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Fuzzy logic programming reduced to reasoning with attribute implications

Tomas Kuhr, Vilem Vychodil
2015 Fuzzy sets and systems (Print)  
We present a link between two types of logic systems for reasoning with graded if-then rules: the system of fuzzy logic programming (FLP) in sense of Vojtáš and the system of fuzzy attribute logic (FAL  ...  We further show that entailment in FLP is reducible to reasoning with Boolean attribute implications and elaborate on related issues including properties of least models.  ...  In addition, each rule (and fact) in a program is assumed to be valid to a degree (i.e., programs are theories in sense of Pavelka's abstract fuzzy logic [24, 34] ).  ... 
doi:10.1016/j.fss.2014.04.013 fatcat:sbr7tegjizc45l45i4en7fcecq

Defining Homomorphisms and Other Generalized Morphisms of Fuzzy Relations in Monoidal Fuzzy Logics by Means of BK-Products [article]

Ladislav J. Kohout
2003 arXiv   pre-print
This was generalized later by Kohout to relations based on fuzzy Basic Logic systems (BL) of H\'ajek and also for relational systems based on left-continuous t-norms.  ...  known Goedel, product logic systems; Lukasiewicz logic and its extension to MV-algebras related to quantum logics), intuitionistic logics and linear logics.  ...  Hence they are generally valid in fuzzy relational calculi based on residuated fuzzy logics.  ... 
arXiv:math/0310175v1 fatcat:li67sifsbfbpln2ocsuf7s5zia

Many-valued logics [chapter]

Erich Peter Klement, Radko Mesiar, Endre Pap
2000 Trends in Logic  
The paper considers the fundamental notions of many-valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics.  ...  And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics.  ...  The distinction between both systems is that LΠ has both t-norms & and and their related (residual) implications and negations among their basic connectives, and that LΠ 1 2 adds a truth degree constant  ... 
doi:10.1007/978-94-015-9540-7_11 fatcat:zzdkno6gxfam3i2b66quaac5ni

Axiomatizing t-norm based logic

Siegfried Gottwald
1999 European Society for Fuzzy Logic and Technology  
In fuzzy logic in wider sense, t-norms got a prominent rôle in recent times. In many-valued logic, the Lukasiewicz systems, the G odel sytems, and also the product logic are t-norm based.  ...  The present paper discusses the more general problem of the adequate axiomatizability for such t-norm based logical systems in general, surveying results of the last years.  ...  Calculations (in BL-algebras) show that the additional connectives ^ _ just have t h e BL-algebraic operations \ as their truth degree functions.  ... 
dblp:conf/eusflat/Gottwald99 fatcat:fn2j3cetbnex7o3o4wva75omqq

On the difference between traditional and deductive fuzzy logic

Libor Běhounek
2008 Fuzzy sets and systems (Print)  
In three case studies on notions of fuzzy logic and fuzzy set theory (Dubois-Prade's gradual elements, the entropy of a fuzzy set, and aggregation operators), the paper exemplifies methodological differences  ...  between traditional and deductive fuzzy logic.  ...  I profited from discussions with Petr Cintula, Martina Daňková, and Petr Hájek.  ... 
doi:10.1016/j.fss.2007.12.004 fatcat:i5siesza3rhnroamia7pxgmduu

Codd's Relational Model of Data and Fuzzy Logic: Comparisons, Observations, and Some New Results

Radim Belohlavek, Vilem Vychodil
2006 2006 International Conference on Computational Inteligence for Modelling Control and Automation and International Conference on Intelligent Agents Web Technologies and International Commerce (CIMCA'06)  
The present paper deals with Codd's relational model of data. In particular, we deal with fuzzy logic extensions of the relational model.  ...  In addition to the observations on relationships between fuzzy logic extensions of the relational model, our paper brings up several new technical results.  ...  We pick socalled complete residuated lattices as our basic structures of truth degrees (i.e., sets of truth degrees equipped with fuzzy logic operations like implication, etc.).  ... 
doi:10.1109/cimca.2006.68 dblp:conf/cimca/BelohlavekV06 fatcat:2dln6h5w5vgchdtv2yqxqa5kry

Fuzzy Description Logics and t-norm based fuzzy logics

Àngel Garcı´a-Cerdaña, Eva Armengol, Francesc Esteva
2010 International Journal of Approximate Reasoning  
Hájek proposed to deal with FDLs taking as basis t-norm based fuzzy logics with the aim of enriching the expressive possibilities in FDLs and to capitalize on recent developments in the field of Mathematical  ...  , validity and subsumption of evaluated formulas.  ...  in the setting of Mathematical Fuzzy Logic where the residuated (fuzzy) logics are widely studied.  ... 
doi:10.1016/j.ijar.2010.01.001 fatcat:x6miui466zh43nnquqdbfqp56q

