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Compiling Fuzzy Answer Set Programs to Fuzzy Propositional Theories [chapter]

Jeroen Janssen, Stijn Heymans, Dirk Vermeir, Martine De Cock
2008 Lecture Notes in Computer Science  
We show how a fuzzy answer set program can be compiled to an equivalent fuzzy propositional theory whose models correspond to the answer sets of the program.  ...  This creates a basis for constructing fuzzy answer set solvers, such as solvers based on fuzzy SAT-solvers or on linear programming.  ...  Fuzzy Completion In this section we show how certain fuzzy answer set programs can be translated to fuzzy theories such that the models of these theories will be y-answer sets and vice versa.  ... 
doi:10.1007/978-3-540-89982-2_34 fatcat:2vqqo2pgjngx3nigx4f6wdjlne

Fuzzy XPath for the Automatic Search of Fuzzy Formulae Models [chapter]

Jesús M. Almendros-Jiménez, Miquel Bofill, Alejandro Luna-Tedesqui, Ginés Moreno, Carlos Vázquez, Mateu Villaret
2015 Lecture Notes in Computer Science  
., proving the existence of at least one model) as usually done in a SAT/SMT setting, our interest moves to the problem of finding the whole set of models (with a finite domain) for a given fuzzy formula  ...  In this paper we deal with propositional fuzzy formulae containing several propositional symbols linked with connectives defined in a lattice of truth degrees more complex than Bool.  ...  Definition 2 (Fuzzy Computed Answer). Let P be a program, Q a goal and σ a substitution.  ... 
doi:10.1007/978-3-319-23540-0_26 fatcat:5lxjthni3vcfjedgcd5ktfovve

Fuzzy answer sets approximations

2013 Theory and Practice of Logic Programming  
AbstractFuzzy answer set programming (FASP) is a recent formalism for knowledge representation that enriches the declarativity of answer set programming by allowing propositions to be graded.  ...  To limit this downside, operators for approximating fuzzy answer sets can be introduced: Given a FASP program, these operators compute lower and upper bounds for all atoms in the program such that all  ...  Fuzzy Answer Set Programming (FASP) aims at combining ASP and fuzzy logic.  ... 
doi:10.1017/s1471068413000471 fatcat:fpyawy5gqzfg5d4244sqi5claa

From Statistical Relational to Neural Symbolic Artificial Intelligence: a Survey [article]

Giuseppe Marra and Sebastijan Dumančić and Robin Manhaeve and Luc De Raedt
2021 arXiv   pre-print
These cannot only be used to characterize and position neural-symbolic artificial intelligence approaches but also to identify a number of directions for further research.  ...  Answer-set programs can have multiple models and support features such as soft and hard constraints and preferences. For a detailed introduction to answer-set programs, we refer to [37] .  ...  Indeed, all the fuzzy systems described in this survey starts from a Boolean theory, relaxes it to a fuzzy theory and, finally, return to Boolean logic to provide answers or to take decisions.  ... 
arXiv:2108.11451v1 fatcat:7joz6x52jbftzchzxlxb3t6r7e

Answers [chapter]

2005 Fuzzy Expert Systems and Fuzzy Reasoning  
\n"; message "<string>"; message "Compiling program ECHO.PAR\n" ; string = "Membership functions for fuzzy sets\:\n" ; string + "First fuzzy set is size, equivalent to region area.  ...  In the theory of fuzzy logic, Klir and Yuan (1995, p. 220 ff.) define four types of fuzzy propositions.  ...  Most importantly, the consequent fuzzy set may be non-numeric. The only disadvantage is that one or two separate rules are required. 7.3 a. Default inference is monotonic. b.  ... 
doi:10.1002/0471698504.answ1 fatcat:7bcplyk66vce3e4mb4tkp6cksy

Book announcements

1993 Discrete Applied Mathematics  
Herbrand's theory. Resolution. Refinements of resolution. Chapter 3: Logic Programming. Answer generation. Horn clause programs. Evaluation strategies. PROLOG. Armen H.  ...  Additional sentation of fuzzy sets. Fuzzy conditionals. Probability qualification. Iterated fuzzy conditionals. Chapter 8: Iterated Conditioning and Miscellaneous Issues.  ... 
doi:10.1016/0166-218x(93)90173-l fatcat:l4psazjvkjcm5ksswvubyespla

On the incorporation of interval-valued fuzzy sets into the Bousi-Prolog system: declarative semantics, implementation and applications [article]

Clemente Rubio-Manzano, Martin Pereira-Fariña
2017 arXiv   pre-print
We show, by using potential applications, that fuzzy logic programming frameworks enhanced with them can correctly work together with lexical resources and ontologies in order to improve their capabilities  ...  In this paper we analyse the benefits of incorporating interval-valued fuzzy sets into the Bousi-Prolog system.  ...  Fuzzy set theory (FS) is a good candidate, but it shows some particular limitations to this aim: i) sometimes, words mean different things to different people and this generates and additional layer of  ... 
arXiv:1711.03147v1 fatcat:snbztbrcg5bgxmou77hppzwyqa

