Thursday, December 15, 2005
Communications on lattice of theories
Communication on Rosen, by Peter Kugler
Rosen only talked about largest models in the context of mechanistic models, e.g. those that involve the subsumption relations, which is also the class of computable models.
His use of largest model was with reference to how all other models were nested using subsumption relations and could be related through deduction relations. The alternative is a class of models that do NOT have an ultimate largest model and where the submodels are not related through subsumption relations. Rosen argued that this class of models was required to capture the behavior of Natural Systems.
The relations linking these submodels can NOT be described using standard monotonic deductive relations [1]. The branching points in these logic relations are the source of the noncomputability (e.g., one of the sources).
[1] It was left as an open question as to whether non-monotonic logics would be found sufficient. In any case, a lattice of models is not present.