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Quantifying over propositions in relevance logic: Nonaxiomatisability of primary interpretations of $${\forall}p$$ and $${\exists}p$$. (English) Zbl 0786.03016
This nicely written paper presents “a quite general method for proving that systems resulting from an algebraically-motivated primary interpretation of propositional quantification are recursively isomorphic to full second-order classical logic” (p. 346). It turns out that both the universal quantifier associated with Urquhart’s semilattice semantics and $$\forall p$$ and $$\exists p$$ associated with Routley and Meyer’s relational semantics are not axiomatizable.
Reviewer: M.Urchs (Leipzig)

##### MSC:
 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
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##### References:
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