The Logic of Multisets Continued: The Case of Disjunction
Author: Tzouvaras, Athanassios
Source: Studia Logica, Volume 75, Number 3, December 2003 , pp. 287-304(18)
Abstract:We continue our work  on the logic of multisets (or on the multiset semantics of linear logic), by interpreting further the additive disjunction ⊔. To this purpose we employ a more general class of processes, called free, the axiomatization of which requires a new rule (not compatible with the full LL), the cancellation rule. Disjunctive multisets are modeled as finite sets of multisets. The ⊔-Horn fragment of linear logic, with the cut rule slightly restricted, is sound with respect to this semantics. Another rule, which is a slight modification of cancellation, added to HF⊔ makes the system sound and complete.
Document Type: Research Article
Affiliations: Depart. of Mathematics, Univ. of Thessaloniki, 540 06 Thessaloniki, Greece, Email: firstname.lastname@example.org
Publication date: December 1, 2003