Dynamic Logic

Abstract

The strength of logic is in structuring problems according to existing knowledge. Its weakness is absence of dynamics and learning. An opposing approach of “connectivism” or neural networks is dynamical and has been conceived to be capable of learning. Its weakness is that it cannot easily incorporate structural knowledge. As discussed in the previous chapter, both approaches faced combinatorial complexity (CC). DL combines structure and dynamics, ability to utilize prior knowledge and ability to learn. In this way it is similar to modelbased approaches. DL fits models to data, while avoiding combinatorial complexity (CC) of the past algorithms and neural networks. DL can be considered as a gradient ascent along variables, which used to be considered as essentially discrete; DL makes discrete variables into continuous and also avoids local maxima. Another way of viewing DL is as a modification of fuzzy logic such that degrees of fuzziness for various models are autonomously updated and reduced along with improved accuracies of the models. DL is a process; its initial state is a vague-fuzzy state (model) in which vagueness corresponds to the uncertainty of knowledge (inaccuracies of models). This DL process “from vagueto- crisp” corresponds to the Aristotelian conception of forms evolving from illogical forms-as-potentialities to logical forms-as actualities. In the DL process vagueness decreases, while models become more similar to patterns in data. The number and types of models are also adjusted to improve the similarity between models and data. In this chapter we define similarity measures, DL process equations, and discuss DL convergence.