Interpreted dynamical systems and qualitative laws

from neural networks to evolutionary systems

Hannes Leitgeb

pp. 189-202

in: Gerhard Schurz, Hannes Leitgeb (eds), Non-monotonic and uncertain reasoning in cognition, Synthese 146, 2005.

Abstract

Interpreted dynamical systems are dynamical systems with an additional interpretation mapping by which propositional formulas are assigned to system states. The dynamics of such systems may be described in terms of qualitative laws for which a satisfaction clause is defined. We show that the systems Cand CL of nonmonotonic logic are adequate with respect to the corresponding description of the classes of interpreted ordered and interpreted hierarchical systems, respectively. Inhibition networks, artificial neural networks, logic programs, and evolutionary systems are instances of such interpreted dynamical systems, and thus our results entail that each of them may be described correctly and, in a sense, even completely by qualitative laws that obey the rules of a nonmonotonic logic system.