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arXiv · 1212.4483

Extending a system in the calculus of structures with a self-dual quantifier

Luca Roversi
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Abstract

We recall that SBV, a proof system developed under the methodology of deep inference, extends multiplicative linear logic with the self-dual non-commutative logical operator Seq. We introduce SBVQ that extends SBV by adding the self-dual quantifier Sdq. The system SBVQ is consistent because we prove that (the analogous of) cut elimination holds for it. Its new logical operator Sdq operationally behaves as a binder, in a way that the interplay between Seq, and Sdq can model β-reduction of linear λ-calculus inside the cut-free subsystem BVQ of SBVQ. The long term aim is to keep developing a programme whose goal is to give pure logical accounts of computational primitives under the proof-search-as-computation analogy, by means of minimal, and incremental extensions of SBV.

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Luca Roversi. 2012-12-18. Extending a system in the calculus of structures with a self-dual quantifier. https://doi.org/10.1093/logcom/exu033

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