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Fuzzy autoepistemic logic and its relation to fuzzy answer set programming

Marjon Blondeel, Steven Schockaert, Martine De Cock, Dirk Vermeir
2014 Fuzzy sets and systems (Print)  
In this paper, we consider a version of fuzzy answer set programming and show that its answer sets can be equivalently described as models in fuzzy autoepistemic logic.  ...  We also define a fuzzy logic of minimal belief and negation-as-failure and use this as a tool to show that fuzzy autoepistemic logic generalizes fuzzy answer set programming.  ...  We have shown that important properties of classical autoepistemic logic are preserved and that the relation between answer set programming and autoepistemic logic remains valid when generalizing to fuzzy  ... 
doi:10.1016/j.fss.2012.09.012 fatcat:mfbvgiydovesrpruo2v5xn3avu

Fuzzy Autoepistemic Logic: Reflecting about Knowledge of Truth Degrees [chapter]

Marjon Blondeel, Steven Schockaert, Martine De Cock, Dirk Vermeir
2011 Lecture Notes in Computer Science  
In this paper we show that many properties from classical autoepistemic logic remain valid under this generalization and that the important relation between autoepistemic logic and answer set programming  ...  is preserved in the sense that fuzzy autoepistemic logic generalizes fuzzy answer set programming.  ...  We also prove that the relation between autoepistemic logic and answer set programming is preserved.  ... 
doi:10.1007/978-3-642-22152-1_52 fatcat:kc3crepsknerpm4fienzuxhmne

On the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief

Marjon Blondeel, Tommaso Flaminio, Steven Schockaert, Lluís Godo, Martine De Cock
2015 Fuzzy sets and systems (Print)  
It has recently been shown that, in the same way as autoepistemic logic generalizes answer set programming, fuzzy autoepistemic logic generalizes fuzzy answer set programming as well.  ...  Besides being related to answer set programming, autoepistemic logic is also closely related to several modal logics.  ...  Acknowledgements The authors are grateful to anonymous reviewers for their helpful comments and suggestions that have helped to improve the final presentation of this paper.  ... 
doi:10.1016/j.fss.2015.02.018 fatcat:tedcqm4f6rd2fepmzkgby4pbva

Fuzzy Answer Set Programming [chapter]

Jeroen Janssen, Steven Schockaert, Dirk Vermeir, Martine de Cock
2012 Answer Set Programming for Continuous Domains: A Fuzzy Logic Approach  
In this chapter, we present a tutorial about fuzzy answer set programming (FASP); we give a gentle introduction to its basic ideas and definitions.  ...  FASP is a combination of answer set programming and fuzzy logics which has recently been proposed.  ...  It is closely related to e.g. autoepistemic, equilibrium and default logic. Equilibrium logic [19] is one of the most general approaches to ASP.  ... 
doi:10.2991/978-94-91216-59-6_3 fatcat:oqzn4dfxkncd3bs5m3oucm4ahy

Fuzzy Answer Set Programming [chapter]

Davy Van Nieuwenborgh, Martine De Cock, Dirk Vermeir
2006 Lecture Notes in Computer Science  
In this chapter, we present a tutorial about fuzzy answer set programming (FASP); we give a gentle introduction to its basic ideas and definitions.  ...  FASP is a combination of answer set programming and fuzzy logics which has recently been proposed.  ...  It is closely related to e.g. autoepistemic, equilibrium and default logic. Equilibrium logic [19] is one of the most general approaches to ASP.  ... 
doi:10.1007/11853886_30 fatcat:rp5q3tsbmfb3hblmfalapiq2ce

Fuzzy Answer Set Programming: An Introduction [chapter]

Marjon Blondeel, Steven Schockaert, Dirk Vermeir, Martine De Cock
2013 Studies in Fuzziness and Soft Computing  
In this chapter, we present a tutorial about fuzzy answer set programming (FASP); we give a gentle introduction to its basic ideas and definitions.  ...  FASP is a combination of answer set programming and fuzzy logics which has recently been proposed.  ...  It is closely related to e.g. autoepistemic, equilibrium and default logic. Equilibrium logic [19] is one of the most general approaches to ASP.  ... 
doi:10.1007/978-3-642-34922-5_15 fatcat:sjdl5zq7znfujhvb45zvte4fhe

Page 4228 of Mathematical Reviews Vol. , Issue 99f [page]

1999 Mathematical Reviews  
Przymusinski [in Logic programming and nonmonotonic reasoning (Washington, DC, 1991), 3-20, MIT Press, Cambridge, MA, 1991; MR 92j:68110], we define the autoepistemic logic of alternative beliefs (AELAB  ...  Part II introduces M logic, which no longer uses the Bayes postulate. In M logic it is possible to distinguish between uncertainty and ignorance.  ... 

