Artificial Intelligence and Law

, Volume 9, Issue 2–3, pp 153–163 | Cite as

Kappa calculus and evidential strength: A note on Åqvist's logical theory of legal evidence

  • Solomon Eyal Shimony
  • Ephraim Nissan


Lennart Åqvist (1992) proposed a logical theory of legal evidence, based on the Bolding-Ekelöf of degrees of evidential strength. This paper reformulates Åqvist's model in terms of the probabilistic version of the kappa calculus. Proving its acceptability in the legal context is beyond the present scope, but the epistemological debate about Bayesian Law isclearly relevant. While the present model is a possible link to that lineof inquiry, we offer some considerations about the broader picture of thepotential of AI & Law in the evidentiary context. Whereas probabilisticreasoning is well-researched in AI, calculations about the threshold ofpersuasion in litigation, whatever their value, are just the tip of theiceberg. The bulk of the modeling desiderata is arguably elsewhere, if one isto ideally make the most of AI's distinctive contribution as envisaged forlegal evidence research.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Åqvist, L. (1992). Towards a Logical Theory of Legal Evidence: Semantic Analysis of the Bolding-Ekelöf Degrees of Evidential Strength. In Martino, A. A. (ed.), Expert Systems in Law, 67-86. North-Holland: Amsterdam.Google Scholar
  2. Bolding, P. O. (1960). Aspects of the Burden of Proof. Scandinavian Studies in Law 4: 9-28.Google Scholar
  3. Charniak, E. and Shimony, S. E. (1990). Probabilistic Semantics for Cost-Based Abduction. In Proceedings of the 11th Annual National Conference on Artificial Intelligence (AAAI'90), 106-111. AAAI Press: Menlo Park, CA.Google Scholar
  4. Charniak, E. and Shimony, S. E. (1994). Cost-Based Abduction and MAP Explanation. Artificial Intelligence, 66: 345-374.Google Scholar
  5. Ekelöf, P. O. (1964). Free Evaluation of Evidence. Scandinavian Studies in Law 8.Google Scholar
  6. Fakher-Eldeen, F., Kuflik, Ts., Nissan, E. Puni, G., Salfati, R., Shaul, Y. and Spanioli, A. (1993). Interpretation of Imputed Behavior in ALIBI (1 to 3) and SKILL. Informatica e Diritto 19, 2nd series, 2(1-2): 213-242.Google Scholar
  7. Henrion, M., Provan, G., Del Favero, B. and Sanders, G. (1994). An Experimental Comparison of Numerical and Qualitative Probabilistic Reasoning. In Lopez de Mantaras, R. and Poole, D. (eds), Uncertainty in Artificial Intelligence: Proceedings of the Tenth Conference, 319-326. Morgan Kaufmann: San Mateo, CA.Google Scholar
  8. Jackson, B. (1998a). On the Atemporality of Legal Time. In Ost, F. and van Hoecke, M. (eds), Temps et Droit. Le droit a-t-il pour vocation de durer, 222-246. Bruylant: Brussels.Google Scholar
  9. Jackson, B. (1998b). Truth or Proof?: The Criminal Verdict. International Journal for the Semiotics of Law 11(33): 227-273.Google Scholar
  10. Jackson, B. (1998c). Bentham, Truth and the Semiotics of Law. (Current Legal Problems, 51.) In Freeman, M. D. A. (ed.), Legal Theory at the End of the Millennium, 493-531. Oxford University Press: Oxford.Google Scholar
  11. Kuflik, Ts., Nissan, E. and Puni, G. (1991). Finding Excuses with ALIBI: Alternative Plans that are Deontically More Defensible. Computers and Artificial Intelligence 10(4): 297-325.Google Scholar
  12. Kvart, I. (1994). Overall Positive Causal Impact. Canadian Journal of Philosophy 24(2): 205-227.Google Scholar
  13. Martino, A. A. and Nissan, E. (eds) (1998a). Formal Models of Legal Time: Law, Computers and Artificial Intelligence, special issue of Information and Communications Technology Law 7(3).Google Scholar
