The "Lottery Paradox" Paradox and other Self-Attacking arguments from the Point of View of Defeasible Argumentation Frameworks”

BODANZA, GUSTAVO ADRIÁN

The Many Sides of Logic

College Publications

Lugar: Londres; Año: 2009; p. 481 - 496

The ``lottery paradox´´ paradox --a problem derived from the well-known lottery paradox-- arises as the result of chaining defeasible reasons that lead from the statement `the lottery is fair´ to the statement `the lottery is not fair´, conforming in consequence a self-attacking argument. This paper shows two simple semantics that capture the intuitions about what kinds of arguments should become justified in such scenarios.  The semantics, called {em sustainable} and {em lax} respectively, are modeled upon argumentation frameworks and constructed on the common ground of the powerful concept of admissibility introduced by P.M. Dung.  Both semantics result to be more ``credulous´´ than preferred semantics, since they enable the acceptance of arguments that are attacked only by other arguments that in time are self-attacking. A special kind of self-attacks are those indirectly provoked by odd-lenght cycles of attack. While sustainable semantics overrule them all (in accordance with most semantics in the defeasble argumentation literature), we show some examples of practical reasoning where such cycles do not clearly imply self-attacks, so the involved arguments could be acceptable. Lax semantics is proposed here to capture also this alternative behavior.