Structuring interactions

Abstract

In this chapter, I first consider mode standard constructive semantic approaches to the formal propositional logics for proofs and refutations. Whilst these illuminate aspects of the structure of interactive logic, they also highlight the shortcomings of standard semantics, even in dualised form. Nonetheless, the way in which these structures “objectify” propositions is useful for considering propositions as stable objects subsequent to their construction in interaction. These ideas are made more precise through the notion of bisimulation equivalence, and closure under bisimulation. To finish, I provide a number of examples, using these to highlight a slightly more liberal conception of the coherence of interactions.