Non-deterministic Boolean Proof Nets

The calculus of structures permits more proofs than the sequent calculus, by allowing inference rules to be applied in any context; while still satisfying proof theoretic

As a result of this unity, the sequent calculus provided logic programming a natural framework in which proof-search could be described for much richer logics (first-order

For example, once Prolog was described as proof search in sequent calculus, there was a direct line to the development of a logic programming language, for example λProlog, that

We have presented a correspondence between proof nets and perfect matchings, and demon- strated its usefulness through several applications of graph theory to linear logic: our

An application of parallel cut elimination in unit-free multi- plicative linear logic to the Taylor expansion of proof nets... unit-free multiplicative linear logic to

Sequentialisation (Theorem 2) Desequentialisation (Proposition 8) Pre-proofs (Definition 4) Valid pre-proofs a.k.a proofs (Definition 8) Cut-free proofs Non-wellfounded proof

From Proof Nets to Combinatorial Proofs - A New Approach to Hilbert’s 24th Problem.. Willem Heijltjes,

We present a formalization of proof-nets (and more generally, proof- structures) for the multiplicative-exponential fragment of linear logic, with a novel treatment of boxes: instead