Another Look at Formal Mathematical Properties

AMC introduced a paper by himself and MK on “Defining Mathematical Properties”. He said that CDs did not necessarily introduce the logical meaning of mathematical symbols. OpenMath should involve the logic community more. While OpenMath has Formal Mathematical Properties (FMPs), there is no differentiation between definitions and consequences. Also, some objects do not have FMPs, e.g. subset. He suggested a new tag, DefMP, which would be like FMPs, but the DefMPs would have to define the mathematical object uniquely. At least in theory, the FMPs would then be formally proved as consequences of the DefMPs. In the Esprit group, there were two objections: one that they would scare many potential users, and the other was that people might want different DefMPs. To the first, he answered that there were many features of OpenMath that not everyone used. For the second, he noted that signatures had been moved to separate files, and maybe this would be appropriate for DefMPs. This led to a lively debate. GHG said that placing the DefMPs in separate files was a move against the general trend towards databases. MK in particular called for genuinely usable OpenMath tools, e.g. for Reduce and Maple. Many agreed with him. [Irrelevancies deleted.] MK proposed that, in the light of the DefMP discussion above, which seemed to conclude that the DefMPs should be in auxiliary files, FMPs should be moved to a different kind of file. AMC agreed, but DPC did not. SB proposed, and