Well-Founded and Partial Stable Semantics Logical Aspects

2009 ◽  
pp. 1-11
Author(s):  
Pedro Cabalar ◽  
Sergei Odintsov ◽  
David Pearce
Keyword(s):  
Stable Semantics

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

An argument game for stable semantics

2008 ◽  
Vol 17 (1) ◽  
pp. 77-90 ◽  
Author(s):  
M. Caminada ◽  
Y. Wu
Keyword(s):  
Stable Semantics

Semi-stable semantics

2011 ◽  
Vol 22 (5) ◽  
pp. 1207-1254 ◽  
Author(s):  
M. W. A. Caminada ◽  
W. A. Carnielli ◽  
P. E. Dunne
Keyword(s):  
Stable Semantics

scholarly journals Ultimate Well-Founded and Stable Semantics for Logic Programs with Aggregates

2001 ◽  
pp. 212-226 ◽  
Author(s):  
Marc Denecker ◽  
Nikolay Pelov ◽  
Maurice Bruynooghe
Keyword(s):  
Logic Programs ◽  
Stable Semantics

scholarly journals Well-founded and stable semantics of logic programs with aggregates

2007 ◽  
Vol 7 (3) ◽  
pp. 301-353 ◽  
Author(s):  
NIKOLAY PELOV ◽  
MARC DENECKER ◽  
MAURICE BRUYNOOGHE
Keyword(s):  
Logic Programming ◽  
Second Order ◽  
Logic Programs ◽  
Consequence Operator ◽  
Trade Offs ◽  
Stable Semantics ◽  
Consequence Operators ◽  
Semantics Of Logic Programs ◽  
Stable Models

AbstractIn this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define extensions of the Kripke-Kleene, the well-founded and the stable semantics for aggregate programs. The semantics is based on the concept of a three-valuedimmediate consequence operatorof an aggregate program. Such an operatorapproximatesthe standard two-valued immediate consequence operator of the program, and induces a unique Kripke-Kleene model, a unique well-founded model and a collection of stable models. We study different ways of defining such operators and thus obtain a framework of semantics, offering different trade-offs betweenprecisionandtractability. In particular, we investigate conditions on the operator that guarantee that the computation of the three types of semantics remains on the same level as for logic programs without aggregates. Other results show that, in practice, even efficient three-valued immediate consequence operators which are very low in the precision hierarchy, still provide optimal precision.

scholarly journals Characterizations of the disjunctive stable semantics by partial evaluation

1997 ◽  
Vol 32 (3) ◽  
pp. 207-228 ◽  
Author(s):  
Stefan Brass ◽  
Jürgen Dix
Keyword(s):  
Partial Evaluation ◽  
Stable Semantics

scholarly journals A Study of Argumentative Characterisations of Preferred Subtheories

2018 ◽  
Author(s):  
Marcello D'Agostino ◽  
Sanjay Modgil
Keyword(s):  
Classical Logic ◽  
Standard Approach ◽  
Dialectical Approach ◽  
Stable Semantics ◽  
Grounded Semantics

Classical logic argumentation (Cl-Arg) under the stable semantics yields argumentative characterisations of non-monotonic inference in Preferred Subtheories. This paper studies these characterisations under both the standard approach to Cl-Arg, and a recent dialectical approach that is provably rational under resource bounds. Two key contributions are made. Firstly, the preferred extensions are shown to coincide with the stable extensions. This means that algorithms and proof theories for the admissible semantics can now be used to decide credulous inference in Preferred Subtheories. Secondly, we show that as compared with the standard approach, the grounded semantics applied to the dialectical approach more closely approximates sceptical inference in Preferred Subtheories.

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