Abstract
We consider substitutions in order sensitive situations, having in the back of our minds the case of dynamic predicate logic (DPL) with a stack semantics. We start from the semantic intuition that substitutions are move instructions on stacks: the syntactic operation [y/x] is matched by the instruction to move the value of the y-stack to the x-stack. We can describe these actions in the positive fragment of DPLE. Hence this fragment counts as a logic for DPL-substitutions. We give a calculus for the fragment and prove soundness and completeness.
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Vermeulen, C. A Calculus of Substitutions for DPL. Studia Logica 68, 357–387 (2001). https://doi.org/10.1023/A:1012439021359
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DOI: https://doi.org/10.1023/A:1012439021359