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.
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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
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:
- Any finite set of rules is a rule complex;
- If
C 1 , C 2 C 1 ∪ C 2 P ( C 1 ) are rule complexes; - If
C 1 ⊆ C 2 C 2 C 1
This means that for rule complexes