Many logics are possible: From a logic where nothing is a consequence of nothing, to a logic where everything is a consequence of eveyrthing passing through a whole spectrum including classical logic, many-valued logic, turbo polar linear logic.

One can wonder if we are not then facing a wilde jungle, from which some monsters like anti-classical logic, the complement of classical logic where a proposition is not a consequence of itself, have to be rejected.

In this tutorial we will discuss these questions. We will also present methodologies to construct logics and frameworks to compare them.

Many examples and concepts will be provided.

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Bibliography:

J-.Y.Beziau, "From consequence operator to universal logic: a survey og general abstract logic" in Logica Universalis; Towards a general theory of logic, Birkhäuser, Basel, 2007, pp.3-17.

Haskell Curry, Foundations of mathematical logic, McGraw-Hill, New York 1963.

Dov Gabbay (ed), What is a logical system? Clarendon, Oxford, 1994.

Jean Porte, Recherches sur la théorie générale des systèmes formels et sur les systèmes connectifs, Gauthiers-Villars, Paris and Nauwelaerts, Louvain, 1965.