logical system by adding to the very old laws of thought an essential yet poorly understood law. It is a necessary law of thought that resides in our biology even deeper than the other three laws. It is related to the rudiments of how we as living beings, and even nonliving things, respond to influences as stimuli. It helps us discriminate between being ourselves and sensing that there is something else that is not ourselves that even amoebas seem to know. It is the intrinsic ability to sense and distinguish. This fourth law is the law of comparisons. Although it has been missing from our logical deductions it underlies the other three laws of thought because without it we cannot know what is and what is not. Full article
(This article belongs to the Special Issue Axioms of Decision Support System)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying article 1-50 on page 1 of 1.
Back to TopTop