scholarly journals The Handling of Loops in Talmudic Logic, with Application to Odd and Even Loops in Argumentation

10.29007/gkg6 ◽  
2018 ◽  
Author(s):  
Michael Abraham ◽  
Dov Gabbay ◽  
Uri J. Schild
Keyword(s):  
Abstract Argumentation ◽  
Talmudic Logic

In this paper we present the notion of the TalmudicShkop extension to an abstract argumentation network (S,R) and compare it with Baroni’sand his colleagues CF2 extensions and with Gabbay’s Equational approach to CF2 semantics.We also offer tableaux methods as well as discuss temporal stamping of arguments and their use in resolving loops

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.

Complexity of fundamental problems in probabilistic abstract argumentation: Beyond independence

2019 ◽  
Vol 268 ◽  
pp. 1-29 ◽  
Author(s):  
Bettina Fazzinga ◽  
Sergio Flesca ◽  
Filippo Furfaro
Keyword(s):  
Abstract Argumentation

scholarly journals Towards fixed-parameter tractable algorithms for abstract argumentation

2012 ◽  
Vol 186 ◽  
pp. 1-37 ◽  
Author(s):  
Wolfgang Dvořák ◽  
Reinhard Pichler ◽  
Stefan Woltran
Keyword(s):  
Fixed Parameter Tractable ◽  
Abstract Argumentation ◽  
Fixed Parameter

Principles Of Talmudic Logic

2018 ◽  
pp. 133-373
Author(s):  
M. Abraham ◽  
D. M. Gabbay ◽  
U. Schild ◽  
Dov M. Gabbay ◽  
Franz Guenthner
Keyword(s):  
Talmudic Logic

A Comparative Test on the Enumeration of Extensions in Abstract Argumentation*

2015 ◽  
Vol 140 (3-4) ◽  
pp. 263-278 ◽  
Author(s):  
Stefano Bistarelli ◽  
Fabio Rossi ◽  
Francesco Santini
Keyword(s):  
Comparative Test ◽  
Abstract Argumentation

scholarly journals Strong admissibility for abstract dialectical frameworks

2021 ◽  
pp. 1-41
Author(s):  
Atefeh Keshavarzi Zafarghandi ◽  
Rineke Verbrugge ◽  
Bart Verheij
Keyword(s):  
Maximal Element ◽  
Decision Problems ◽  
Current Work ◽  
Argument Evaluation ◽  
Abstract Argumentation ◽  
Proper Generalization

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling argumentation allowing general logical satisfaction conditions and the relevant argument evaluation. Different criteria used to settle the acceptance of arguments are called semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. However, the notion of strongly admissible semantics studied for abstract argumentation frameworks has not yet been introduced for ADFs. In the current work we present the concept of strong admissibility of interpretations for ADFs. Further, we show that strongly admissible interpretations of ADFs form a lattice with the grounded interpretation as the maximal element. We also present algorithms to answer the following decision problems: (1) whether a given interpretation is a strongly admissible interpretation of a given ADF, and (2) whether a given argument is strongly acceptable/deniable in a given interpretation of a given ADF. In addition, we show that the strongly admissible semantics of ADFs forms a proper generalization of the strongly admissible semantics of AFs.

scholarly journals Synthesizing Argumentation Frameworks from Examples

2019 ◽  
Vol 66 ◽  
pp. 503-554 ◽  
Author(s):  
Andreas Niskanen ◽  
Johannes Wallner ◽  
Matti Järvisalo
Keyword(s):  
Natural Extension ◽  
Research Abstract ◽  
Expressive Power ◽  
Synthesis Problem ◽  
Constraint Optimization ◽  
Abstract Argumentation ◽  
Central Notion ◽  
Definition Of ◽  
The Given ◽  
Representation Formalism

Argumentation is today a topical area of artificial intelligence (AI) research. Abstract argumentation, with argumentation frameworks (AFs) as the underlying knowledge representation formalism, is a central viewpoint to argumentation in AI. Indeed, from the perspective of AI and computer science, understanding computational and representational aspects of AFs is key in the study of argumentation. Realizability of AFs has been recently proposed as a central notion for analyzing the expressive power of AFs under different semantics. In this work, we propose and study the AF synthesis problem as a natural extension of realizability, addressing some of the shortcomings arising from the relatively stringent definition of realizability. In particular, realizability gives means of establishing exact conditions on when a given collection of subsets of arguments has an AF with exactly the given collection as its set of extensions under a specific argumentation semantics. However, in various settings within the study of dynamics of argumentation---including revision and aggregation of AFs---non-realizability can naturally occur. To accommodate such settings, our notion of AF synthesis seeks to construct, or synthesize, AFs that are semantically closest to the knowledge at hand even when no AFs exactly representing the knowledge exist. Going beyond defining the AF synthesis problem, we study both theoretical and practical aspects of the problem. In particular, we (i) prove NP-completeness of AF synthesis under several semantics, (ii) study basic properties of the problem in relation to realizability, (iii) develop algorithmic solutions to NP-hard AF synthesis using the constraint optimization paradigms of maximum satisfiability and answer set programming, (iv) empirically evaluate our algorithms on different forms of AF synthesis instances, as well as (v) discuss variants and generalizations of AF synthesis.

scholarly journals Revisiting the Foundations of Abstract Argumentation – Semantics Based on Weak Admissibility and Weak Defense

2020 ◽  
Vol 34 (03) ◽  
pp. 2742-2749
Author(s):  
Ringo Baumann ◽  
Gerhard Brewka ◽  
Markus Ulbricht
Keyword(s):  
Classical Case ◽  
Research Area ◽  
Major Research ◽  
Abstract Argumentation ◽  
New Concepts ◽  
Key Concepts ◽  
Problematic Issue ◽  
Rigorous Study ◽  
Grounded Semantics ◽  
Special Case

In his seminal 1995 paper, Dung paved the way for abstract argumentation, a by now major research area in knowledge representation. He pointed out that there is a problematic issue with self-defeating arguments underlying all traditional semantics. A self-defeat occurs if an argument attacks itself either directly or indirectly via an odd attack loop, unless the loop is broken up by some argument attacking the loop from outside. Motivated by the fact that such arguments represent self-contradictory or paradoxical arguments, he asked for reasonable semantics which overcome the problem that such arguments may indeed invalidate any argument they attack. This paper tackles this problem from scratch. More precisely, instead of continuing to use previous concepts defined by Dung we provide new foundations for abstract argumentation, so-called weak admissibility and weak defense. After showing that these key concepts are compatible as in the classical case we introduce new versions of the classical Dung-style semantics including complete, preferred and grounded semantics. We provide a rigorous study of these new concepts including interrelationships as well as the relations to their Dung-style counterparts. The newly introduced semantics overcome the issue with self-defeating arguments, and they are semantically insensitive to syntactic deletions of self-attacking arguments, a special case of self-defeat.

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