Familiar logical relations and operations correspond to well-understood set-theoretic relations and operations on ranges.
One of the perennial topics in philosophy of science concerns inter-theoretic relations.
However, examples of the semantic approach focusing on mathematical structures and satisfaction of set-theoretic relations have focused on syntactic features including the axiomatic form of a theory in the discussion of reduction (Sarkar 1998, da Costa and French 2003).
Structuralism involves theses about "theory-nets," theory-relative theoretical vs. non-theoretical terms, a diversity of intra- and inter-theoretic laws with different degrees of generality, a typology of inter-theoretic relations, and a rich account of correspondence rules in scientific practice (see Moulines 2002; Pereda 2013; Schmidt 2014; Ladyman 2014).
One important point here is that it had not yet been shown that all the usual apparatus of set-theoretic mathematics (relations, ordering relations, functions, cardinal equivalence functions, order-isomorphisms, etc).
A system featuring a set-theoretic generating relation thus does not count as nominalistic.
For instance the model-theoretic consequence relation for some logics of time presupposes some facts about the physical structure of time.
And if we are allowed to keep some structure on the domain of worlds or times fixed, the question immediately arises why we should not also keep some structure on the domain of objects fixed: for example, the set-theoretic membership relation, the mereological part/whole relation, or the distinction between existent and nonexistent objects (see the entry on free logics).
Accordingly with theoretic sampling, the relation among the objectives and the information obtained will be reviewed permanently, in order to advance in the refining of the deliberated sampling.
For alternative general discussions of a control theoretic framework in relation to modelling the performance of human machine systems, consider the following sources: Flach et al. (2011, 2013), Jagacinski and Flach (2003), Leveson (2012) and Sheridan and Ferrell (1974).
