(University of Birmingham)

In three-valued logic one considers a third truth value besides the usual "true" and "false", namely, "unknown". This is a useful concept when one is dealing with situations where knowledge is partial (as in many AI applications) or uncomputable.In four-valued logic, a further value is considered, representing "contradiction". This, too, arises naturally when one tries to formalise the knowledge that one holds (or that one has been told) about aspects of the real-world.

For a logic we need more than the truth values, however, and one can wonder what logical connectives would be appropriate in these multi-valued settings, and what their proof rules should be. In this talk I will present a point of view (developed jointly with Drew Moshier) which is strongly model-theoretic. By studying sets of models, one is led fairly naturally to consider axiomatisations of three- and four-valued logic which make a clear distinction between "logic" and "information". Furthermore, it emerges that there is in fact a 1-1 translation between the three- and four-valued approach.

Robert Recorde Room

Department of Computer Science