Derivability of rules from rule complexes

Anna Gomolińska



In the paper we focus upon the problem of derivability of rules from rule complexes. The notion of a rule complex is the main mathematical notion of generalized game theory (GGT for short). Derivability of rules, as defined here, comprises the concept of an extension from a default theory [9] as well as the classical notion of derivability of rules in logic. The idea of localness of reasoning, reasoning with a limited access to rules, is realized by the concept of relative derivability. Starting with derivability of rules, we next touch upon the questions of the activation of rules and (in)consistency of rule complexes.


rule complex; derivability of rules; activation of rules; (in)consistency of a rule complex; generalized game theory

Full Text:



Ajdukiewicz, K., “Główne zasady metodologii nauk i logiki formalnej”, in Język i poznanie, volume 1, pages 62–78, Warszawa, 1985. Państwowe Wydawnictwo Naukowe. Originally published in 1928, Warsaw, pages 262–299.

Burns, T.R, and A. Gomolińska. “Modelling social game systems by rule complexes”, pages 581–584 in L. Polkowski and A. Skowron, Proc. 1st Int. Conf. Rough Sets and Current Trends in Computing (RSCTC’1998), Warsaw, Poland, 1998, June, 22–26th, Lecture Notes in AI, vol. 1424, Springer-Verlag,

Berlin, 1998.

Burns, T.R., and A. Gomolińska, “The theory of socially embedded games: The mathematics of social relationships, rule complexes, and action modalities”, Quality and Quantity Int. J. Methodology, 34(4):379–406, 2000.

Burns, T.R., and A. Gomolińska, “Socio-cognitive mechanisms of belief change: Applications of generalized game theory to belief revision, social fabrication, and self-fulfilling prophesy”, Cognitive Systems Research, 2(1):39–54, 2001.

Burns, T.R., A. Gomolińska, and L.D. Meeker, “The theory of socially embedded games: Applications and extensions to open and closed games”, Quality and Quantity Int. J. Methodology, 35(1):1–32, 2001.

Gomolińska, A., “Rule complexes for representing social actors and interactions”, Studies in Logic, Grammar and Rethoric, 3(16):95–108, 1999.

Gomolińska, A., “Fundamental mathematical notions of the theory of socially embedded games: A granular computing perspective”, in S.K. Pal, L. Polkowski, and A. Skowron, editors, Rough-Neuro Computing: Techniques for Computing with Words, Springer-Verlag, Berlin, 2002. To appear.

Pogorzelski, W.A., Notions and Theorems of Elementary Formal Logic, Białystok Division of Warsaw University, Białystok, 1994.

Reiter, R., “A logic for default reasoning”, Artificial Intelligence J., 13:81–132, 1980.

von Neumann, J., and O. Morgenstern, Theory of Games and Economic Behaviour, Princeton University Press, 1944. Edition from 1972.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism