We describe a polymorphic, typed lambda calculus with substructural features. This calculus extends the first-order substructural lambda calculus αλ associated with bunched logic. A particular novelty of our new calculus is the substructural treatment of second-order variables. This is accomplished through the use of bunches of type variables in typing contexts. Both additive and multiplicative...

Multiplicative calculus, also called non-Newtonian represents an alternative approach to the usual calculus of Newton (1643–1727) and Leibniz (1646–1716). This type was first introduced by Grossman Katz it provides a defined calculation, from start, for positive real numbers only. In this investigation, we propose study symmetrical fractional multiplicative inequalities Simpson type. For this, ...

Based on multiplicative calculus, the finite difference schemes for the numerical solution of multiplicative differential equations and Volterra differential equations are presented. Sample problems were solved using these new approaches.

We introduce the calculus of structures: it is more general than the sequent calculus and it allows for cut elimination and the subformula property. We show a simple extension of multiplicative linear logic, by a self-dual noncommutative operator inspired by CCS, that seems not to be expressible in the sequent calculus. Then we show that multiplicative exponential linear logic benefits from its...

This paper investigates the proof theory of multiplicative additive system virtual (MAV). MAV combines two established proof calculi: multiplicative additive linear logic (MALL) and basic system virtual (BV). Due to the presence of the self-dual non-commutative operator from BV, the calculus MAV is defined in the calculus of structures — a generalisation of the sequent calculus where inference ...