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

Norm (sociology)

Social norms are the accepted behaviors within a society or group. This sociological and social psychological term has been defined as "the rules that a group uses for appropriate and inappropriate values, beliefs, attitudes and behaviors. These rules may be explicit or implicit...

, 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

Game theory

Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

, rules and rule complexes can be used to define the behavior and interactions of the players (although in generalized game theory

Generalized game theory

Generalized game theory is an extension of game theory incorporating social theory concepts such as norm, value, belief, role, social relationship, and institution. The theory was developed by Tom R. Burns, Anna Gomolinska, and Ewa Roszkowska but has not had great influence beyond these immediate...

, the rules are not necessarily static. Rule complexes are especially associated with sociologist

Sociology

Sociology is the study of society. It is a social science—a term with which it is sometimes synonymous—which uses various methods of empirical investigation and critical analysis to develop a body of knowledge about human social activity...

 Tom R. Burns

Tom R. Burns

Tom R. Burns is a European/American sociologist.-Education:He grew up in Arkansas, and was in a Franciscan Monastery for a number of years. As a teenager, he attended Phillips Academy Andover in Massachusetts, before going to Stanford University to study physics and mathematics...

 and Anna Gomolinska and the Uppsala Theory Circle.

Rules

In this setting, a rule is type of knowledge (in the sense of epistemic logic

Epistemic logic

Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields, including philosophy,...

 (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 ). 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 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

Union (set theory)

In set theory, the union of a collection of sets is the set of all distinct elements in the collection. The union of a collection of sets S_1, S_2, S_3, \dots , S_n\,\! gives a set S_1 \cup S_2 \cup S_3 \cup \dots \cup S_n.- Definition :...

 and power set, and preserves inclusion:

1. Any finite set of rules is a rule complex;
2. If are rule complexes, then and are rule complexes;
3. If and is a rule complex, then is a rule complex.

This means that for rule complexes and , are also rule complexes. A complex is a subcomplex of the complex if or may be obtained from by deleting some rules from and/or redundant parentheses (Burns, 2005).