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Weak and Strong Disjunction in Possibilistic ASP [chapter]

Kim Bauters, Steven Schockaert, Martine De Cock, Dirk Vermeir
2011 Lecture Notes in Computer Science  
In particular, in addition to the view of ordinary ASP where disjunctions are used to induce a non-deterministic choice, the possibilistic setting naturally leads to a more epistemic view of disjunction  ...  Possibilistic answer set programming (PASP) unites answer set programming (ASP) and possibilistic logic (PL) by associating certainty values with rules.  ...  In Section 2 we start by introducing some background on ASP, PL and PASP. In Section 3 we present the strong semantics for possibilistic disjunctive ASP.  ... 
doi:10.1007/978-3-642-23963-2_37 fatcat:jrscnavmqzbu7lcbec3nhuo26q

Characterizing and extending answer set semantics using possibility theory

2014 Theory and Practice of Logic Programming  
Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP.  ...  In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity.  ...  This treatment corresponds with the understanding of disjunction in disjunctive ASP and will be referred to as strong disjunction.  ... 
doi:10.1017/s147106841300063x fatcat:qi6sp2bwgveqzopi7ovxzagr7q

Semantics for possibilistic answer set programs: Uncertain rules versus rules with uncertain conclusions

Kim Bauters, Steven Schockaert, Martine De Cock, Dirk Vermeir
2014 International Journal of Approximate Reasoning  
Possibilistic ASP (PASP) is a natural extension of ASP in which certainty weights are associated with each rule.  ...  Although Answer Set Programming (ASP) is a powerful framework for declarative problem solving, it cannot in an intuitive way handle situations in which some rules are uncertain, or in which it is more  ...  Let P be a possibilistic disjunctive program and P Π brave (l, λ) the classical disjunctive program as defined in Definition 8.  ... 
doi:10.1016/j.ijar.2013.09.006 fatcat:iyuqti3g4zbydickv736cdk43q

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  
Possibilistic Ordered Disjunction (LPPODs).  ...  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  ...  We will manage the strong negation (¬), in our logic programs, as it is done in ASP [1] .  ... 
doi:10.1007/s10472-012-9311-0 fatcat:c54szncy5re2jp65tokbft37tu

Possibilistic Well-Founded Semantics [chapter]

Mauricio Osorio, Juan Carlos Nieves
2009 Lecture Notes in Computer Science  
One of the main implications of having just one model associated to a possibilistic logic program is that one can perform queries directly to a possibilistic program and answering these queries in accordance  ...  In this paper, we introduce an extension of the Well-Founded Semantics, which represents a sceptical reasoning approach, in order to capture possibilistic logic programs.  ...  The views expressed in this paper are not necessarily those of the ALIVE consortium.  ... 
doi:10.1007/978-3-642-05258-3_2 fatcat:3fdtwr635jbhhopssh37257c5q

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  
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.  ...  possibilistic answer set programming.  ...  The following and last section discusses the possibilistic logic interpretation of classical Answer Set Programming (ASP).  ... 
doi:10.1016/j.scient.2011.04.008 fatcat:dtptwlqa2bhkbbyhug4tiqgtoa

A Crash Course on Generalized Possibilistic Logic [chapter]

Didier Dubois, Henri Prade
2018 Lecture Notes in Computer Science  
We offer a brief presentation of basic possibilistic logic, and of its generalisation that comes close to a modal logic albeit with simpler more natural epistemic semantics.  ...  It shows that three traditions of reasoning under or about uncertainty (setfunctions, epistemic logic and three-valued logics) can be reconciled in the setting of possibility theory.  ...  Then possibilistic formulas can be combined with all propositional connectives, including disjunction and negation. This is generalized possibilistic logic (GPL) [17] .  ... 
doi:10.1007/978-3-030-00461-3_1 fatcat:gkxvcnah55hf3jfev4cotvhbba

Answer Sets in a Fuzzy Equilibrium Logic [chapter]

Steven Schockaert, Jeroen Janssen, Dirk Vermeir, Martine De Cock
2009 Lecture Notes in Computer Science  
In this paper, we combine the expressiveness of both approaches, and define answer sets of arbitrary fuzzy propositional theories as models in a fuzzification of equilibrium logic.  ...  Finally, as an illustration of its modeling power, we show how fuzzy equilibrium logic can be used to find strong Nash equilibria.  ...  and weak negation.  ... 
doi:10.1007/978-3-642-05082-4_10 fatcat:2icliihgjrggrepgqvz35efhde

Belief Base Revision for Further Improvement of Unified Answer Set Programming [article]

