Center for Logic and
is about what-follows-from-what. The idea that an argument is to
sanction the derivation of one conclusion from a set of
premises is just as intuitive as, unfortunately, technically wanting. A
more generous and more symmetric account of consequence and entailment
should in fact allow for the derivation of a set of
alternatives as the conclusion of the argument. As it has been argued
by universal logicians, the right choice of framework is important from
a methodological, a philosophical, and a mathematical point of view.
And that choice is nothing but fundamental if logic is to deserve a
distinguished place at an updated Bourbakian architecture of
The aim of this tutorial is to present the advantages and purview of a multiple-conclusion approach to logic and metalogic. Such an approach helps not only to eliminate any still existing bias towards truth (when falsity is just as respectable), but also to help expressing and comparing different kinds of logical systems. The very basic, though lamentably still insufficiently well-known, general issues and techniques related to multiple-conclusion reasoning will be presented in the tutorial.
The first lecture will compare the single-conclusion and multiple-conclusion approaches, for a motivation, and will survey some standard approximations to the very concept of logic.
The second lecture will investigate what happens in such an environment with the general metalogical tools and concepts, both from an abstract and a semantical standpoints.
The third lecture will deal with specific applications, further illustrations, and more esoteric results.
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