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The logic of defeasible argumentation

Bart Verheij

Course in the post-graduate program
of the Computer Science Department
at the Universidad Nacional del Sur
in Bahia Blanca, Argentina

April - May, 1999

Course overview

1 Introduction
2 Arguments
3 Attack and defeat
4 Argument structure, attack and defeat
5 Rules
6 Argumentation as a process + dialectical arguments
7 Argumentation as social discourse
8 Semantics and proof theory

1 Introduction

- Introductory remarks
- The abundance and diversity of models
- Formal modeling
- An informal view on defeasible argumentation
- The themes of the course

38 slides

Further reading:
Haack 1978
Loui 1992
Pollock 1995
Van Eemeren and Grootendorst 1987
Verheij 1996a: chapter 1

2 Arguments

- Models of defeasible argumentation vs. nonmonotonic logics
- What is an argument?
- Argument forms
- Arguments as reason/conclusion-structures
- Suppositional arguments
- A typology of argument forms

67 slides

Further reading:
Pollock 1995
Prakken and Sartor 1996
Simari and Loui 1992
Van Eemeren and Grootendorst 1987
Verheij 1996a: chapter 5, section 2; chapter 6, section 1
Verheij 1998a, 1998b, ICAIL99
Vreeswijk 1997

3 Attack and defeat

- Pollock’s undercutters and rebutters
- Two metaphors of argument defeat
- The difference between attack and defeat
- Dung’s admissible sets of arguments
- Defeat statuses and argumentation stages
- Computing defeat statuses
- Other approaches

63 slides

Further reading:
Dung 1995
Pollock 1995
Prakken and Sartor 1996
Simari, Chesñevar, García 1994
Verheij 1996a: chapter 5, sections 4 and 6; chapter 6, sections 3, 4 and 6
Verheij 1996b
Vreeswijk 1997

4 Argument structure, attack and defeat

- Structure, attack and defeat
- CumulA’s defeaters
- Defeater schemes
- A catalogue of types of defeat
- Initials, narrowings and defeat
- Argumentation stages with structured arguments
- A classification of types of defeat
- Accrual of reasons

57 slides

Further reading:
Bondarenko, Toni and Kowalski 1993
Pollock 1995
Prakken and Sartor 1996
Simari and Loui 1992
Verheij 1996a: chapter 5, sections 2, 3, 4 and 6; chapter 6, sections 2 and 6
Verheij 1998a
Vreeswijk 1997

5 Rules

- Rules and arguments
- The material implication
- Rules and principles in the law
- Reason-Based Logic
- Rules and principles (revisited)
- Reconstructing reasoning by analogy
- Approaches to rules

91 slides

Further reading:
Dworkin 1978
Hage 1996, 1997
Reiter 1980
Verheij 1996a: chapters 2, 3 and 4
Verheij 1998c
Verheij, Hage and Van den Herik 1998

6 Argumentation as a process + dialectical arguments

- Argumentation as a process
- Argument construction
- Change of status
- Lines of argumentation
- Level n arguments

- Automated argument assistance
- Argue!, ArguMed 1.0, ArguMed 2.0
- Comparing argument systems
- Dialectical arguments

20 + 79 slides
Further reading:
Dung 1995
Gordon and Karacapilidis 1997
Loui et al. 1997
Pollock 1995
Simari, Chesñevar, García 1994
Toulmin 1958
Verheij 1996a: chapter 5, section 5; chapter 6, sections 5 and 6
Verheij 1996b
Verheij 1998a, 1998b, 1999

7 Argumentation as social discourse

Roles of dialogue and discourse in argumentation:

- Characterizing truth in a model (dialogical semantics)
- Characterizing logical consequence (dialogical proof theory)
- Modeling argument defeat

- Providing the basis for justification
- Identifying issues
- Establishing the law

57 slides

Further reading:
Gordon 1995
Hage 1997, 1998
Hage, Leenes and Lodder 1994
Hintikka and Sandu 1997
Lodder 1998
Lodder and Verheij 1999
Lorenzen and Lorenz 1978
Rawls 1972

8 Semantics and proof theory

- Semantics and proof theory in classical logic
- Semantic constraints and rules of inference for rules
- Reiter's extensions
- Dialogical proof theory
- Semantics vs. proof theory for defeasible argumentation

36 slides

Further reading:
Dung 1995
Hintikka and Sandu 1997
Prakken 1997
Reiter 1980
Toulmin 1958
Verheij 1996a: chapter 2, sections 2, 4 and 5
Verheij 1998c, 1999

