- Full text PDF available (64)
Mathematical approaches to modeling the mind since the 1950s are reviewed, including artificial intelligence, pattern recognition , and neural networks. I analyze difficulties faced by these algorithms and neural networks and relate them to the fundamental inconsistency of logic discovered by Gödel. Mathematical discussions are related to those in… (More)
Fuzzy Logic is extended toward dynamic adaptation of the degree of fuzziness. The motivation is to explain the process of learning as joint model improvement and fuzziness reduction. A learning system with fuzzy models is introduced. Initially, the system is in a highly fuzzy state of uncertain knowledge, and it dynamically evolves into a low-fuzzy state of… (More)
Fuzzy Dynamic Logic transforms signals into concepts; it involves instincts, emotions, intuitions, and integrates cogni-tion and language at a pre-conceptual level.
An emotional version of Sapir-Whorf hypothesis suggests that differences in language emotionalities influence differences among cultures no less than conceptual differences. Conceptual contents of languages and cultures to significant extent are determined by words and their semantic differences; these could be borrowed among languages and exchanged among… (More)
Theories of music origins and the role of musical emotions in the mind are reviewed. Most existing theories contradict each other, and cannot explain mechanisms or roles of musical emotions in workings of the mind, nor evolutionary reasons for music origins. Music seems to be an enigma. Nevertheless, a synthesis of cognitive science and mathematical models… (More)
This brief describes neural modeling fields (NMFs) for object perception, a bio-inspired paradigm. We discuss previous difficulties in object perception algorithms encountered since the 1950s, and describe how NMF overcomes these difficulties. NMF mechanisms are compared to recent experimental neuroimaging observations, which have demonstrated that initial… (More)
Processes in the mind: perception, cognition, concepts, instincts, emotions, and higher cognitive abilities for abstract thinking, beautiful music are considered here within a neural modeling fields (NMFs) paradigm. Its fundamental mathematical mechanism is a process ¿from vague-fuzzy to crisp,¿ called dynamic logic (DL). This paper discusses why this… (More)
What is the role of language in cognition? Do we think with words, or do we use words to communicate made-up decisions? The paper briefly reviews ideas in this area since 1950s. Then we discuss mechanisms of cognition, recent neuroscience experiments, and corresponding mathematical models. These models are interpreted in terms of a biological drive for… (More)
The Cramer-Rao bound is obtained for the joint problem of concurrent association and track parameter estimation for the problem of tracking in clutter and tracking multiple targets. Simplified rule-of-thumb expressions are obtained to quantify the possibility and requirements for tracking in heavy clutter.