As an attempt to uncover the topological nature of composition of strategies in game semantics, we present a “topological” game for Multiplicative Additive Linear Logic without propositional variables, including cut moves. We recast the notion of (winning) strategy and the question of cut elimination in this context, and prove a cut elimination theorem. Finally, we prove soundness and completen...

We give some basic results of the theory of proof nets for multiplicative linear logic and multiplicative exponential linear logic with mix. The relation between proof nets and the lambda-calculus is precisely described. 1 Multiplicative Proof Nets 1.1 Multiplicative Linear Logic We assume given a denumerable set of atoms X, Y , . . . The formulas of multiplicative linear logic (MLL) are define...

The convergence of the multiplicative multisplitting-type method for solving the linear complementarity problem with an H-matrix is discussed using classical and new results from the theory of splitting. This directly results in a sufficient condition for guaranteeing the convergence of the multiplicative multisplitting method. Moreover, the multiplicative multisplitting method is applied to th...