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Arguments, Stories and Criminal Evidence pp 101–162Cite as

A Formal Logical Hybrid Theory of Argumentation and Explanation

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Part of the book series: Law and Philosophy Library ((LAPS,volume 92))

Abstract

A logical account of the hybrid theory. This logical theory combines abductive, model-based reasoning (as is often used in diagnostical knowledge systems) with a formal framework for defeasible argumentation. A formal dialogue game, detailing a protocol for a rational discussion about the facts, is also defined.

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Notes

  1. 1.

    The formal theory has been published in a more condensed form as (Bex et al., 2010).

  2. 2.

    This conception of rule is based on, but not the same, as Hage and Verheij’s definition of a rule, see (Verheij et al., 1998) 2003 .

  3. 3.

    Note that these rules may have different names in the various deductive systems. See (Gabbay et al., 1993) for an overview.

  4. 4.

    Hage’s theory of rules and reasons was initiated by Hage and further formally developed in cooperation with Verheij (cf. Verheij, 1996; Verheij et al., 1998) .

  5. 5.

    Sartor argues that the legality of a (legal) norm (n: p ⇒ q is legal), modelled in the logic of Prakken and Sartor (Prakken and Sartor, 1996, see p. 4), allows for the derivation of the norm n itself.

  6. 6.

    For more on the discussion of model-theoretic semantics for nonmonotonic logics, see Prakken and Vreeswijk, 2002.

  7. 7.

    Prakken uses the argumentation system from his thesis in much of his work and has proposed extensions of his basic work together with Sartor (e.g. Prakken and Sartor, 1997). In this thesis, I will mostly refer to Prakken’s original system.

  8. 8.

    art. 339 par. 1 sub. 1 and art. 340 DPC, which determine that a judge’s observations are legally valid evidence.

  9. 9.

    Formally, consistency of the set I E can only be defined if the pieces of evidence are not labelled with their names. However, here it will be simply assumed that consistency is determined on the basis of the propositional content of the evidential data, ignoring the names.

  10. 10.

    Strictly speaking, these events can be either events or states of affairs.

  11. 11.

    However, model-based diagnosis should not be equated with abductive reasoning, as there are other types of model-based reasoning (e.g. Bayesian Belief Networks) and other types of symbolic diagnosis (e.g. consistency-based diagnosis). See Lucas, 1997 for an overview.

  12. 12.

    In the current framework, time is not explicitly represented. However, it is assumed that events can only be caused by other events which precede them and thus a sequence of events implicitly assumes temporal relations between the events.

  13. 13.

    Recall that a suspect’s testimony is here also regarded as a witness testimony.

  14. 14.

    However, in the simple examples below the arguments for the explananda will often not be explicitly mentioned.

  15. 15.

    Note that a player may be committed to two arguments that attack each other or to two alternative explanations for the explananda.

  16. 16.

    See (Bex and Prakken, 2004) for a way to integrate such a speech act in a dialogue game similar to the current game.

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Authors and Affiliations

  1. University of Dundee, School of Computing, DD1 4HN, Dundee, UK

    Floris J. Bex

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Correspondence to Floris J. Bex .

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Bex, F.J. (2011). A Formal Logical Hybrid Theory of Argumentation and Explanation. In: Arguments, Stories and Criminal Evidence. Law and Philosophy Library, vol 92. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0140-3_5

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