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Original Articles

Equational approach to argumentation networks

Pages 87-142 | Received 19 Apr 2011, Accepted 15 Jun 2012, Published online: 24 Jul 2012

References

  • Baroni , P. , Giacomi , M. and Guida , G. 2005 . SCC-Recursiveness: A General Schema for Argumentation Semantics . Artificial Intelligence , 168 ( 1–2 ) : 162 – 210 .
  • Baroni , P. , Cerutti , F. , Giacomin , M. and Guida , G. 2009 . “ Encompassing Attacks to Attacks in Abstract Argumentation Frameworks ” . In ECSQARU , Edited by: Sossai , C. and Chemello , G. 83 – 94 . Springer . Lecture Notes in Computer Science 5590
  • Baroni , P. , Cerutti , F. , Dunne , P. E. and Giacomin , M. Computing with Infinite Argumentation Frameworks: The Case of AFRAs . Proceeding TAFA’11 Proceedings of the First international Conference on Theory and Applications of Formal Argumentation . Berlin . pp. 197 – 214 . Heidelberg : Springer-Verlag .
  • Barringer , H. and Gabbay , D. M. 2010 . “ Modal and Temporal Argumentation Networks’, in the Amir Pnueli Memorial Volume ” . In Time for Verification , Edited by: Peled , D. and Manna , Z. 1 – 25 . Berlin, Heidelberg : LNCS, Springer .
  • Barringer , H. , Gabbay , D. M. and Woods , J. 2005 . “ Temporal Dynamics of Argumentation Networks ” . In Mechanising Mathematical Reasoning , Edited by: Hutter , D. and Stephan , W. 58 – 98 . Berlin, Heidelberg : Springer . LNCS 2605
  • Barringer , H. , Gabbay , D. M. and Woods , J. 2008 . “ Network Modalities ” . In Linguistics, Computer Science and Language Processing. Festschrift for Franz Guenthner on the Occasion of his 60th Birthday , Edited by: Gross , G. and Schulz , K. 79 – 102 . London , , UK : College Publications .
  • Barringer , H. , Gabbay , D. M. and Woods , J. 2012 . Temporal, Numerical and Meta-Level Dynamics in Argumentation Networks . Argument & Computation , 3 ( 2–3 ) (to appear).
  • Bench-Capon , T. J.M. 2003 . Persuasion in Practical Argument Using Value-Based Argumentation Frameworks . Journal of Logic and Computation , 13 : 429 – 448 .
  • Boella , G. , Gabbay , D. M. , van der Torre , L. and Villata , S. 2010 . “ Support in Abstract Argumentation ” . In Computational models of Argument, COMMA 2010 , Edited by: Baroni , P. , Cerutti , F. , Giacomi , M. and Simari , G. 111 – 122 . Amsterdam : IOS Press .
  • Boella , G. , Gabbay , D. M. , van der Torre , L. and Villata , S. 2011b . “ Support in Abstract Argumentation ” . In Expanded Version for Annals of Mathematics and Artificial Intelligence, 2012 , Berlin, Heidelberg : Springer Verlag . to appear.
  • Boole , G. 1847 . The Mathematical Analysis of Logic Macmillan, Barclay, & Macmillan; London: George Bell, 1847, Cambridge and London.
  • Brewka , G. and Woltran , S. 2010 . “ Abstract Dialectical Frameworks ” . In Proceedings of Twelfth International Conference KR 2010 , 02 – 111 . Chicago and London : AAAI Press . KR-2010, 2010
  • Brewka , G. , Dunne , P. and Woltran , S. 2011 . “ Relating the Semantics of Abstract Dialectical Frameworks and Standard AFs ” . In Proceedings of Twenty-Second International Joint Conference on Artificial Intelligence (IJCAI-11) , 780 – 785 . Palo Alto , , California : AAAI press .
  • Caminada , M. and Gabbay , D. M. 2009 . A Logical Account of Formal Argumentation . Studia Logica , 93 ( 2–3 ) : 109 – 145 .
  • Caminada , M. and Wu , Y. On the Limitations of Abstract Argumentation . Proceedings of BNAIC 2011; the 23rd Benelux Conference on Artificial Intelligence . November 3–4 2011 , Ghent , Belgium. Edited by: De Causmaecker , P. , Verbeeck , K. , Maervoet , J. and Messelis , T. pp. 69 – 66 .
  • Cayrol , C. and Lagasquie-Schiex , M. C. 2005 . “ On the Acceptability of Arguments in Bipolar Argumentation Frameworks ” . In ECSQARU , Lecture Notes in Computer Science 3571 Edited by: Godo , L. 378 – 389 . Berlin, Heidelberg : Springer .
  • Cayrol , C. and Lagasquie-Schiex , M. C. 2010 . Coalitions of Arguments: A Tool for Handling Bipolar Argumentation Frameworks . International Journal of Intelligent Systems , 25 ( 1 ) : 83 – 109 .
  • Couturat , L. 1914 . The Algebra of Logic , Chicago and London : Open Court .
  • D'Agostino , M. and Gabbay , D. 2011 . “ Depth-Bounded Logics 1 ” . In Equational Nets for Classical and Paraconsistent Reasoning with Arbitrary Boolean Operators Paper 425. 1st draft, April 18, 2011.
  • Dung , P. M. 1995 . On the Acceptability of Arguments and its Fundamental Role in Non-Monotonic Reasoning, Logic Programming and n-Person Games . Artificial Intelligence , 77 : 321 – 357 .
