Abstract We show that some classical identities about multiplicative functions, and the Riemann zeta-function, may conveniently be interpreted in terms of the addition of ±1 to some alphabets. Résumé Nous montrons que des identités classiques concernant des fonctions multiplicatives de la théorie des nombres, et la fonction zeta de Riemann, s’interprètent commodément en terme de l’opération : “...

Propositional linear logic is known to be undecidable. In the current paper we prove that full propositional linear aÆne logic containing all the multiplicatives, additives, exponentials, and constants is decidable. The proof is based on a reduction of linear aÆne logic to sequents of speci c \normal forms", and on a generalization of Kanovich computational interpretation of linear logic adapte...

We define infinitary count-invariance for categorial logic, extending countinvariance for multiplicatives (van Benthem, 1991) and additives and bracket modalities (Valentı́n et al., 2013) to include exponentials. This provides an e↵ective tool for pruning proof search in categorial parsing/theorem-proving.

The literature on categorial type logic includes proposals for semantically inactive additives, quantifiers, and modalities Morrill (1994[17]), Hepple (1990[2]), Moortgat (1997[9]), but to our knowledge there has been no proposal for semantically inactive multiplicatives. In this paper we formulate such a proposal (thus filling a gap in the typology of categorial connectives) in the context of ...