# What is the status of fuzzy logic for TCS in 2011?

I am reviewing the Handbook of Nature-Inspired and Innovative Computing for SIGACT News. It's a very interesting read. Each chapter, though, has the flavor, "This is my research area, and damn it's awesome!" So part of what I am trying to do is to separate out the hype, and make a sober assessment of the book's contents.

One chapter is on fuzzy logic and fuzzy systems, and how frikkin awesome they are. And maybe they are, I frankly don't know. The intuitive sense I've gotten from hanging around computer scientists is that fuzzy logic and fuzzy modeling of control systems, etc., are "dead." I don't know if that's true, though -- and, even if it is true, I don't know if it's true for a "good reason."

Would anyone like to weigh in here? What's the current status of research into fuzzy systems? Does fuzzification see real-world applications? Did it used to and people moved away because of problems? Or do people "in the trenches" use it all the time, and it's just that theorists have moved away from it? Or... something else? (I have no idea what is true.)

I will probably cite answers to this question in the book review, unless an answerer specifically asks me not to.

Thanks.

• Verging on the border of subjective and argumentative with a fuzziness of 0.326. – Dave Clarke Apr 5 '11 at 14:31
• @Dave Clarke: :-)!!! I know. But there was even a question on this site, one of the "what research area should I go into" questions, where someone who answered said that fuzzy logic was not an active research area. If you want to close this question, I won't be offended. Still, I find the situation curious, and if there's a diplomatic way to find out about it, I'd like to. – Aaron Sterling Apr 5 '11 at 14:36
• Thanks Aaron for raising this question. I'm not much familiar with fuzzy logic, but knowing if a field is dead or alive is interesting. You may also ask for "current trends in fuzzy logic" to make it even more interesting (if any!). I think the "Federated Logic Conference (FLoC)" is a good place to seek such trends (not sure). – M.S. Dousti Apr 5 '11 at 15:07
• Thank you for changing the title. The status of fuzzy logic may be a little broad, but I do not think that the current question (revision 3) is subjective. – Tsuyoshi Ito Apr 5 '11 at 15:34
• Zadeh had a paper in 2008: Is there a need for fuzzy logic? – Kaveh Apr 5 '11 at 17:47

I wouldn't consider fuzzy logic dead. For control systems, I don't know. However, there's been a lot of activity in fuzzy logics for proof theorists for the last several years: look for papers by Ciabattoni, Olivetti, Fermüller, Metcalfe, and Baaz for starters.

Edit: Some specific references from my BibTeX file:

