Topic: PARACONSISTENCY
The Dialogical Dynamics of Adaptive Paraconsistency
Shahid Rahman & Jean Paul van Bendegem
The dialogical approach to paraconsistency as developed by Rahman and Carnielli ([1]), Rahman and Roetti ([2]) and Rahman ([3], [4] and [5]) suggests a way of studying the dynamic process of arguing with inconsistencies.
In his paper on Paraconsistency and Dialogue Logic ([6]) Van Bendegem suggests that an adaptive version of paraconsistency is the natural way of capturing the inherent dynamics of dialogues. The aim of this paper is to develop a formulation of dialogical paraconsistent logic in the spirit of an adaptive approach and which explores the possibility of eliminating inconsistencies by means of logical preference strategies.
One way to formulate paraconsistent logic within the dialogical approach as developed in Rahman and Carnielli ([1]), Rahman and Roetti ([2]) and Rahman ([4]) can be achieved in the following way. Assume that to the structural rules of the standard dialogical logic [i] we add the following:Negative Literal Rule:
The Proponent is allowed to attack the negation of an atomic (propositional) statement (the so called negative literal) if and only if the Opponent has already attacked the same statement before.
This structural rule can be considered in analogy to the formal rule for positive literals. The idea behind this rule is the following: An inconsistency of the Opponent may be tolerated by using a type of charity principle. The inconsistency might involve different semantic contexts in which, say, aand ?ahave been asserted. Now, if the Opponent attacks ?awith ahe concedes thereby that there is some common context between ?aand awhich makes an attack on ?apossible. This allows the Proponent to attack the corresponding negation of the Opponent.
In Rahman and Carnielli ([1]) the logics produced by this rule were called Literal Dialogues , or shorter: L-D. In order to distinguish between the intuitionistic and the classical version Rahman and Carnielli wrote L-D i(for the intuitionistic version) and L-D c(for the classical version). To be precise we should call these logical systems literal dialogues with classical structural rules and literal dialogues with intuitionistic structural rules respectively.
(...)
The Proponent loses because he is not allowed to attack the move (5) (see negative literal rule). In other words the Opponent may have contradicted himself, but the semantic context of the negative literal is not available to the Proponent until the Opponent starts an attack on the same negative literal ?an attack which in this case will not take place.
Link
Posted by Tony Marmo
at 01:01 BST
Updated: Tuesday, 7 September 2004 16:52 BST
