A RECONSTRUCTION OF ABSTRACT ARGUMENTATION ADMISSIBLE SEMANTICS INTO DEFAULTS AND ANSWER SETS PROGRAMMING

AbstractIn the last years, abstract argumentation has met with great success in AI, since it has served to capture several non-monotonic logics for AI. Relations between argumentation framework (AF) semantics and logic programming ones are investigating more and more. In particular, great attention has been given to the well-known stable extensions of an AF, that are closely related to the answer sets of a logic program. However, if a framework admits a small incoherent part, no stable extension can be provided. To overcome this shortcoming, two semantics generalizing stable extensions have been studied, namely semi-stable and stage. In this paper, we show that another perspective is possible on incoherent AFs, called paracoherent extensions, as they have a counterpart in paracoherent answer set semantics. We compare this perspective with semi-stable and stage semantics, by showing that computational costs remain unchanged, and moreover an interesting symmetric behaviour is maintained.

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Bipolar Abstract Argumentation with Dual Attacks and Supports

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning ◽

10.24963/kr.2020/69 ◽

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.

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A Semantic Perspective on Omission Abstraction in ASP

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning ◽

10.24963/kr.2020/75 ◽

2020 ◽

Author(s):

Zeynep G. Saribatur ◽

Thomas Eiter

Keyword(s):

Problem Solving ◽

Program Analysis ◽

Abstract Level ◽

Answer Sets

The recently introduced notion of ASP abstraction is on reducing the vocabulary of a program while ensuring over-approximation of its answer sets, with a focus on having a syntactic operator that constructs an abstract program. It has been shown that such a notion has the potential for program analysis at the abstract level by getting rid of irrelevant details to problem solving while preserving the structure, that aids in the explanation of the solutions. We take here a further look on ASP abstraction, focusing on abstraction by omission with the aim to obtain a better understanding of the notion. We distinguish the key conditions for omission abstraction which sheds light on the differences to the well-studied notion of forgetting. We demonstrate how omission abstraction fits into the overall spectrum, by also investigating its behavior in the semantics of a program in the framework of HT logic.

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Chain Answer Sets for Logic Programs with Generalized Atoms

Logics in Artificial Intelligence - Lecture Notes in Computer Science ◽

10.1007/978-3-030-19570-0_30 ◽

2019 ◽

pp. 462-478 ◽

Cited By ~ 1

Author(s):

Mario Alviano ◽

Wolfgang Faber

Keyword(s):

Logic Programs ◽

Answer Sets

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Modular Paracoherent Answer Sets

Logics in Artificial Intelligence - Lecture Notes in Computer Science ◽

10.1007/978-3-319-11558-0_32 ◽

2014 ◽

pp. 457-471 ◽

Cited By ~ 4

Author(s):

Giovanni Amendola ◽

Thomas Eiter ◽

Nicola Leone

Keyword(s):

Answer Sets

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Grounding and Solving in Answer Set Programming

AI Magazine ◽

10.1609/aimag.v37i3.2672 ◽

2016 ◽

Vol 37 (3) ◽

pp. 25-32 ◽

Cited By ~ 27

Author(s):

Benjamin Kaufmann ◽

Nicola Leone ◽

Simona Perri ◽

Torsten Schaub

Keyword(s):

Problem Solving ◽

Propositional Logic ◽

Logic Program ◽

Answer Set Programming ◽

Key Issues ◽

Answer Sets ◽

Answer Set

Answer set programming is a declarative problem solving paradigm that rests upon a workflow involving modeling, grounding, and solving. While the former is described by Gebser and Schaub (2016), we focus here on key issues in grounding, or how to systematically replace object variables by ground terms in a effective way, and solving, or how to compute the answer sets of a propositional logic program obtained by grounding.

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