The glorious past! A grim future? Petr Cintula 1 and Carles Noguera 2 1 Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic 2 Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic Petr Cintula and Carles Noguera (CAS) The future of MFL I 1 / 27
A story . . . On a foggy autumn day nearly 800 years ago a traveller happened upon a large group of workers adjacent to the River Avon. Curiosity convinced him to inquire about their work. Petr Cintula and Carles Noguera (CAS) The future of MFL I 2 / 27
A story . . . On a foggy autumn day nearly 800 years ago a traveller happened upon a large group of workers adjacent to the River Avon. Curiosity convinced him to inquire about their work. With a slight detour he moved toward the first of the three tradesmen and said “my dear fellow what is it that you are doing?” Petr Cintula and Carles Noguera (CAS) The future of MFL I 2 / 27
A story . . . On a foggy autumn day nearly 800 years ago a traveller happened upon a large group of workers adjacent to the River Avon. Curiosity convinced him to inquire about their work. With a slight detour he moved toward the first of the three tradesmen and said “my dear fellow what is it that you are doing?” The man continued his work and grumbled, “I am cutting stones.” Petr Cintula and Carles Noguera (CAS) The future of MFL I 2 / 27
A story . . . On a foggy autumn day nearly 800 years ago a traveller happened upon a large group of workers adjacent to the River Avon. Curiosity convinced him to inquire about their work. The traveller moved toward the second of the three and repeated the question. The man stopped his work, ever so briefly, and stated: Petr Cintula and Carles Noguera (CAS) The future of MFL I 2 / 27
A story . . . On a foggy autumn day nearly 800 years ago a traveller happened upon a large group of workers adjacent to the River Avon. Curiosity convinced him to inquire about their work. The traveller moved toward the second of the three and repeated the question. The man stopped his work, ever so briefly, and stated: “I am stonecutter, I came to Salisbury from the north to work but as soon as I earn ten quid I will return home.” Petr Cintula and Carles Noguera (CAS) The future of MFL I 2 / 27
A story . . . On a foggy autumn day nearly 800 years ago a traveller happened upon a large group of workers adjacent to the River Avon. Curiosity convinced him to inquire about their work. When he reached the third worker he once again asked the original question. This time the worker paused and replied Petr Cintula and Carles Noguera (CAS) The future of MFL I 2 / 27
A story . . . On a foggy autumn day nearly 800 years ago a traveller happened upon a large group of workers adjacent to the River Avon. Curiosity convinced him to inquire about their work. When he reached the third worker he once again asked the original question. This time the worker paused and replied “I am a mason and I am building a cathedral.” Petr Cintula and Carles Noguera (CAS) The future of MFL I 2 / 27
A story . . . The worker continued, I have journeyed many miles to be part of the team that is constructing this magnificent cathedral. I have spent many months away from my family and I miss them dearly. However, I know how important Salisbury Cathedral will be one day and I know how many people will find sanctuary and solace here. I know this because the Bishop once told me his vision for this great place. He described how people would come from all parts to worship here. He also told that the Cathedral would not be completed in our days but that the future depends on our hard work. Petr Cintula and Carles Noguera (CAS) The future of MFL I 3 / 27
Now, the real story Petr Cintula and Carles Noguera (CAS) The future of MFL I 4 / 27
Now, the real story of MFL Petr Cintula and Carles Noguera (CAS) The future of MFL I 4 / 27
Origin 1: Philosophy — Vagueness Problem: Petr Cintula and Carles Noguera (CAS) The future of MFL I 5 / 27
Origin 1: Philosophy — Vagueness Problem: There are heaps of sand Petr Cintula and Carles Noguera (CAS) The future of MFL I 5 / 27
Origin 1: Philosophy — Vagueness Problem: There are heaps of sand If I remove one grain from a heap of sand, I still have a heap of sand. Petr Cintula and Carles Noguera (CAS) The future of MFL I 5 / 27
Origin 1: Philosophy — Vagueness Problem: There are heaps of sand If I remove one grain from a heap of sand, I still have a heap of sand. Therefore, one grain of sand is a heap of sand . Petr Cintula and Carles Noguera (CAS) The future of MFL I 5 / 27
Origin 2: Logic — Many-valued logics Problem: Petr Cintula and Carles Noguera (CAS) The future of MFL I 6 / 27
Origin 2: Logic — Many-valued logics Problem: Classical logic is boring http://www.xkcd.com/74/ Petr Cintula and Carles Noguera (CAS) The future of MFL I 6 / 27
Origin 2: Logic — Many-valued logics Problem: Classical logic is boring http://www.xkcd.com/74/ Having more truth degrees to play with is fun even for such noble logicians as: Łukasiewicz, Tarski, Gödel, Skolem, Horn, . . . Petr Cintula and Carles Noguera (CAS) The future of MFL I 6 / 27
Origin 3: Engineering — Fuzzy set theory Problem: Petr Cintula and Carles Noguera (CAS) The future of MFL I 7 / 27
Origin 3: Engineering — Fuzzy set theory Problem: to deal with too much precision in control theory Petr Cintula and Carles Noguera (CAS) The future of MFL I 7 / 27
The road to Mathematical Fuzzy Logic Pavelka 1979 Pultr 1984 Takeuti, Titani 1984, 1992 Mundici 1987, 1993 Novák 1990 Gottwald 1993 Höhle 1995 Baaz 1996 Hájek–Esteva–Godo 1996 Hájek, 1998 Novák, Perfilileva, Moˇ ckoˇ r, 1999 Cignoli, d’Ottaviano, Mundici, 2000 Petr Cintula and Carles Noguera (CAS) The future of MFL I 8 / 27
Mathematical Fuzzy Logic stems from those origins It was established as a respectable branch of mathematical logic in Metamathematics of fuzzy logic by Petr Hájek Kluwer, 1998 . Citations: 1400 + (WOS) and 3500 + (Google Scholar) Petr Cintula and Carles Noguera (CAS) The future of MFL I 9 / 27
On the back cover Petr says: This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. Petr Cintula and Carles Noguera (CAS) The future of MFL I 10 / 27
On the back cover Petr says: This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. Petr Cintula and Carles Noguera (CAS) The future of MFL I 10 / 27
On the back cover Petr says: This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. There are two main groups of intended readers. Petr Cintula and Carles Noguera (CAS) The future of MFL I 10 / 27
On the back cover Petr says: This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. There are two main groups of intended readers. First, logicians: they can see that fuzzy logic is indeed a branch of logic and may find several very interesting open problems. Petr Cintula and Carles Noguera (CAS) The future of MFL I 10 / 27
On the back cover Petr says: This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. There are two main groups of intended readers. Second, equally important, researchers involved in fuzzy logic applica- tions and soft computing. Petr Cintula and Carles Noguera (CAS) The future of MFL I 10 / 27
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