Logics from Galois connections

Jouni Järvinen, Michiro Kondo, Jari Kortelainen
2008 International Journal of Approximate Reasoning  
In addition to the three classical propositional logic axioms and the inference rule of modus ponens, ILGC contains only two auxiliary rules of inference mimicking the performance of Galois connections  ...  Namely, a certain composition of Galois connection mappings forms a lattice-theoretical interior operator, and this motivates us to axiomatize a logic of these compositions.  ...  Acknowledgements The authors thank the anonymous referees for their comments and several improvements. Jouni Järvinen wants also to thank Wojciech Dzik for fruitful discussions.  ... 
doi:10.1016/j.ijar.2008.06.003 fatcat:rk4lvk6yvna2xpqiqqbixfwuoq

Fuzzy sets and formal logics

Lluís Godo, Siegfried Gottwald
2015 Fuzzy sets and systems (Print)  
The paper discusses the relationship between fuzzy sets and formal logics as well as the influences fuzzy set theory had on the development of particular formal logics.  ...  Acknowledgments The authors are grateful to an anonymous reviewer and to Carles Noguera for their useful comments and suggestions.  ...  Godo acknowledges partial support by the Spanish projects EdeTRI (TIN2012-39348-C02-01) and 2014 SGR 118.  ... 
doi:10.1016/j.fss.2015.06.021 fatcat:jstlgpnzrze3pkikat2rcbeeh4

Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part I: Model-Based and Axiomatic Approaches

Siegfried Gottwald
2006 Studia Logica: An International Journal for Symbolic Logic  
For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes  ...  Our emphasis will be on various approaches toward (more or less naively formed) universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.  ...  Their background (fuzzy) logic is the first-order system LΠ with identity which is a combination of the infinite valued Lukasiewicz logic L ∞ with the product logic Π (both understood as t-norm based residuated  ... 
doi:10.1007/s11225-006-7197-8 fatcat:vxo5u3lvy5g53ewkj5bdddfa6y

Axiomatizations of t-norm based logics – A survey

S. Gottwald
2000 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
In fuzzy logic in wider sense, i.e. in the field of fuzzy sets applications, t-norms got a prominent rôle in recent times.  ...  In many-valued logic, the Lukasiewicz systems, the Gödel sytems, and also the product logic all are t-norm based systems.  ...  lattice with a continuous t-norm, cf  ... 
doi:10.1007/s005000000048 fatcat:byjasgtervbcdhkaur6lnkzdpq

Substructural Fuzzy-Relevance Logic

Eunsuk Yang
2015 Notre Dame Journal of Formal Logic  
This paper proposes a new topic in substructural logic for use in research joining the fields of relevance and fuzzy logics. For this, we consider old and new relevance principles.  ...  We present ways to obtain relevant companions of the weakening-free uninorm (based) systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication (without distributivity  ...  We introduced several fuzzy-relevance logics with and without constants T, F and provided completeness results for them by showing that such logics are WI-FLs.  ... 
doi:10.1215/00294527-3132824 fatcat:cdyvqatkezcoxdr43d5nhmhzde

Attribute Implications in a Fuzzy Setting [chapter]

Radim Bělohlávek, Vilém Vychodil
2006 Lecture Notes in Computer Science  
The paper is an overview of recent developments concerning attribute implications in a fuzzy setting.  ...  Attribute implications are studied in several areas of computer science and mathematics. We focus on two of them, namely, formal concept analysis and databases.  ...  A general choice of a set of truth degrees plus logical connectives is represented by so-called complete residuated lattices (equipped possibly with additional operations).  ... 
doi:10.1007/11671404_3 fatcat:w6rmxv4xmjhhdcrxbeuoj44r6i

On Scaling of Fuzzy FCA to Pattern Structures

Aleksey Buzmakov, Amedeo Napoli
2016 International Conference on Concept Lattices and their Applications  
In this paper we consider two important extensions: fuzzy FCA and pattern structures, and discuss the relation between them.  ...  FCA is a mathematical formalism having many applications in data mining and knowledge discovery. Originally it deals with binary data tables.  ...  Below we discuss these two generalizations and their relation. Fuzzy FCA Fuzzy FCA works with fuzzy logic instead of crisp-logic, used in standard FCA.  ... 
dblp:conf/cla/BuzmakovN16 fatcat:3d4bczki7rc5xp3mmscsbdo4xu

On Finitely Valued Fuzzy Description Logics: The Łukasiewicz Case [chapter]

Marco Cerami, Francesc Esteva, Àngel García-Cerdaña
2012 Communications in Computer and Information Science  
We also deal with the corresponding reasoning tasks and their relationships, and we report some results on decidability and computational complexity.  ...  One of them consists in the definition and development of a family of description languages, each one having as underlying fuzzy logic the expansion with an involutive negation and truth constants of the  ...  The authors also want to thank Carles Noguera for his helpful comments and suggestions.  ... 
doi:10.1007/978-3-642-31715-6_26 fatcat:igbpsyga2bayjlujmoaa4bcp4m
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