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Possibilistic Answer Set Programming Revisited [article]

Kim Bauters, Steven Schockaert, Martine De Cock, Dirk Vermeir
2012 arXiv   pre-print
Possibilistic answer set programming (PASP) extends answer set programming (ASP) by attaching to each rule a degree of certainty.  ...  To develop a more suitable semantics, we first introduce a characterization of answer sets of classical ASP programs in terms of possibilistic logic where an ASP program specifies a set of constraints  ...  Acknowledgements The authors would like to thank the anonymous reviewers for their useful comments, in particular for pointing out the link between our work and residuated logic programs.  ... 
arXiv:1203.3466v1 fatcat:djswyskstfbgrj6esaplg4erxm

Dealing with explicit preferences and uncertainty in answer set programming

Roberto Confalonieri, Juan Carlos Nieves, Mauricio Osorio, Javier Vázquez-Salceda
2012 Annals of Mathematics and Artificial Intelligence  
In this paper, we show how the formalism of Logic Programs with Ordered Disjunction (LPODs) and Possibilistic Answer Set Programming (PASP) can be merged into the single framework of Logic Programs with  ...  As a result, preferences and uncertainty can be used to select the preferred uncertain default rules of an LPPODs and, consequently, to order its possibilistic answer sets.  ...  This revisited possibilistic semantics has recently also been extended to possibilistic disjunctive logic programs [5] .  ... 
doi:10.1007/s10472-012-9311-0 fatcat:c54szncy5re2jp65tokbft37tu

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  
Special models of these constraints are then identified as possibilistic answer sets.  ...  AbstractAnswer Set Programming (ASP) is a popular framework for modelling combinatorial problems. However, ASP cannot be used easily for reasoning about uncertain information.  ...  A valuation V is said to be the answer set of a possibilistic simple program if V = P ⋆ and V is consistent. Answer sets of possibilistic normal programs are defined using a reduct.  ... 
doi:10.1017/s147106841300063x fatcat:qi6sp2bwgveqzopi7ovxzagr7q

Rules and meta-rules in the framework of possibility theory and possibilistic logic

D. Dubois, H. Prade, S. Schockaert
2011 Scientia Iranica. International Journal of Science and Technology  
answer set programming.  ...  Starting from the expression of different forms of fuzzy rules that have been identified in the setting of possibility theory, we study their counterparts in the extensions of possibilistic logic.  ...  This distinction has enabled us to bridge a generalization of possibilistic logic with possibilistic answer set programming.  ... 
doi:10.1016/j.scient.2011.04.008 fatcat:dtptwlqa2bhkbbyhug4tiqgtoa

Fuzzy Multi Criteria Decision Making and its Applications: A Brief Review of Category

Lazim Abdullah
2013 Procedia - Social and Behavioral Sciences  
Multi criteria decision making was introduced in the early seventies along side with the inception of fuzzy set theory.  ...  Flexible programming, possibilistic programming, possibilistic linear programming using fuzzy max, robust programming, possibilistic programming with fuzzy preference relations, possibilistic linear programming  ...  The aims of this review paper are to revisit the uncertain membership of fuzzy sets and also to elucidate the categories of fuzzy MCDM.  ... 
doi:10.1016/j.sbspro.2013.10.213 fatcat:3edw6rmcineu7cc5nfpjy3crya

The legacy of 50 years of fuzzy sets: A discussion

Didier Dubois, Henri Prade
2015 Fuzzy sets and systems (Print)  
and possibility theory, two important settings introduced by L.  ...  The discussion is organized on the basis of three potential understanding of the grades of membership to a fuzzy set, depending on what the fuzzy set intends to represent: a group of elements with borderline  ...  . • Many methods using type 2 fuzzy sets revisit calculations with fuzzy intervals, without referring to the corresponding state of the art.  ... 
doi:10.1016/j.fss.2015.09.004 fatcat:yqsjyfemjfhyzoqthwumsbiok4

Author Index to Volume 157

2006 Fuzzy sets and systems (Print)  
Guerra (9) 1248-1259 Tiryaki, F., Interactive compensatory fuzzy programming for decentralized multi-level linear programming (DMLLP) problems (23) 3072-3090 Toma´s, M.S., C. Alsina and J.  ...  Vychodil, An answer to Demirci's open question, a clarification of his result, and a correction of his interpretation of the result (2) 205-211 Benoit, E., see L.  ... 
doi:10.1016/s0165-0114(06)00449-0 fatcat:md4ypqoznjh4zgc6cixgwim6oa

