Floppy Logic as a Generalization of Standard Boolean Logic

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21260%2F20%3A00344283" target="_blank" >RIV/68407700:21260/20:00344283 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.14311/NNW.2020.30.014" target="_blank" >https://doi.org/10.14311/NNW.2020.30.014</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14311/NNW.2020.30.014" target="_blank" >10.14311/NNW.2020.30.014</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Floppy Logic as a Generalization of Standard Boolean Logic

Popis výsledku v původním jazyce

The topic of this article is floppy logic, a new multi-valued logic. Floppy logic is related to fuzzy logic and the theory of probability, but it also has interesting links to probability logic and standard Boolean logic. It provides a consistent and simple theory that is easy to apply in practice. This article examines the isomorphism theorem, which plays an important role in floppy logic. The theorem is described and proved. The most important consequences of the isomorphism theorem are: 1. All statements which are equivalent in standard Boolean logic are also equivalent in floppy logic. 2. Floppy logic has all the properties of standard Boolean logic which can be formulated as an equivalence. These include, for example, distributivity, the contradiction law, the law of excluded middle, and others. The article mainly examines floppy implication. We show that floppy implication does not satisfy Adam’s Thesis and that floppy logic is not limited by Lewis’ triviality result. We also present a range of inference rules which are generalizations of modus ponens and modus tollens. These rules hold in floppy logic, and of course, also apply to standard Boolean logic. All these results lead us to the notion that floppy logic is a many-valued generalization of standard Boolean logic.

Název v anglickém jazyce

Floppy Logic as a Generalization of Standard Boolean Logic

Popis výsledku anglicky

The topic of this article is floppy logic, a new multi-valued logic. Floppy logic is related to fuzzy logic and the theory of probability, but it also has interesting links to probability logic and standard Boolean logic. It provides a consistent and simple theory that is easy to apply in practice. This article examines the isomorphism theorem, which plays an important role in floppy logic. The theorem is described and proved. The most important consequences of the isomorphism theorem are: 1. All statements which are equivalent in standard Boolean logic are also equivalent in floppy logic. 2. Floppy logic has all the properties of standard Boolean logic which can be formulated as an equivalence. These include, for example, distributivity, the contradiction law, the law of excluded middle, and others. The article mainly examines floppy implication. We show that floppy implication does not satisfy Adam’s Thesis and that floppy logic is not limited by Lewis’ triviality result. We also present a range of inference rules which are generalizations of modus ponens and modus tollens. These rules hold in floppy logic, and of course, also apply to standard Boolean logic. All these results lead us to the notion that floppy logic is a many-valued generalization of standard Boolean logic.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Neural Network World

ISSN

1210-0552

e-ISSN

—

Svazek periodika

30

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

17

Strana od-do

193-209

Kód UT WoS článku

000572850100004

EID výsledku v databázi Scopus

2-s2.0-85092418146