To link present-day observations to past behavior and the mediating effect of culture, archaeological research begins with patterning found in the material domain and then abductively connects that patterning to the ideational domain of culture through formulating (using current knowledge) likely explanatory arguments that causally connect the ideational domain to the material domain. Thus the abductive process reverses the inductive research ontology that begins with patterning delineated in the material domain to a deductive ontology that begins with the properties in the ideational domain that would, through the mediating effect of culture, cause the observed patterning in the material domain. The reversal also involves switching between two different kinds of models, hence two different kinds of formal representations. On the one hand, models formulated as a way to represent the logic of cultural idea systems are likely to be in the form of theory models (Read 2008) that express properties arrived at deductively from assumed structuring processes, such as a model of the structure of a kinship terminology derived deductively from posited, primary kinship concepts that are part of the cultural domain for the members of a particular society (see Read 1984, 2007b, 2010, 2011, Bennardo and Read 2007, Leaf and Read 2012 [among others] for examples of deductive reasoning applied to the cultural domain). Models like this lend themselves to formal representation using mathematical ideas (Read 2011).