A tutorial on uncertainty modeling for machine reasoning

Branko Ristic, Christopher Gilliam, Marion Byrne, Alessio Benavoli
2019 Information Fusion  
By revisiting the Zadeh example using the possibilistic approach and the combination rule (15) , one can observe that it gives the same result as the Bayesian approach.  ...  The two extremes of imprecision are: the precise (true) answer (in this case 324) and the null answer (the entire domain of legal values).  ... 
doi:10.1016/j.inffus.2019.08.001 fatcat:us3nujlfb5arnh22dgdj7vwdia

The Emergence of Fuzzy Sets: A Historical Perspective [chapter]

Didier Dubois, Henri Prade
2016 Studies in Fuzziness and Soft Computing  
survey some developments of possibility theory, focusing on two specific issues: the elicitation of qualitative or quantitative possibility distributions, and the forms of inconsistency representable in a possibilistic  ...  logic setting.  ...  [31] M Inuiguchi, J Ramik Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem Fuzzy sets  ... 
doi:10.1007/978-3-319-31093-0_1 fatcat:zc63ekhuend2ddmj5tvor5m7yq

Graphical Models: Queries, Complexity, Algorithms

Martin C. Cooper, Simon de Givry, Thomas Schiex, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
Non-serial Dynamic Programming An alternative approach for answering the query above consists in using non-serial dynamic programming (DP) [11] , also called Variable-Elimination (VE), bucket elimination  ...  The dual of this relaxation is exactly the linear program used by OSAC [29] to find an optimal transformation (set of EPTs) [116] .  ... 
doi:10.4230/lipics.stacs.2020.4 dblp:conf/stacs/CooperGS20 fatcat:rqyjypnqozd47frmaobbcpo5ei

Linear Fuzzy Regression Using Trapezoidal Fuzzy Intervals [chapter]

Amory Bisserier, Reda Boukezzoula, Sylvie Galichet
2010 Studies in Fuzziness and Soft Computing  
In this paper, a revisited approach for possibilistic fuzzy regression methods is proposed.  ...  A revisited ap- Intervals and Fuzzy Intervals • Conventional intervals An interval is defined by the set of elements lying between its lower and upper limits as: Given an interval a, its midpoint M(  ...  The first proposed by Tanaka which minimizes the total spread of the output is named possibilistic regression.  ... 
doi:10.1007/978-3-642-10728-3_1 fatcat:ape4jrlfvjfktkln5uznftkljm

Workflows for the Management of Change in Science, Technologies, Engineering and Mathematics [chapter]

Serge Autexier, Catalin David, Dominik Dietrich, Michael Kohlhase, Vyacheslav Zholudev
2011 Lecture Notes in Computer Science  
But in contrast to the fully formal setting, where adaptations of impacted documents can be automated to some degree, the flexiformal setting requires much more user interaction and thus a much tighter  ...  The system achieves this by providing embedded user assistance through an extended set of user interactions with documents based on an extensible set of client-and server side services that draw on explicit  ...  In order to be "complete", we have to follow a possibilistic approach to propagate impacts and thus may get false positives, i.e., spurious impacts.  ... 
doi:10.1007/978-3-642-22673-1_12 fatcat:4fjlexsuqbdbznwz3uyv2gbrcu

Bayesian epistemic values: focus on surprise, measure probability!

J. M. Stern, C. A. De Braganca Pereira
2013 Logic Journal of the IGPL  
Section 7 will revisit this issue, explaining how, in the authors' view, the e-value is a worthy answer to Kempthorne's challenge.  ...  In this sense, p-values have a 'possibilistic' appearance.  ... 
doi:10.1093/jigpal/jzt023 fatcat:x5c5dg6uujh45mdwcgspjnwpmu

Preferences in AI: An overview

Carmel Domshlak, Eyke Hüllermeier, Souhila Kaci, Henri Prade
2011 Artificial Intelligence  
We revisit the different types of compact representations and some related issues in the next section.  ...  Ordered disjunctions have also been introduced in logic programming languages [172] [173] [174] .  ... 
doi:10.1016/j.artint.2011.03.004 fatcat:gvag5wqw6reb7eauni7547bcye

Questions guiding the choice of a multicriteria decision aiding method

Bernard Roy, Roman Słowiński
2013 EURO Journal on Decision Processes  
Otherwise, she must revisit her answers to these questions, and accept some less satisfactory answers with the aim of permitting to find a method.  ...  In possibilistic case, it is set to a ''mean value'' of fuzzy number representing possibilistic distribution (Dubois and Prade 1987) .  ... 
doi:10.1007/s40070-013-0004-7 fatcat:qgmigrnfn5bq5e6q7sbgeqkznu
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