On the definition of modal operators in fuzzy logic

Author(s):  
H. Thiele
2019 ◽  
Vol 29 (8) ◽  
pp. 1311-1344 ◽  
Author(s):  
Lauri T Hella ◽  
Miikka S Vilander

Abstract We propose a new version of formula size game for modal logic. The game characterizes the equivalence of pointed Kripke models up to formulas of given numbers of modal operators and binary connectives. Our game is similar to the well-known Adler–Immerman game. However, due to a crucial difference in the definition of positions of the game, its winning condition is simpler, and the second player does not have a trivial optimal strategy. Thus, unlike the Adler–Immerman game, our game is a genuine two-person game. We illustrate the use of the game by proving a non-elementary succinctness gap between bisimulation invariant first-order logic $\textrm{FO}$ and (basic) modal logic $\textrm{ML}$. We also present a version of the game for the modal $\mu $-calculus $\textrm{L}_\mu $ and show that $\textrm{FO}$ is also non-elementarily more succinct than $\textrm{L}_\mu $.


Author(s):  
Евгений Николаевич Коровин ◽  
Екатерина Ивановна Новикова ◽  
Олег Валерьевич Родионов

В статье рассматриваются разработки методов интеллектуальной поддержки процесса диагностики сахарного диабета, а также определение его типа. В последние годы количество людей, страдающих данным заболеванием, неуклонно растет, а без своевременной диагностики эта патология может нанести огромный вред организму человека. Сахарный диабет 1 типа опасен тем, что в основном возникает у людей молодого возраста. Оперативное обнаружение диабета, а также определение его типа, поможет не только избежать возможных осложнений, но и в некоторых случаях предотвратить смерть пациента. Информационные технологии все чаще используются в различных сферах деятельности для разработки новых или совершенствования существующих методов обработки данных, особенно это можно заметить в сфере медицины. В настоящее время врач самостоятельно ставит диагноз, основываясь на результатах различных анализов, однако, для ускорения процесса принятия решения, можно воспользоваться методами математического моделирования, а именно: моделями диагностики диабета на основе нечеткой логики. Для наибольшего удобства данный способ распознавания заболевания впоследствии можно реализовать в информационно-программное обеспечение, которое сможет еще больше увеличить эффективность и скорость распознавания патологии The article discusses the issues of the incidence of diabetes in the population, in particular, the definition of its type. In recent years, the number of people suffering from this disease has been steadily growing, and without timely diagnosis, this pathology can cause enormous harm to the human body. Prompt detection of diabetes, as well as determination of its type, will help not only avoid possible complications, but also in some cases prevent the death of the patient. Information technology is increasingly being used in various fields of activity to develop new or improve existing methods of data processing, especially in the field of medicine. Currently, the doctor independently makes a diagnosis based on the results of various analyzes, however, to speed up the decision-making process, you can use the methods of mathematical modeling, namely, models of diabetes diagnostics based on fuzzy logic. For the greatest convenience, this method of disease recognition can subsequently be implemented in information software, which can further increase the efficiency and speed of pathology recognition


Author(s):  
Amira Aloui ◽  
Amel Grissa Touzi

Flexible queries have recently received increasing attention to better characterize the data retrieval. In this paper, a new flexible querying approach using ontological knowledge is proposed. This approach presents an FCA based methodology for building ontologies from scratch then interrogating them intelligently through the fusion of conceptual clustering, fuzzy logic, and FCA. The main contribution is the definition of the ontology rom classes resulting from a preliminary classification of the data and not the initial data. The data cleansing provides a simple ontology and an optimal research of relevant data taking into account the preferences cited by the user in his initial interrogation. To realize this approach, a new platform called “FO-FQ Tab plug-in” is implemented. This plug-in is integrated within the ontology editor Protégé to allow building fuzzy ontologies from large databases and querying them intelligently


Author(s):  
Lajmi Fatma ◽  
Jalel Ghabi ◽  
Hedi Dhouibi

In this article, the authors propose a new approach for modelling and failure analysis by combining the graphical representation provided by Petri nets and fuzzy logic. The graphical method is used for describing the relationship between conditions and events. The use of Petri nets in failure analysis enables replacing logic gate functions in fault trees. The Fuzzy logic technique allows natural language descriptions of process entities as well as an if-then rule-based definition of production. In addition, this study devises an alternative, a trapezoidal graph method in order to account for failure scenarios. Examples validating this novel method in dealing with failure analysis are also provided.


1982 ◽  
Vol 14 (1) ◽  
pp. 37-42 ◽  
Author(s):  
S. V. L. N. Rao ◽  
J. Prasad
Keyword(s):  

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