Two Types of Multiple-Conclusion Systems

Hypersequents are nite sets of ordinary sequents. We show that multiple-conclusion sequents and single-conclusion hypersequents represent two di erent natural methods of switching from a singleconclusioncalculusto a multiple-conclusionone. The useof multiple-conclusionsequentscorresponds to using a multiplicativedisjunction,while the use of single-conclusionhypersequentscorrespondsto using an additive one. Moreover: each of the two methods is usually based on a di erent natural semantic idea and accordinglyleads to a di erentclass of algebraicstructures. In the cases we consider here the use of multiple-conclusion sequents corresponds to focusing the attention on structures in which there is a full symmetry between the sets of designatedand antidesignated elements. The use of single-conclusionhypersequents, on the other hand, corresponds to the use of structures in which all elementsexceptone are designated. Not surprisingy,the use of multiple-conclusionhypersequents corresponds to th...

• Type: Journal
• Year: 1998
• Where: IGPL
• Authors: Arnon Avron
• Keywords: Erent Natural Methods, IGPL 1998, Multiple-conclusion Sequents, Natural Semantic Idea