A dynamical approach to logical decisions

✍ Scribed by Eduardo Mizraji; Juan Lin

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 147 KB
• Volume: 2
• Category: Article
• ISSN: 1076-2787
• DOI: 10.1002/(sici)1099-0526(199701/02)2:3<56::aid-cplx12>3.0.co;2-s

✦ Synopsis

We propose a first approximation to the modeling of cognitive decisions based on the theory of associative memories. The basic structure are the matrix memories of Anderson-Kohonen adapted to include the modulation of associations via tensorial preprocessing of inputs. This view admits an easy implementation of logical operations as matrix operators. From this "vectorial logic" springs a variety of models for fuzzy decision processes. Degrees of fuzziness are introduced at two different levels: (a) by the operators of modal logic, and (b) by using logical variables as vectors with projections inside the interval [0,1]. The outcomes of this vectorial logic can be projected onto unit vectors yielding scalar difference equations. As examples we study the dynamics of contradictory self-referential systems and processes leading to competition between options. These models exhibit a variety of dynamical patterns that include stable steady states, oscillations, and deterministic chaos.