• D. Galmiche and Y. Sahli, Labelled Calculi for Łukasiewicz Logics, Int. Workshop on Logic, Language, Information and Computation, WoLLIC'08, Edinburgh, LNAI 5110, 2008.
• M. Baaz and G. Metcalfe, Proof Theory for First Order Łukasiewicz Logic. TABLEAUX 2007.
• D. Galmiche and D. Larchey-Wendling and Y. Salhi, Provability and Countermodels in Gödel-Dummett Logics, DISPROVING'07: Workshop on Disproving Non-Theorems, Non-Validity, and Non-Provability, 2007.
• S. Bova and F. Montagna, Proof search in Häjek's Basic Logic, ACM Trans. Comput. Log., 2007.
• D.M. Gabbay and G. Metcalfe, Fuzzy logics based on [0,1)-continuous uninorms, AML 46(5), 2007.
• G. Metcalfe and F. Montagna, Substructural fuzzy logics. JSL 72(3), 2007.
• R. Dyckhoff and S. Negri, Decision methods for linearly ordered {H}eyting algebras. AML 45, 2006.
• G. Metcalfe and N. Olivetti and D. Gabbay, Sequent and Hypersequent calculi for Abelian and Łukasiewicz Logics. ACM Trans. Comput. Log. 6(3), 2005.
• M. Baaz and A. Ciabattoni and F. Montagna, Analytic calculi for monoidal t-norm based logic, Fund. Inf. 59(4), 2004.
• S. Negri and J. van Plato, Proof systems for lattice theory, Math. Struct. in Comp. Science 14(4), 2004.
• A. Ciabattoni and C.G. Fermüller and G. Metcalfe, Uniform Rules and Dialogue Games for Fuzzy Logics. LPAR 2004.
• A. Ciabattoni, Automated Generation of Analytic Calculi for Logics with Linearity. CSL 2004.
• F. Montagna and L. Saccetti, Kripke-style semantics for many-valued logics, Math. Log. Q. 49(6), 2003. Correction in MLQ 50(1), 2004.
• D. Larchey-Wendling, Countermodel search in Gödel-Dummett logics, IJCAR 2004, LNAI 3097, Springer, 2004.
• G. Metcalfe, Proof Theory for Propositional Fuzzy Logics, PhD Thesis, Department of Computer Science, King's College, 2004.
• D. Gabbay and G. Metcalfe and N. Olivetti, Hypersequents and Fuzzy Logic, Revista de la Real Academia de Ciencias 98(1), 2004.
• A. Ciabattoni and G. Metcalfe, Bounded Łukasiewicz Logics. TABLEAUX 2003.
• M. Baaz and A. Ciabattoni and C. G. Fermüller, ypersequent Calculi for Gödel Logics---a Survey. JLC 13(6), 2003.
• M. Baaz and A. Ciabattoni and C. G. Fermüller, Sequent of Relations Calculi: A Framework for Analytic Deduction in Many-Valued Logics. Beyond Two: Theory and Applications of Multiple-Valued Logic, M. Fitting and E. Orlowska, eds., Physica-Verlag, 2003.
• N. Olivetti, Tableaux for Łukasiwicz Infinite Valued Logic. Studia Logica 73(1), 2003.
• G. Metcalfe and N. Olivetti and D. Gabbay, Analytic Sequent Calculi for Abelian and Łukasiewicz Logics. TABLEAUX 2002.
• A. Ciabattoni and C. G. Fermüller, Hypersequents as a Uniform Framework for Urquhart's C, MTL and Related Logics.Proceedings of the 31th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2001), 2001.
• F. Esteva and L. Godo, Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy Sets and Systems 124(3), 2001.
• M. Baaz and R. Zach, Hypersequent and the Proof Theory of Intuitionistic Fuzzy Logic. CSL 2000.
• A. Avron, A Tableau System for Gödel-Dummett Logic Based on a Hypersequent Calculus. TABLEAUX 2000, LNAI 1847, 2000.
• A. Ciabattoni and M. Ferrari, Hypertableau and Path-Hypertableau Calculi for some families of intermediate logics. TABLEAUX 2000, LNAI 1847, 2000.
• R.L.O. Cignoli and I.M.L. D'Ottaviano and D. Mundici, Algebraic Foundations of Many-Valued Reasoning, Kluwer, London, 2000.
• S. Aguzzoli and A. Ciabattoni, Finiteness in Infinite-Valued Łukasiewicz Logic. J. Logic, Language and Information 9, 2000.
• R. Dyckhoff, A Deterministic Terminating Sequent Calculus for Gödel-Dummett logic, IGPL 7(3), 1999.
• M. Baaz and A. Ciabattoni and C. G. Ferm{\"u}ller and H. Veith, Proof Theory of Fuzzy Logics: Urquhart's C and Related Logics. Mathematical Foundations of Computer Science 1998, 23rd International Symposium, MFCS'98, Brno, Czech Republic, August 24-28, 1998, Proceedings, 1998.
• P. Häjek, Metamathematics of Fuzzy Logics, Kluer, 1998.
• R. Hähnle, Proof theory of many-valued logic--linear optimization--logic design: connections and interactions. Soft Comput. 1(3), 1997.

These are largely proof-theory and automated deduction references, though,

• How about some more details Rob? – Dave Clarke Apr 6 '11 at 17:40
• Edited reply with specific references. – Rob Apr 6 '11 at 19:50
• Wow. That's quite a list. – Dave Clarke Apr 6 '11 at 19:52
• Rob, this is an interesting answer. I think most of these results are not dealing with Zadeh's fuzzy logic (as is used in control systems, $\land$ being interpreted as min) but with the more general notion. – Kaveh Apr 8 '11 at 8:40
• Most fuzzy logics interpret $\land$ as min and $\lor$ as max. Been a while, but I recall that Zadeh's logic is the same as Łukasiewicz w.r.t. implication. (I might be wrong on that.) – Rob Apr 8 '11 at 9:03