Rule complex
A rule complex is a set consisting of rules and/or other rule complexes. This is a generalization of a set of rules, and provides a tool to investigate and describe how rules can function as values, norms, judgmental or prescriptive rules, and meta-rules. Also possible is to examine objects consisting of rules such as roles, routines, algorithms, models of reality, social relationships, and institutions. In game theory, rules and rule complexes can be used to define the behavior and interactions of the players (although in generalized game theory, the rules are not necessarily static. Rule complexes are  especially associated with sociologist Tom R. Burns and Anna Gomolinska and the Uppsala Theory Circle. Formalization. Rules. In this setting, a rule is type of knowledge (in the sense of epistemic logic (see Fagin, 2003)) formalized as a set of premises or conditions, a set of justifications, and a set of conclusions (this may be written as a triple, a rule formula_1). Elements of "X" should hold, and of "Y" may hold. If "Y", the justifications, do not hold, then the rule cannot be applied. If "X", the premises, obtain and the justifications are not known to not apply , then the rule is applied, and formula_2 is concluded. If "X" and "Y" are empty, then the rule is axiomatic (a "fact" or unconditional directive). Thus, rules can be seen as the basic objects of knowledge. Rule complex. Formally, a rule complex is the class which contains all finite sets of rules, is closed under set-theoretical union and power set, and preserves inclusion: This means that for rule complexes formula_8 and formula_7, formula_11 are also rule complexes. A complex formula_12 is a subcomplex of the complex formula_13 if formula_14 or formula_12 may be obtained from formula_13 by deleting some  rules from formula_13 and/or redundant parentheses (Burns, 2005). socially embedded games: A granular computing perspective. In S. K. Pal, L. Polkowski and A. Skowron (eds). "Rough-Neural Computing: Techniques for Computing with Words", Springer, Berlin Heidelberg, pages 411–434.