Problem
Research questions and friction points this paper is trying to address.
proof-theoretic semantics
continuation-passing semantics
intuitionistic propositional logic
completeness
meaning and use
Continuations and Completeness in Proof-theoretic Semantics
📝 Abstract
This is a short paper about the relationship between logic and computation. More specifically, it is about a relationship between the completeness proof for intuitionistic propositional logic within the form of proof-theoretic semantics that is known as base-extension semantics and a fundamental idea from the theory of computation called continuation-passing semantics. The latter is explained herein both in terms of reduction in natural deduction and the lambda calculus and in terms of proof-search. The relationship between completeness and continuations is explored through an analysis of Sandqvist's proof of the completeness theorem as seen from the mathematical perspective of Kripke's and Heyting's semantics. Our analysis can be seen to reveal how syntactic representations of continuations embody intensional semantical intuitions about the relationship between their meaning and use. These intuitions are made precise using the tools of proof-theoretic semantics.
Innovation
Methods, ideas, or system contributions that make the work stand out.
continuation-passing semantics
proof-theoretic semantics
base-extension semantics
completeness theorem
intuitionistic propositional logic
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