[FML1502] Ross Horne, Alwen Tiu, Bogdan Aman, Gabriel Ciobanu. Polarised Nominal Quantifiers Model
Private Names in NonCommutative Logic.pp 53, May, 2015 (Revised:
September, 2017) ISSN
1842  1490 
Abstract (click to show/hide)
This paper explores the proof theory necessary for recommending an expressive but decidable firstorder system, named MAV1, featuring a de Morgan dual pair of nominal quantifiers.
These nominal quantifiers called `new' and `wen' are distinct from the selfdual GabbayPitts and MillerTiu nominal quantifiers.
The novelty of these nominal quantifiers 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.
The technical challenge is to establish a cut elimination result, from which essential properties including the transitivity of implication follow.
Since the system is defined using the calculus of structures, a generalisation of the sequent calculus, novel techniques are employed.
The proof relies on an intricately designed multisetbased measure of the size of a proof, which is used to guide a normalisation technique called splitting.
The presence of equivariance, which swaps successive quantifiers, induces complex interdependencies between nominal quantifiers, additive conjunction and multiplicative operators in the proof of splitting.
Every rule is justified by an example demonstrating why the rule is necessary for soundly embedding processes and ensuring that cut elimination holds.
