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)

Publisher: Springer

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Abstract:

We continue our work [5] 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.

Keywords: Horn fragment; Multiset; disjunctive multiset; linear logic; semantics of the Horn fragment

Document Type: Research Article

DOI: http://dx.doi.org/10.1023/B:STUD.0000009561.61962.5a

Affiliations: Depart. of Mathematics, Univ. of Thessaloniki, 540 06 Thessaloniki, Greece, Email: tzouvara@math.auth.gr

Publication date: December 1, 2003

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