Rule complex

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 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 r:=(X,Y,alpha)). 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 alpha 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:

#Any finite set of rules is a rule complex;
#If C_1, C_2 are rule complexes, then C_1 cup C_2 and P(C_1) are rule complexes;
#If C_1 subseteq C_2 and C_2 is a rule complex, then C_1 is a rule complex.

This means that for rule complexes C_1 and C_2, C_1 cap C_2, C_1 - C_2 are also rule complexes. A complex B is a subcomplex of the complex A if B=A or B may be obtained from A by deleting some rules from A and/or redundant parentheses (Burns, 2005).

References

*Fagin, Ronald et al. Reasoning about Knowledge. Cambridge: MIT Press, 2003.
*Burns T.R., Roszkowska E. (2005) Generalized Game Theory: Assumptions, Principles, and Elaborations Grounded in Social Theory, In Search of Social Order, “Studies in Logic, Grammar, and Rhetoric”, Vol. 8(21):7-40.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Rule 184 — is a one dimensional binary cellular automaton rule, notable for solving the majority problem as well as for its ability to simultaneously describe several, seemingly quite different, particle systems:* Rule 184 can be used as a simple model for… …   Wikipedia

  • Rule 30 — is a one dimensional binary cellular automaton rule introduced by Stephen Wolfram in 1983. [cite journal|author = Wolfram, S.|title = Statistical mechanics of cellular automata|journal = Rev. Mod. Phys.|volume = 55|pages = 601–644|year = 1983|doi …   Wikipedia

  • Complex event processing — (CEP) consists of processing many events happening across all the layers of an organization, identifying the most meaningful events within the event cloud, analyzing their impact, and taking subsequent action in real time. Complex event… …   Wikipedia

  • rule against perpetuities — often cap R&P: a common law rule stating that in order for a future interest to be good it must vest after its creation (as at the death of a testator) within a life in being or lives in being plus 21 years plus the period of gestation of any… …   Law dictionary

  • Rule bank — is a set of user defined rules that allow a condition to be changed according to data that is encountered at the transaction level.DefinitionThe Rule Bank determines which of several alternate conditions are to be assigned based upon logic… …   Wikipedia

  • Complex structure theory in English law — refers to an attempt to circumvent the general rule that one cannot sue for solely pure economic loss in English tort law. Contents 1 Example 2 Status 3 See also 4 References …   Wikipedia

  • Rule 110 — The Rule 110 cellular automaton (often simply Rule 110) is a one dimensional two state cellular automaton with the following rule table:Interesting propertiesAround 2000, Matthew Cook verified a 1985 conjecture by Stephen Wolfram by proving that… …   Wikipedia

  • Complex (chemistry) — The term complex in chemistry is usually used to describe molecules or ensembles formed by the combination of ligands and metal ions. Originally, a complex implied a reversible association of molecules, atoms, or ions through weak chemical bonds …   Wikipedia

  • Rule in Allhusen v Whittell — The rule in Allhusen v Whitell (1867) LR 4 Eq 295 is a rule of equity which requires the trustee of a trust to strike a fair balance between the beneficiaries who are tenants for life and those who are remaindermen in respect of payment of the… …   Wikipedia

  • Complex quadratic polynomial — A complex quadratic polynomial is a quadratic polynomial whose coefficients are complex numbers. Contents 1 Forms 2 Conjugation 2.1 Between forms 2.2 With doubling map …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”