SEMANTICS FOR REDUCTIVE LOGIC
This chapter provides a systematic model-theoretic account of reductive logic. Here, the challenge is to provide semantic structures that are rich enough to account not only for the space of proofs, but also for the (larger) space to reductions — all proofs may be seen as successful reductions whereas many reductions fail to determine proofs. The techniques used are those of categorical model theory and categorical proof theory, and essential use is made of the interplay between the semantics of proofs given by algebraic realizers and the meaning of propositions given by Kripke's account of truth-functional semantics.
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