Journal of Logic and Computation, Volume 8, Issue 5, pp. 665-668: Abstract.
Saturated formulas in full linear logic
M Castellan1 and M Piazza2
Department of Mathematics, University of Siena, via del Capitano 15, 53100 Siena, Italy. E-mail: email@example.com, 2Department of Philosophy (Section of Epistemology), University of Genoa, Via Balbi 4, 16126 Genoa, Italy. E-mail: firstname.lastname@example.org
In this note, we show by a proof-theoretical arguement that in full linear logic the set of formulas for which contraction and weakening are admissible (the set of saturated formulas) does not coincide (up to equivalences) with the set of exponentiated formulas. This solves an open problem of Schellinx.
Key words: Linear logic, modalities, proof-theory, sequent calculus.