R. Statman. -denable functionals and  conversion. Arch. Math. Logik Grundlagenforsch, 23:21-26, 1983.  Home/Search   Document Not in Database   Summary   Related Articles

....semantics s, the answer to our question is positive, we say that the semantics is injective: two di erent proof nets without cuts have di erent interpretations in the semantics s. This kind of question has been studied for the pure and simply typed calculus in several papers (see for example [Sta83]) It is somehow surprising that, while the question of surjectivity of the semantics (also known as full completeness ) has been extensively studied for LL, the question of injectivity was never studied before [TdF00b] To ask the question of injectivity of (say) the coherent semantics of LL, ....

....for the multiplicative and exponential fragment of LL, without axiom links but with the links introducing the multiplicative constants 1 and . In the set based case, the non injectivity is obvious (see [TdF00b] for more details) 4.2.3. Remark. Our counterexamples show also that the result of [Sta83] on the maximality of the equivalence for the simply typed calculus does not extend to MELL (see [TdF00b] for more details) Let us conclude the present section by observing that in both our counterexamples the presence of weakenings is crucial, and that none of our proof nets is polarized. ....

R. Statman. -denable functionals and  conversion. Arch. Math. Logik Grundlagenforsch, 23:21-26, 1983.

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