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Isomorphic formulae in classical propositional logic. (English) Zbl 1262.03119
Any categorical interpretation of logic determines a notion of isomorphism between two formulae. The paper under review investigates such isomorphisms in classical propositional logic: in that case, following a remark by Joyal [J. Lambek and P. J. Scott, Introduction to higher order categorical logic. Cambridge etc.: Cambridge University Press (1986; Zbl 0596.03002)], if one restricts to Cartesian closed models, isomorphism collapses to logical equivalence and becomes irrelevant.
Therefore, the authors drop the Cartesian closedness condition and turn to categories where morphisms are generated by compositions and monoidal operations from a set of primitive arrows, subject to coherence equations. Syntactic characterizations of pairs of isomorphic formulae are then obtained, in the spirit of coherence results in monoidal categories [G. M. Kelly and S. MacLane, J. Pure Appl. Algebra 1, 97–140 (1971; Zbl 0212.35001)].

03F03 Proof theory in general (including proof-theoretic semantics)
03B05 Classical propositional logic
03F07 Structure of proofs
03F52 Proof-theoretic aspects of linear logic and other substructural logics
03G30 Categorical logic, topoi
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