  14. Martino, A. A. and Nissan, E. (1998b). La prova giudiziaria: area emergente dell' “AI & Law”. Oltre la statistica forense e l'algebra delle giurie, l'integrazione di metodi AI per affrontare un dominio proteiforme. Proceedings of AI, 104-108. Padua: Italy.Google Scholar
  15. Nissan, E. (1995). SEPPHORIS: An Augmented Hypergraph-Grammar Representation for Events, Stipulations, and Legal Prescriptions. Law, Computers, and Artificial Intelligence 4(1): 33-77.Google Scholar
  16. Nissan, E. (1997a). Emotion, Culture, Communication. Pragmatics and Cognition 5(2): 355-369.Google Scholar
  17. Nissan, E. (1997b). Notions of Place (2 parts). In Martino, A. A. (ed.), Logica delle norme, 256-302 + 303-361. SEU: Pisa.Google Scholar
  18. Nissan, E. (1999). Artificial Intelligence and Criminal Evidence: A Few Topics. Proceedings of the Second World Conference on New Trends in Criminal Investigation and Evidence. Amsterdam, 10-15 December 1999. Edited by C. M. Breur et al., 495-521. Antwerpen: Intersentia.Google Scholar
  19. Nissan, E. (2000). The Jama Legal Narrative. Part II: A Foray into Concepts of Improbability. Preproceedings of the AISB 2000 Symposium on AI and Legal Reasoning, 37-45 Birmingham, 17 April 2000, pp. 37-45. Now in Information and Communications Technology Law 10(1), 2001, special issue, edited by D. M. Peterson et al., pp. 39-52.Google Scholar
  20. Nissan, E. (2001). Can You Measure Circumstantial Evidence? The Background of Probative Formalisms for Law. Review article on I. Rosoni, Quae singula non prosunt collecta iuvant: La teoria della prova indiziaria nell'età medievale e moderna (Giuffrè, Milan, 1995). Information and Communications Technology Law (in press).Google Scholar
  21. Nissan, E. and Dragoni, A. F. (2000). Exoneration, and Reasoning About It: A Quick Overview of Three Perspectives. At Intelligent Decision Support for Legal Practice (IDS 2000). In Proceedings of the International ICSC Congress “Intelligent Systems & Applications” (ISA'2000), December 11-15, University of Wollongong, Australia, Vol. 1, pp. 94-100.Google Scholar
  22. Pearl, J. (1993). From Conditional Thoughts to Qualitative Decision Theory. In Uncertainty in AI, Proceedings of the Ninth Conference, 12-20.Google Scholar
  23. Santos, E., Jr. and Shimony, S. E. (1994). Belief Updating by Enumerating High-Probability Independence-Based Assignments. In Lopez de Mantaras, L. and Poole, D. (eds), Uncertainty in Artificial Intelligence: Proceedings of the Tenth Conference, 506-513. Morgan Kaufmann: San Mateo, CA.Google Scholar
  24. Shimony, S. E. (1993). The Role of Relevance in Explanation. I: Irrelevance as Statistical Independence. International Journal of Approximate Reasoning 8(4): 281-324.Google Scholar
  25. Shimony, S. E. and Charniak, E. (1990). A New Algorithm for Finding MAP Assignments to Belief Networks. In Bonissone, P. P., Henrion, M., Kanal, L. N. and Lemmer, J. F. (eds), Uncertainty in Artificial Intelligence: Proceedings of the Sixth Conference, 185-193. North-Holland: Amsterdam.Google Scholar
  26. Schum, D. (2001). Evidence Marshaling for Imaginative Fact Investigation. Artificial Intelligence and Law 9: 165-188.Google Scholar
  27. Spohn, W. (1988). A Dynamic Theory of Epistemic States. In Harper, W. L. and Skyrms, B. (eds), Causation in Decision, Belief Change, and Statistics, 105-134. D. Reidel, Dordrecht: Holland.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Solomon Eyal Shimony
    • 1
  • Ephraim Nissan
    • 2
  1. 1.Department of Computer ScienceBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.School of Computing and Information SystemsThe University of GreenwichGreenwich, LondonUK

Personalised recommendations