  • Dunne , P. , Hunter , A. , McBurney , P. , Parsons , S. and Wooldridge , M. 2011 . Weighted Argument Systems . Artificial Intelligence , 175 : 457 – 486 .
  • Dvorak , W. and Woltran , S. 2011 . On the Intertranslatability of Argumentation Semantics . Journal of Artificial Intelligence Research , 41 : 445 – 475 .
  • Gabbay , D. M. 2008 . “ Reactive Kripke Semantics and Arc Accessibility ” . In Pillars of Computer Science: Essays dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of his 85th Birthday , Edited by: Avron , A. , Dershowitz , N. and Rabinovich , A. 292 – 341 . Berlin, Heidelberg : Springer-Verlag . Earlier version of this paper was published in Proceeding of CombLog04 http://www.cs.math.ist.utl.pt/comblog04/, eds. W. Carnielli, F.M. Dionesio, and P. Mateus, Centre of Logic and Computation University of Lisbon 2004, pp. 7–20. ftp://logica.cle.unicamp.br/pub/e-prints/comblog04/gabbay.pdf
  • Gabbay , D. M. 2009a . Provability Foundations for Argumentation Networks . Studia Logica , 93 ( 2–3 ) : 181 – 198 .
  • Gabbay , D. M. 2009b . Fibring Argumentation Frames . Studia Logica , 93 ( 2–3 ) : 231 – 295 .
  • Gabbay , D. M. 2009c . Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: Overview . Studia Logica , 93 : 355 – 379 .
  • Gabbay , D. M. Introducing Equational Semantics for Argumentation Networks . Proceedings of ECSQARU’11 . Berlin . pp. 19 – 35 . Heidelberg : Springer-Verlag . LNAI 6717
  • Gabbay , D. M. 2012a . “ The Equational Approach to CF2 Semantics ” . February 2012, arXiv:1203.0220v1 [cs.AI].
  • Gabbay , D. M. 2012b . “ Linear Logic loop Checker for Handling Odd Loops in Argumentation Networks ” . February 2012, paper 461.
  • Gabbay , D. M. 2012c . The Equational Approach to CF2 Semantics . to appear in COMMA 2012.
  • Gabbay , D. M. 2012d . “ The Equational Approach to Logic Programs’, to appear in LNCS 7265 ” . In Festschrift for Vladimir Lifschitz Edited by: Erdem , E. , Lee , J. , Lierler , Y. and Pearce , D. 279 – 295 .
  • Gabbay , D. M. 2012e . “ What is Negation as Failure Paper Written in 1985’, revised version published in Sergot Festschrift ” . Edited by: Alexander , Artikis , Robert , Craven , Kesim Cicekli , Nihan and Sadighi , Babak . 52 – 78 . Kostas Stathis: Logic Programs, Norms and Action – Essays in Honor of Marek J. Sergot on the Occasion of His 60th Birthday Springer 2012, LNAI 7360, Heidelberg: Springer
  • Gabbay , D. M. 2011 . Dung's Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce-Quine Dagger . Logica Universalis , 5 ( 2 ) : 255 – 318 . DOI:10.1007/s11787-011-0036-3.
  • Gabbay , D. M. Meta-Logical Investigations in Argumentation Networks , Research Monograph for Springer under contract.
  • Gabbay , D. M. and Modgil , S. 2009 . Modal Argumentation , Draft, May 2009.
  • Gabbay , D. M. and d'Avila Garcez , A. 2009 . Logical Modes of Attack in Argumentation Networks . Studia Logica , 93 ( 2–3 ) : 199 – 230 .
  • Gabbay , D. M. and Szał as , A. 2009 . Annotation Theories Over Finite Graphs . Studia Logica , 93 ( 2–3 ) : 147 – 180 .
  • Gratie , C. and Maqda Florea , A. Fuzzy Labelling for Argumentation Frameworks . ArgMas2011, 8th International Workshop on Argumentation in Multi-Agent Systems . May 2011 , Taipei , Taiwan. pp. 18 – 25 .
  • Hanh , D. D. , Dung , P. M. and Thang , P. M. 2010 . “ Inductive Defence for Sceptical Semantics of Extended Argumentation ” . In Journal of Logic and Computation , Vol. 21 2 , 307 – 349 . Oxford , , UK : Oxford University Press . April 2011
  • Modgil , S. An Abstract Theory of Argumentation that Accommodates Defeasible Reasoning about Preferences . Proceedings of 9th European Conference, ECSQARU 2007 . October 31–November 2 2007 , Hammamet , Tunisia. pp. 648 – 659 . Springer . Lecture Notes in Computer Science 4724
  • Modgil , S. 2009 . Reasoning About Preferences in Argumentation Frameworks . Artificial Intelligence , 173 : 901 – 993 .
  • Schröder , E. Vorlesungen über die Algebra die Logik (3 vols) , 1890 – 1904 . Leipzig : B.G. Tuebner . Reprints, Chelsea, 1966; Thoemmes Press, 2000.
  • Sobolev , V. I. 2001 . “ Brouwer Theorem’, in Hazewinkel, Michiel ” . In Encyclopaedia of Mathematics , Berlin, Heidelberg : Springer .
  • Wu , Y. , Caminada , M. and Gabbay , D. 2009 . Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming . Studia Logica , 93 ( 2–3 ) : 381 – 401 .

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