Kumar Sankar Ray, Sandip Paul, Diganta Saha
2020 arXiv   pre-print
The belief base is represented using Unified Answer Set Programs which is capable of representing imprecise and uncertain information and perform nonomonotonic reasoning with them.  ...  Weak Disjunction: The disjunction principle is too strong for base revision with logic programs and hence is weakened [13] .  ...  However, logic programs under ASP, being nonmontonic in nature, base revision for ASP is more challenging and requires modified set of postulates.  ... 
arXiv:2003.04369v2 fatcat:6pi72z5o7jeh5p3vauz34ixk2a

A simple logic for reasoning about incomplete knowledge

Mohua Banerjee, Didier Dubois
2014 International Journal of Approximate Reasoning  
This paper proposes a simple logic whose atoms express epistemic attitudes about formulae expressed in another basic propositional language, and that allows for conjunctions, disjunctions and negations  ...  In the next section, the syntax and the axiomatic setting of the logic MEL are provided.  ...  The second author wishes to thank colleagues for useful discussions on this paper, especially Guillaume Aucher, Laurence Cholvy, Lluis Godo, Andreas Herzig, and Vincenzo Marra.  ... 
doi:10.1016/j.ijar.2013.11.003 fatcat:ss43tf3rcra5zpdqu4wjrblosy

Weighted logics for artificial intelligence – an introductory discussion

Didier Dubois, Lluís Godo, Henri Prade
2014 International Journal of Approximate Reasoning  
However, the systematic use of truth-tables for basic connectives in these approaches looks questionable as such notions have a strong epistemic flavor closer to ideas of uncertainty, while truth is an  ...  Typical graded notions One heavily entrenched tradition in AI, especially in knowledge representation and reasoning is to rely on Boolean logic.  ...  One may also distinguish between weak and strong permissions [77] .  ... 
doi:10.1016/j.ijar.2014.08.002 fatcat:hri6ffyszzernoyexdemade37m

A general approach to belief change in answer set programming [article]

James Delgrande, Torsten Schaub, Hans Tompits, Stefan Woltran
2009 arXiv   pre-print
We introduce methods for revising and merging logic programs, respectively.  ...  For merging, we consider operators following arbitration merging and IC merging, respectively.  ...  Following an introductory background section, we show that there is a ready mapping between concepts in belief revision in classical logic and in ASP; this serves to place belief revision in ASP firmly  ... 
arXiv:0912.5511v1 fatcat:mfzokxjpuvdqjbtlbdqsf2cmxq

An introduction to fuzzy answer set programming

Davy Van Nieuwenborgh, Martine De Cock, Dirk Vermeir
2007 Annals of Mathematics and Artificial Intelligence  
As fuzzy logic gives the user great flexibility regarding the choice for the interpretation of the notions of negation, conjunction, disjunction and implication, the FASP framework is highly configurable  ...  In this paper we show how the concepts of answer set programming and fuzzy logic can be successfully combined into the single framework of fuzzy answer set programming (FASP).  ...  acceptable as we have two relatively strong buying advices for c2 and only a very weak selling advice.  ... 
doi:10.1007/s10472-007-9080-3 fatcat:dwkwadkwefggznuvowf65paukq

A Model-Theoretic Approach to Belief Change in Answer Set Programming

James Delgrande, Torsten Schaub, Hans Tompits, Stefan Woltran
2013 ACM Transactions on Computational Logic  
Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy all or nearly all of the AGM postulates for revision.  ...  We first consider belief revision: for logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P * Q.  ...  Following an introductory background section, we show that there is a ready mapping between concepts in belief revision in classical logic and in ASP; this serves to place belief revision in ASP firmly  ... 
doi:10.1145/2480759.2480766 fatcat:xwacxk6cijfkze67iifrcbs2me

Repairing inconsistent answer set programs using rules of thumb: A gene regulatory networks case study

Elie Merhej, Steven Schockaert, Martine De Cock
2017 International Journal of Approximate Reasoning  
In particular, we evaluate how frequently each given rule of thumb is violated in the sample of repairs, and use the Z-score of this distribution to set the weight of that rule.  ...  We describe the rules of thumb that express available expert knowledge from the biological literature and explain how they can be encoded while repairing inconsistencies.  ...  The research in [45, 46, 47] presents the notion of strong and weak answer sets depending on how strongly encoded preferences are taken into account.  ... 
doi:10.1016/j.ijar.2017.01.012 fatcat:qu2mxo4ohfdhxczzjcl6oo3yoq
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