References

  • Bondarenko, A., Toni, F., and Kowalski, R.A. (1993). An assumption-based framework for non-monotonic reasoning. Logic programming and non-monotonic reasoning. Proceedings of the second international workshop (eds. L.M. Pereira and A. Nerode), pp. 171-189. The MIT Press, Cambridge (Massachusetts).
  • Dung, P.M. (1995). On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence, Vol. 77, pp. 321-357.
  • Dworkin, R. (1978). Taking Rights Seriously. New Impression with a Reply to Critics. Duckworth, London.
  • Eemeren, F.H. van, Grootendorst, R. and Kruiger, T. (1987). Handbook of Argumentation Theory. A Critical Survey of Classical Backgrounds and Modern Studies. Foris Publications, Dordrecht. Translation of van Eemeren et al. (1981).Vreeswijk, Gerard A.W. (1997). Abstract argumentation systems. Artificial Intelligence, Vol. 90, pp. 225-279.
  • Gordon, T.F. (1995). The Pleadings Game. An Artificial Intelligence Model of Procedural Justice. Kluwer Academic Publishers, Dordrecht.
  • Gordon, T.F., and Karacapilidis, N. (1997). The Zeno Argumentation Framework. The Sixth International Conference on Artificial Intelligence and Law. Proceedings of the Conference, pp. 10-18. ACM, New York (New York).
  • Haack, S. (1978). Philosophy of logics. Cambridge University Press, Cambridge.
  • Hage, J. (1996). A Theory of Legal Reasoning and a Logic to Match. Artificial Intelligence and Law, Vol. 4, pp. 199-273.
  • Hage, J. (1997). Reasoning with Rules. An Essay on Legal Reasoning and Its Underlying Logic. Kluwer Academic Publishers, Dordrecht.
  • Hage, J. (1998). Dialectical Models in Artificial Intelligence and Law. To appear in Artificial Intelligence and Law.
  • Hage, Jaap C., Leenes, Ronald, and Lodder, Arno R. (1994). Hard Cases: A Procedural Approach. Artificial Intelligence and Law, Vol. 2, pp. 113-167.
  • Hintikka, J., and Sandu, G. (1997). Game-Theoretical Semantics. Handbook of logic and language (eds. J. van Benthem and A. ter Meulen), pp. 361-410. Elsevier Science.
  • Lodder, A.R. (1998). DiaLaw. On legal justification and dialog games. Dissertation. Universiteit Maastricht, Maastricht.
  • Lodder, A.R., and Verheij, B. (1999). Computer-mediated legal argument: towards new opportunities in education. The Journal of Information, Law and Technology (JILT), 1999 (2), http://www.law.warwick.ac.uk/jilt/99-2/lodder.html.
  • Lorenzen, P., and Lorenz, K. (1978). Dialogische Logik. Wissenschaftliche Buchgesellschaft, Darmstadt.
  • Loui, R.P. (1992). Process and Policy: Resource-Bounded Non-Demonstrative Reasoning. Report WUCS-92-43. Washington University, Department of Computer Science, Saint Louis (Missouri).
  • Loui, R.P., Norman, J., Altepeter, J., Pinkard, D., Craven, D., Lindsay, J., and Foltz, M. (1997). Progress on Room 5. A Testbed for Public Interactive Semi-Formal Legal Argumentation. The Sixth International Conference on Artificial Intelligence and Law. Proceedings of the Conference, pp. 207-214. ACM, New York (New York).
  • Pollock, J.L. (1995). Cognitive Carpentry: A Blueprint for How to Build a Person. The MIT Press, Cambridge (Massachusetts).
  • Prakken, H. (1997). Logical Tools for Modelling Legal Argument. A Study of Defeasible Reasoning in Law. Kluwer Academic Publishers, Dordrecht.
  • Prakken, H., and Sartor, G. (1996). A Dialectical Model of Assessing Conflicting Arguments in Legal Reasoning. Artificial Intelligence and Law, Vol. 4, pp. 331-368.
  • Rawls, J. (1972). A Theory of Justice. Oxford University Press, Oxford.
  • Reiter, R. (1980). A Logic for Default Reasoning. Artificial Intelligence, Vol. 13, pp. 81-132.
  • Simari, G.R., and Loui, R.P. (1992). A mathematical treatment of defeasible reasoning and its applications. Artificial Intelligence, Vol. 53, pp. 125-157.
  • Simari, G.R., Chesñevar, C.I., and García, A.J. (1994). The Role of Dialectics in Defeasible Argumentation. Proceedings of the XIV International Conference of the Chilean Computer Science Society. Universidad de Concepción, Concepción.
  • Toulmin, S.E. (1958). The uses of argument. University Press, Cambridge.
  • Verheij, B. (1996a). Rules, Reasons, Arguments. Formal studies of argumentation and defeat. Dissertation. Universiteit Maastricht, Maastricht.
  • Verheij, B. (1996b). Two approaches to dialectical argumentation: admissible sets and argumentation stages. NAIC'96. Proceedings of the Eighth Dutch Conference on Artificial Intelligence (eds. J.-J.Ch. Meyer and L.C. van der Gaag), pp. 357-368. Universiteit Utrecht, Utrecht. A preliminary version was presented at the Computational Dialectics Workshop at FAPR-96. June 3-7, 1996, Bonn.
  • Verheij, B. (1998a). Argue! - an implemented system for computer-mediated defeasible argumentation. NAIC '98. Proceedings of the Tenth Netherlands/Belgium Conference on Artificial Intelligence (eds. Han La Poutré and Jaap van den Herik), pp. 57-66. CWI, Amsterdam.
  • Verheij, B. (1998b). ArguMed - A Template-Based Argument Mediation System for Lawyers. Legal Knowledge Based Systems. JURIX: The Eleventh Conference (eds. J.C. Hage, T.J.M. Bench-Capon, A.W. Koers, C.N.J. de Vey Mestdagh and C.A.F.M. Grütters), pp. 113-130. Gerard Noodt Instituut, Nijmegen.
  • Verheij, B. (1998c). Formalism and interpretation in the logic of law. Review of H. Prakken’s ‘Logical Tools for Modelling Legal Argument’. To appear in Artificial Intelligence and Law.
  • Verheij, B. (1999). Automated Argument Assistance for Lawyers. Accepted for the Seventh International Conference on Artificial Intelligence and Law (ICAIL99).
  • Verheij, B., Hage, J.C., and Herik, H.J. van den (1998). An integrated view on rules and principles. Artificial Intelligence and Law, Vol. 6, No. 1, pp. 3-26.
  • Vreeswijk, G.A.W. (1997). Abstract argumentation systems. Artificial Intelligence, Vol. 90, pp. 225-279.

    Contact information

    Bart Verheij
    Department of Metajuridica
    Universiteit Maastricht
    P.O. Box 616
    6200 MD Maastricht
    The Netherlands

    +31 43 3883048
    b.verheij at ai dot rug dot nl
    http://www.ai.rug.nl/~verheij/

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