Implications as Rules in Dialogical Semantics

Abstract

The conception of implications as rules is interpreted in Lorenzen-style dialogical semantics. Implications-as-rules are given attack and defense principles, which are asymmetric between proponent and opponent. Whereas on the proponent’s side, these principles have the usual form, on the opponent’s side implications function as database entries that can be used by the proponent to defend assertions independent of their logical form. The resulting system, which also comprises a principle of cut, is equivalent to the sequent-style system for implications-as-rules. It is argued that the asymmetries arising in the dialogical setting are not deficiencies but reflect the pre-logical ‘structural’ character of the notion of rule.