We provide a proofs-as-concurrent-programs interpretation for a large class of intermediate logics that can be formalized by cut-free hypersequent calculi. Obtained by adding classical disjunctive tautologies to intuitionistic logic, these logics are used to type concurrent λ-calculi by Curry–Howard correspondence; each of the calculi features a specific communication mechanism, enhanced expressive power when compared to the λ-calculus, and implements forms of code mobility. We thus confirm Avron's 1991 thesis that intermediate logics formalizable by hypersequent calculi can serve as basis for concurrent λ-calculi.

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关于中间逻辑的并发计算内容

我们为大量的中间逻辑提供了“并发程序作为解释”的解释，这些逻辑可以通过免割的超序结石进行形式化。通过在直觉逻辑中添加经典的析取重言式获得，这些逻辑用于通过Curry-Howard对应关系键入并发的λ-计算。每个演算都具有特定的通信机制，与λ演算相比，表达能力增强，并实现了代码移动性的形式。因此，我们确认了Avron 1991年的论点，即通过超继演算可形式化的中间逻辑可以作为并发λ-演算的基础。