Lidé na fakultě
Mgr. Pavel Provinský, Ph.D.

2021

The text introduces floppy logic, which is a new multi-valued logic. Floppy logic consistently links fuzzy sets to probability theory. The most important results of this work include proof that all statements equivalent in standard two-valued logic are also equivalent in floppy logic. It follows that floppy logic retains all the properties of standard two-valued logic which can be expressed as an equivalence. Another important result is the proof that floppy logic is a model of Kolmogorov probability theory. We can therefore apply all the concepts and tools of probability theory in floppy logic. Much focus was given to practical examples of work with floppy logic. Floppy logic is compared to several other theories and also presented in historical context.

Disertační práce (PhD)

2020, Neural Network World, 30 (3), p. 193-209), ISSN 1210-0552

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.

Článek v periodiku excerpovaném SCI Expanded

2018, Rozhledy matematicko-fyzikální, 93 (3), p. 1-8), ISSN 0035-9343

Článek pojednává o mnoha druzích dláždění, periodických i o kvaziperiodických. Výklad je provázen mnoha obrázky.

Článek v odborném recenzovaném periodiku česky

2018, Neural Network World, 28 (5), p. 473-494), ISSN 1210-0552

This article provides a simple and practical tutorial on how to use floppy logic. The floppy logic is a method suitable for systems control and description. It preserves the simplicity of the fuzzy logic and the accuracy of the probability theory. The floppy logic allows to work consistently and simultaneously with data in the form of exact numbers, probability distributions and fuzzy sets.

Článek v periodiku excerpovaném SCI Expanded

2018, Young Transportation Engineers Conference 2018, Praha, Fakulta dopravní), ISBN 978-80-01-06464-1

Floppy logika je nový nástroj pro popis a řízení systémů. Může být použita např. při řízení křižovatek či autonomních vozidel, může ale i předpovídat počasí. Floppy logika je založena na prověřené a úspěšné fuzzy logice, ale, v porovnání s ní, má několik velkých výhod: Floppy logika může konzistentně pracovat s přesnými čísly, rozděleními pravděpodobnosti, fuzzy množinami i přesnými množinami současně. Floppy logika je kompatibilní s teorií pravděpodobnosti, tudíž můžeme používat všechny pravděpodobnostní nástroje. Všechny výroky, které jsou ekvivalentní ve standardní dvouhodnotové logice, jsou ve floppy logice ekvivalentní také. Všechny logické operace jsou jednoznačné. Není zde možnost výběru z mnoha různých triangulárních norem a konorem jako ve fuzzy logice.

Stať ve sborníku z mezinár. konf. česky

2017, Neural Network World, 27 (5), p. 479-497), ISSN 1210-0552

This article introduces a floppy logic - a new method of work with fuzzy sets. This theory is a nice connection between the logic, the probability theory and the fuzzy sets. The floppy logic has several advantages compared to the fuzzy logic: All propositions, which are equivalent in the bivalent logic, are equivalent in the floppy logic too. Logical operations are modeled unambiguously, not by using many alternative t-norms and t-conorms. In floppy logic, we can use the whole apparatus of Kolmogorov's probability theory. This theory allows to work consistently with systems that are described by fuzzy sets, probability distributions and accurate values simultaneously.

Článek v periodiku excerpovaném SCI Expanded