Characterizing and extending answer set semantics using possibility theory

KIM BAUTERS, STEVEN SCHOCKAERT, MARTINE DE COCK, DIRK VERMEIR
2014 Theory and Practice of Logic Programming  
As such, it allows us to model and reason about uncertain information in an intuitive way.  ...  Special models of these constraints are then identified as possibilistic answer sets.  ...  Alternatively, the answer set semantics of normal programs can be defined in terms of autoepistemic logic (Marek and Truszczyński 1991) , a well-known non-monotonic modal logic.  ... 
doi:10.1017/s147106841300063x fatcat:qi6sp2bwgveqzopi7ovxzagr7q

Expressive reasoning with horn rules and fuzzy description logics

Theofilos Mailis, Giorgos Stoilos, Giorgos Stamou
2010 Knowledge and Information Systems  
A Description Logic (DL) allows us to define sets of objects referred as concepts (corresponding to unary relations), and relationships between objects called roles (corresponding to binary relations).  ...  We introduce the decision problems of answering to conjunctive queries, unions of conjunctive queries and the existential entailment problem and provide a sound and complete algorithm that permits reasoning  ...  His main research interest include knowledge representation and reasoning (description logics, logic programming, fuzzy logic, ontology and rule languages), theory of uncertainty (fuzzy sets and systems  ... 
doi:10.1007/s10115-010-0304-1 fatcat:ujedrdu27bdr7liio2ha3k7afa

Uncertainty Management in Medical Applications [chapter]

2009 Nonlinear Biomedical Signal Processing, Fuzzy Logic, Neural Networks, and New Algorithms  
Fuzzy relations are among the most important concepts in fuzzy set theory. A fuzzy relation R between X and Y is defined as a fuzzy set oflx Y.  ...  If we have three universes X, Y, and Z, it is useful to combine fuzzy relations between them. The max-min composition of two fuzzy relations ^onlx Y and R 2 on Y x Z defines a fuzzy relation i? = i?  ...  • The system is evolutionary, which makes it difficult to describe precisely each of its states.  ... 
doi:10.1109/9780470545362.ch1 fatcat:dnvxckvc2zdpvhtlcen6bnrqwa

Reiter's Default Logic Is a Logic of Autoepistemic Reasoning And a Good One, Too [article]

Marc Denecker, Victor W. Marek, Miroslaw Truszczynski
2011 arXiv   pre-print
The first goal of this paper is to show that some problems of Reiter's default logic as a formal way to reason about informal defaults are directly attributable to the autoepistemic nature of default logic  ...  We then discuss the formalization of this perspective in the logics of Moore and Reiter, respectively, using the unifying semantic framework for default and autoepistemic logics that we developed earlier  ...  We showed that this rather fuzzy notion leads to multiple perspectives on autoepistemic reasoning and to multiple dialects of the autoepistemic language, induced by different notions of what can be derived  ... 
arXiv:1108.3278v1 fatcat:5an7m6atife55dq4sk6vyff46q

An empirical evaluation of the inferential capacity of defeasible argumentation, non-monotonic fuzzy reasoning and expert systems

Lucas Rizzo, Luca Longo
2020 Expert systems with applications  
It contributes to the field of logic and non-monotonic reasoning by situating defeasible argumentation among similar approaches of non-monotonic reasoning under uncertainty through a novel empirical comparison  ...  This is an ill-defined construct, and its formalisation can be seen as a reasoning activity under uncertainty.  ...  For instance, Delladio et al. (2006) investigate the relations between 110 a normal default logic and a variant of a defeasible logic programming.  ... 
doi:10.1016/j.eswa.2020.113220 fatcat:p6iolac7cfdgnlw52p36fwtfi4

Imperfection of Domain Knowledge and Its Formalization in Context of Design of Robust Software Systems

Meenakshi Sridhar, Naseeb Singh Gill
2015 Journal of Software Engineering and Applications  
, events, and time; properties and categories of these entities, and relations between entities.  ...  One of the qualitative requirements for software to be developed, is that it be robust i.e. it does not break down while encountering unpredictable situations.  ...  Acknowledgements Our thanks to Prof. Manohar Lal, SOCIS, IGNOU, New Delhi (India) for his valuable suggestions. References  ... 
doi:10.4236/jsea.2015.89047 fatcat:lpxwd2glnfedlgumdlhkawqkae

Answer Set Programming's Contributions to Classical Logic [chapter]

Marc Denecker, Joost Vennekens, Hanne Vlaeminck, Johan Wittocx, Maurice Bruynooghe
2011 Lecture Notes in Computer Science  
Ultimately, a clear picture should emerge of what the achievements of answer set programming mean in the context of classical logic, so that they may be given their proper place in the canon of science  ...  to the classical setting.  ...  The distinction between general logic programs and answer set programs lays purely on the informal level.  ... 
doi:10.1007/978-3-642-20832-4_2 fatcat:yrydik5mlrgmxd7azmhpuudz7i

Fuzzy Description Logic Programs [chapter]

Umberto Straccia
2008 Uncertainty and Intelligent information Systems  
We allow (i) to express that a sentence is not just true or false, but certain to some degree, which is taken from a certainty lattice; and (ii) combine the logic with annotated logic programming, in which  ...  It is generally accepted that knowledge based systems would be smarter if they can manage uncertainty.  ...  Acknowledgments I'm in debt with the anonymous reviewers who provided useful comments to correct and improve an early version of this paper.  ... 
doi:10.1142/9789812792358_0029 fatcat:irpowhue4jc33dmmchjgt6ffyq
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