A Purely Logical Account of Sequentiality in Proof Search
A strict correspondence between the proof-search space of a logical formal system and computations in a simple process algebra is established. Sequential composition in the process algebra corresponds to a logical relation in the formal system in this sense our approach is purely logical, no axioms or encodings are involved. The process algebra is a minimal restriction of CCS to parallel and sequential composition; the logical system is a minimal extension of multiplicative linear logic. This way we get the first purely logical account of sequentiality in proof search. Since we restrict attention to a small but meaningful fragment, which is then of very broad interest, our techniques should become a common basis for several possible extensions. In particular, we argue about this work being the first step in a two-step research for capturing most of CCS in a purely logical fashion.
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