Rule complex
This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)
|
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,
Formalization
Rules
In this setting, a rule is type of knowledge (in the sense of
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 are rule complexes, then and are rule complexes;
- 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).
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.
- Gomolińska Anna, (1999) Rule complexes for representing social actors and interactions. "Studies in Logic, Grammar and Rhetoric", Volume 3(16):95–108.
- Gomolińska, Anna (2004) Fundamental mathematical notions of the theory of
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.