Action and Procedure in Reasoning

  • Johan van Benthem
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 94)


Meaningful comparisons between “logic” and “legal reasoning” must evolve with their relata. In this Article, I explain some basics of “logical dynamics,” a current procedure-oriented view of reasoning and other cognitive tasks, using games as a model for many-agent interaction. Against this background, I speculate about possible new connections between logical dynamics and legal reasoning.


Nash Equilibrium Imperfect Information Winning Strategy Legal Reasoning Game Tree 
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    There are many further analogies between major logical issues in computation/cognition and in law. We mention just a few: (a) rule subsumption vs. pattern recognition, (b) worst vs. average case performance, (c) avoiding errors of two types (false positives, false negatives), and (d) protocols for achieving secrecy.Google Scholar
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    For this way of thinking, see generally Johan van Benthem, Exploring Logical Dynamics (1996).Google Scholar
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    Note that reasoning still makes sense in the update setting. It provides a “red thread” of significant assertions through successive updates, as may be seen in realistic problem solving. This is one instance of the general issue how abstract “information” is turned into concrete “knowledge.” Moreover, the strict order dependence of premise updates may be unrealistic. Consider the following information: A-3-B, BvC, A. Most people would first combine the third premise with the first, and then use the second to arrive at the facts A, -B, C. On the other hand, real-time argumentation makes such choices irrevocable, which is another form of order-dependence.Google Scholar
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  7. Many other notions are naturally subject to updating. Consider agents’ preferences. These, too, may change because of incoming information and logical calculi performing “upgrades” have been proposed by Wolfgang Spohn and Frank Veltman. Compare the review of update logics in Reinhard Muskens, Dynamics, in Handbook of Logic and Language 588–648 (Johan van Benthem & Alice ter Meulen eds., 1997); Frank Veltman, Defaults in Update Semantics, 25 J. Phil. Logic, 221–61 (1997).Google Scholar
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    Another way of thinking about this particular game is as “matching pennies.”Google Scholar
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    More precisely, construction games may be represented by the well-known logical technique of “semantic tableaus,” viewed this time as “dynamic objects.”Google Scholar
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    See Henri Prakker & Giovanni Sartor, Argument-based Extended Logic Programming with Defeasible Priorities, J. Applied Non-Classical Logics 25–75 (1997), (last visited March 30, 2001). Google Scholar
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    This section only scratches the surface of a complex interaction between game theory and logic. There are many further topics of investigation here. Preferences in games also suggest “deontic dynamics.” One might make preferences themselves an issue for gaming, providing mechanisms for changing them. See Lamber M.M. Royakkers, Extending Deontic Logic for the Formalisation of Legal Rules (1998).Google Scholar
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    In computer science, one has intermediate cases, where a game would be played a sufficient number of times (i.e., a sufficient number of branches of the full game tree is traversed) to make it highly plausible that Verifier has a winning strategy. The most famous algorithm for achieving optimal performance in one-shot situations comes from a judicial setting, however, viz. Cake Cutting. This seems to derive from old Germanic procedures in dividing the loot of a raid. One party divides, the other gets the first choice as is still visible in the Dutch expression “kiezen of delen” (“Do you wish to choose, or divide up?”).Google Scholar
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    This anecdote is mentioned in Nicholas Rescher, Introduction to Logic 203 (1964).Google Scholar
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    In Amsterdam, Ron Allen gave a more substantial legal analysis, reproduced here from a private communication: The contract entered into explicitly calls for the fee to “be the first money his student made in winning a law-suit.” The suit does not call for a fee if his student wins a suit; it calls for a fee if he makes money winning a suit. When the teacher sues the student, whether the student “wins” or “loses,” the student will not make money; therefore, no payment would be due under the contractual provision. Since no payment would be due under the contractual provision no matter how the lawsuit against the student comes out, obviously the lawsuit has no basis and will be dismissed. This result is unfair only if the student somehow misled the teacher. For example, perhaps the student was only interested in learning about the law, but never intended to practice it. In order to get a free legal education, however, perhaps he feigned an interest in practice, inculcating the belief in the teacher that the student intended to practice, thus inducing the teacher to enter into this contract. Well, the law handles this as well. It is called “fraud in the inducement.” If the teacher can prove that there was such fraud, he can recover his damages. And in American courts, maybe punitive damages as well.Google Scholar
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    One case was Josephson’s lecture on legal abduction procedures at the Amsterdam conference. H is an abductive conclusion from D if: (a) H implies D (together with some background theory), (b) D are correct data, and (c) there is no “better” hypothesis H’ which also derives D. Unpacking this in a logic game between “Proposer” and “Critic,” one gets moves corresponding to the three clauses: (a) attack the inference from H to D, i.e., be Builder in a construction game for (H, -’D), (b) attack at least one of D, (c) using the quantifier form of “being best,” attack (c) by presenting some H’ for which you claim that it also derives D, and that it is better. Proposer can then attack either conjunct of this, again entirely via the rules for a standard logic game. The latter may be cast as a game for checking if some proposed hypothesis H is really a best explanation for a given data D. Some further interesting points in Josephson’s account also relate to “game logic.” First, one of the options for “Critic” vs. “Proposer” is to derive a false consequence from H. This seems to correspond to a further requirement that “H has to be true,” or at least “consistent with what is known.” Second, Proposer can dispose of a whole bunch of alternative hypotheses at once. This is not needed in our game; it would tell him to reveal more of his strategy than is warranted. (But mentioning a lot of potential points for your opponent, even if you do not have a strong refutation, is a well-known rhetorical trick. At least, your opponent incurs the odium of saying something “predictable.”) Third, the requirement for a defense lawyer is that she should produce an alternative explanation, after the prosecution has come up with explanation H (normally, the guilt of the accused). This seems stronger than what would be minimally required, viz., showing the evidence to be consistent with the negation of H. Fourth, one commentator described the judge’s task as choosing between alternative “stories” in which the data D “fit.” Are these then like models, hypotheses, or a mixture of both ways of thinking?Google Scholar
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    What logicians already know is that restrictions to various fine-structure formats of assertion, and accompanying “lightweight calculi,” can improve performance in consistency checking and proof search dramatically. It might be of interest to see whether these correspond to anything in legal reasoning.Google Scholar
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    Winning strategies may be too costly to execute, so we must sometimes settle for less. This can be modeled by assigning costs to actions in a game tree, and then computing optimal strategies through the tree given initial resources of players.Google Scholar
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    There have been suggestions for “science courts,” where legal-style debate would be used to get the best current opinions on issues that have been under scientific debate for a very long time and where some temporary resolution would be useful (e.g., when preparing funding decisions).Google Scholar

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© Physica-Verlag Heidelberg 2002

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  • Johan van Benthem

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