Private names in non-commutative logic

Horne, Ross and Tiu, Alwen and Aman, Bogdan and Ciobanu, Gabriel; Desharnais, Josée and Jagadeesan, Radha, eds. (2016) Private names in non-commutative logic. In: 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics . Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, Saarbrücken/Wadern, 31:1-31:16. ISBN 9783959770170 (https://doi.org/10.4230/LIPIcs.CONCUR.2016.31)

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Abstract

We present an expressive but decidable first-order system (named MAV1) defined by using the calculus of structures, a generalisation of the sequent calculus. In addition to first-order universal and existential quantifiers the system incorporates a de Morgan dual pair of nominal quantifiers called `new' and `wen', distinct from the self-dual Gabbay-Pitts and Miller-Tiu nominal quantifiers. The novelty of the operators `new' and `wen' is they are polarised in the sense that `new' distributes over positive operators while `wen' distributes over negative operators. This greater control of bookkeeping enables private names to be modelled in processes embedded as predicates in MAV1. Modelling processes as predicates in MAV1 has the advantage that linear implication defines a precongruence over processes that fully respects causality and branching. The transitivity of this precongruence is established by novel techniques for handling first-order quantifiers in the cut elimination proof.

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