BILATERAL RULES AS COMPLEX RULES

Proof-theoretic semantics is an inferentialist theory of meaning originally devel-oped in a unilateral framework. Its extension to bilateral systems opens bothopportunities and problems. The problems are caused especially by Coordina-tion Principles (a kind of rule that is not present in unilateral systems) andmismatches between rules for assertion and rules for rejection. In this paper,a solution is proposed for two major issues: the availability of a reduction proce-dure fortonkand the existence of harmonious rules for the paradoxical zero-aryconnective center dot. The solution is based on a reinterpretation of bilateral rules as com-plex rules, that is, rules that introduce or eliminate connectives in a subordinateposition. Looking at bilateral rules from this perspective, the problems faced bybilateralism can be seen as special cases of general problems of complex systems,which have been already analyzed in the literature. In the end, a comparison withother proposed solutions underlines the need for further investigation in order tocomplete the picture of bilateral proof-theoretic semantics.