Multiple-conclusion logic

A multiple-conclusion logic is one in which logical consequence is a relation, \vdash, between two sets of sentences (or propositions). \Gamma \vdash \Delta is typically interpreted as meaning that whenever each element of \Gamma is true, some element of \Delta is true; and whenever each element of \Delta is false, some element of \Gamma is false.

This form of logic was developed in the 1970s by D. J. Shoesmith and Timothy Smiley[1] but has not been widely adopted.

Some logicians favor a multiple-conclusion consequence relation over the more traditional single-conclusion relation on the grounds that the latter is asymmetric (in the informal, non-mathematical sense) and favors truth over falsity (or assertion over denial).

See also


  1. D. J. Shoesmith and T. J. Smiley, Multiple Conclusion Logic, Cambridge University Press, 1978

This article is issued from Wikipedia - version of the 12/30/2010. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.