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Formal dialectic systems have been suggested as a means to model inter-agent communication in multi-agent systems. The formal dialectic systems of Hamblin are practical models for the computational implementation of such a system of argumentative dialogue. This paper introduces a formal framework for the specification of Hamblin-type systems that has a range of benefits for theoretical work in the area including: yielding concise sets of clearly defined moves; allowing the moves of both existing and new games to be specified in a consistent manner; facilitating the use of dialectical shifts and dialogue embeddings independent of ruleset; facilitating the investigation of the coupling between sets of moves and dialogue situations; defining the attributes possessed by the general Hamblin-style formal dialectical system and thereby enabling the systematic exploration of the types of moves that these systems might encompass; and facilitating the rapid development of software applications that use formal dialectic to regulate communications.