A General Framework for Modelling Conditional Reasoning -- Preliminary Report

Conditionals are generally considered the backbone of human (and AI) reasoning: the "if-then" connection between two propositions is the stepping stone of arguments and a lot of the research effort in formal logic has focused on this kind of connection. A conditional connection satisfies different properties according to the kind of arguments it is used for. The classical material implication is appropriate for modelling the "ifthen" connection as it is used in Mathematics, but the equivalence between the material implication A B and A B is not appropriate for many other contexts.