InterJournal Complex Systems, 331 Status: Submitted |
Manuscript Number: [331] Submission Date: 405 Revised On: 607 |
Logic Based Framework for modeling of complex systems |
Subject(s): CX.0, CX.34, CX.67, CX.06
Category: Article
Abstract:
We propose a new conceptual framework for modeling of complex systems based on predicate logic. The classical definition of a system is virtually identical to the definition of Model in predicate calculus. Both, Model and System are defined as a pair {Objects, Relations} where Objects is a set of objects described and Relations is a set of relations i.e. predicates of different arity that pertains to the objects. The similarity between the definitions of a system and of a model brings forth the possibility of designing a Model Theory based framework for Systems Analysis and Modeling. The main assumptions are as follows: The development of a system S over time t may be represented as a sequence of model fragments: M[t0, t0],M[t0, t1], , M[t0,t1, tn], where M[t0,t1 ti] is a model describing the dynamics of S within a period [t0, ti]. The problem of the modeling the dynamics of system S is the problem of finding the computational function F such that: M[t0,t1, tk+1] = F(M[t0,t1, tk], .) for all k : 0< k< n . Any reasonable statement about system s organization, history, or properties of objects could be represented in a formal way as a formula that is true on the model. Pattern of organization could be defined in a natural way as a formula with free variables. All models where this formula has an interpretation have that pattern. This definition of pattern generalizes geometrical patterns , patterns of CAs, patterns of social interactions. Iterative maps, CAs, Lindenmeyer systems could be easily embedded within the framework proposed. Besides that the framework could inspire development of new abstract model of CAS. One such model is Abstract Computational Ecosystem. The implementation of this model in the form of a general-purpose ecological simulator LEM is discussed in the end of the article.
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