Input/output logics
The authors propose that we think of logic not merely as an inference engine, but as a way of preparing information for a more general method of input/output transformation. Four such `logics' are described, from the `simple-minded', in which all the (classically) logical consequences of a (propositional) input \(A\) are become input and the output is again closed under logical consequence, to a more useful `basic', which accommodates disjunctive inputs, to `reusable' extensions of each, in which outputs are returned to become inputs. All four are described both semantically and as sets of derivation procedures, with corresponding soundness and completeness results. Further properties are also presented, such as the possibility of permuting the order of application of derivation procedures in the different systems. This treatment of logic has application especially to such notions as conditional obligation, preferences, actions and beliefs, in which the type of input is not always the same as the type of output.
scientific article; zbMATH DE number 1512964