The "lottery paradox" paradox: an extension semantics for dealing with this and other self-attacking arguments

BODANZA, GUSTAVO ADRIÁN

Paraty, RJ

Simposio; XIV Latin American Symposium on Mathematical Logic; 2009

Sociedad Brasileira de Logica

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. In the argument systems community, the common intuition is that the subargument concluding `the lottery is fair´ should not be defeated by the whole, self-attacking argument. This paper shows two simple extension semantics that capture this intuition.  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 (cite{cite1}).  Sustainable semantics results to be more ``credulous´´ than preferred semantics, since enables the acceptance of arguments that are attacked only by other arguments that in time are self-attacking. Lax semantics, on the other hand, behaves the same as sustainable semantics, in addition to the acceptance of arguments that are self-attacking only in an indirect way (viz., those involved in odd-length cycles of attack).