A (Basis for a) Philosophy of a Theory of Fuzzy Computation

Apostolos Syropoulos
2018 Kairos: Journal of Philosophy & Science  
Fuzzy set theory is a mathematical model of vagueness that has been used to define vague models of computation. The prominent model of vague computation is the fuzzy Turing machine.  ...  Based on the properties of this and other models of vague computing, an attempt is made to formulate a basis for a philosophy of a theory of fuzzy computation.  ...  Fuzzy Set Theory in a Nutshell Fuzzy set theory was introduced by Lotfi Askar Zadeh [37] as an extension of ordinary set theory.  ... 
doi:10.2478/kjps-2018-0009 fatcat:nhaab7mnirevtny3u53rmoygzm

An inference engine toolkit for computing with words

Elham S. Khorasani, Purvag Patel, Shahram Rahimi, Daniel Houle
2012 Journal of Ambient Intelligence and Humanized Computing  
The scope of the presented toolkit, as opposed to many available fuzzy logic tools, goes beyond simple fuzzy-if-then rules and performs a chain of inferences on complex fuzzy propositions containing fuzzy  ...  arithmetics, fuzzy quantifiers, and fuzzy probabilities.  ...  If found, the answer to a query is returned in three forms: (1) a fuzzy set on the domain of the query variable, (2) a linguistic term that best describes the output fuzzy set, and (2) a numeric value  ... 
doi:10.1007/s12652-012-0137-8 fatcat:fubdcxwuhzaapce27pbo2ff7mu

Page 7802 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
Disjunctive partial deduction is also applied to optimizing abductive logic programs and compiling propositional disjunctive programs.” 97m:68035 68N17 68Q55 Stuckey, Peter J. (5S-MELB-C; Parkville) ;  ...  It is also proved that the success set of a specific subclass of monadic programs (‘simple’ programs) corresponds exactly to regular languages with star-height not exceeding 1.” 97m:68032 68N17 03B70 68Q25  ... 

SEDPA, an expert system for disease diagnosis in eel rearing systems

J.C. Gutiérrez-Estrada, E. De Pedro Sanz, R. López-Luque, I. Pulido-Calvo
2005 Aquacultural Engineering  
Starting from this kind of information, the system obtains its conclusions treating this information with a fuzzy controller and transmitting the uncertainty using the Dempster-Shafer theory (DST).  ...  On the other hand, the use of different fuzzy associative memory (FAM) or representation of the different human experts's knowledge level indicated the system adaptability to the different work scenarios  ...  Acknowledgements The authors wishes to thank two anonymous reviewers for their constructive criticism of the system, suggestions and comments on an earlier version of the manuscript.  ... 
doi:10.1016/j.aquaeng.2004.12.003 fatcat:hswigutwkzbphljmcwfia46hhy

Page 5782 of Mathematical Reviews Vol. , Issue 2001H [page]

2001 Mathematical Reviews  
Pehoushek, Counting models using connected com- ponents (157-162); Deborah East and Mirostaw Truszczynski, DATALOG with constraints—an answer-set programming sys- tem (163-168); Narendra Jussien and Olivier  ...  Yager and Slawomir Zadrozny, A fuzzy logic based approach to linguistic summaries of databases (813-834); Oliver Nelles, Alexander Fink, Robert BabuSka and Magne Setnes, Comparison of two construc- tion  ... 

The paradoxical success of fuzzy logic

C. Elkan, H.R. Berenji, B. Chandrasekaran, C.J.S. de Silva, Y. Attikiouzel, D. Dubois, H. Prade, P. Smets, C. Freksa, O.N. Garcia, G.J. Klir, Bo Yuan (+11 others)
1994 IEEE Expert  
At its simplest, fuzzy logic is a generalization of standard propositional logic from two truth values, false and true, to degrees of truth between 0 and 1. Formally, let A denote an assertion.  ...  A fuzzy logic system is intended to allow an indefinite variety of numerical truth values.  ...  Acknowledgments The author is grateful to many colleagues for useful comments on earlier versions of this article.  ... 
doi:10.1109/64.336150 fatcat:33nqixzz6femrnbhcffxcuvuxm

Book report Book report

1998 Computers and Mathematics with Applications  
Instead, we decided to publish every important material detail concerning those books submitted to us by publishers, which we judge to be of potential interest to our readers.  ...  Publishers should submit books intended for review to the Editor-in-Chief,  ...  Applications to dimension theory and dynamical systems. 5. Dimension of Cantor-like sets and symbolic dynamics. 6. Multifractal formalism. 7.  ... 
doi:10.1016/s0898-1221(98)00144-8 fatcat:zkxmkiuxo5dnpenmkk5v2uazii

Formalization of Generalized Constraint Language: A Crucial Prelude to Computing With Words

Elham S. Khorasani, Shahram Rahimi, Wesley Calvert
2013 IEEE Transactions on Cybernetics  
It provides an agenda to express the imprecise and fuzzy information embedded in natural language and allows reasoning with perceptions.  ...  Second, it determines the scope of GCL as well as its set of well-formed formula and hence facilitates the translation of natural language expressions into GCL.  ...  A GCL program consists of three parts: a set of declarations, a factbase, and a set of queries.  ... 
doi:10.1109/tsmcb.2012.2204743 pmid:22801519 fatcat:2qhonoefufgffe2nri4azhfw3u
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