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Fuzzy autoepistemic logic and its relation to fuzzy answer set programming

2014
*
Fuzzy sets and systems (Print)
*

In this paper, we consider a version of

doi:10.1016/j.fss.2012.09.012
fatcat:mfbvgiydovesrpruo2v5xn3avu
*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*...##
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Fuzzy Autoepistemic Logic: Reflecting about Knowledge of Truth Degrees
[chapter]

2011
*
Lecture Notes in Computer Science
*

In this paper we show that many properties from classical

doi:10.1007/978-3-642-22152-1_52
fatcat:kc3crepsknerpm4fienzuxhmne
*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. ...##
###
On the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief

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. ...

##
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Fuzzy Answer Set Programming
[chapter]

2012
*
Answer Set Programming for Continuous Domains: A Fuzzy Logic Approach
*

In this chapter, we present a tutorial about

doi:10.2991/978-94-91216-59-6_3
fatcat:oqzn4dfxkncd3bs5m3oucm4ahy
*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. ...##
###
Fuzzy Answer Set Programming
[chapter]

2006
*
Lecture Notes in Computer Science
*

In this chapter, we present a tutorial about

doi:10.1007/11853886_30
fatcat:rp5q3tsbmfb3hblmfalapiq2ce
*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. ...##
###
Fuzzy Answer Set Programming: An Introduction
[chapter]

2013
*
Studies in Fuzziness and Soft Computing
*

In this chapter, we present a tutorial about

doi:10.1007/978-3-642-34922-5_15
fatcat:sjdl5zq7znfujhvb45zvte4fhe
*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. ...##
###
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

2014
*
Theory and Practice of Logic Programming
*

As such,

doi:10.1017/s147106841300063x
fatcat:qi6sp2bwgveqzopi7ovxzagr7q
*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*. ...##
###
Expressive reasoning with horn rules and fuzzy description logics

2010
*
Knowledge and Information Systems
*

A Description

doi:10.1007/s10115-010-0304-1
fatcat:ujedrdu27bdr7liio2ha3k7afa
*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 ...##
###
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. ...

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

2011
*
arXiv
*
pre-print

The first goal of this paper is

arXiv:1108.3278v1
fatcat:5an7m6atife55dq4sk6vyff46q
*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 ...##
###
An empirical evaluation of the inferential capacity of defeasible argumentation, non-monotonic fuzzy reasoning and expert systems

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*. ...

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

2015
*
Journal of Software Engineering and Applications
*

, events,

doi:10.4236/jsea.2015.89047
fatcat:lpxwd2glnfedlgumdlhkawqkae
*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 ...##
###
Answer Set Programming's Contributions to Classical Logic
[chapter]

2011
*
Lecture Notes in Computer Science
*

Ultimately, a clear picture should emerge of what the achievements of

doi:10.1007/978-3-642-20832-4_2
fatcat:yrydik5mlrgmxd7azmhpuudz7i
*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. ...##
###
Fuzzy Description Logic Programs
[chapter]

2008
*
Uncertainty and Intelligent information Systems
*

We allow (i)

doi:10.1142/9789812792358_0029
fatcat:irpowhue4jc33dmmchjgt6ffyq
*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. ...
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