Physics of the Mind, Dynamic Logic, and Monotone Boolean functions

Author(s):  
Leonid I. Perlovsky
2006 ◽  
Vol 02 (01) ◽  
pp. 43-55 ◽  
Author(s):  
LEONID I. PERLOVSKY

Fuzzy logic is extended toward dynamic adaptation of the degree of fuzziness. The motivation is to explain the process of learning as a 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 certain knowledge. We present an image recognition example of patterns below clutter. The paper discusses relationships to formal logic, fuzzy logic, complexity and draws tentative connections to Aristotelian theory of forms and working of the mind.


Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1035
Author(s):  
Ilya Shmulevich

Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations. We consider networks comprised of monotone Boolean functions and derive asymptotic formulas for the Lyapunov exponent of almost all monotone Boolean networks. The formulas are different depending on whether the number of variables of the constituent Boolean functions, or equivalently, the connectivity of the Boolean network, is even or odd.


2014 ◽  
Vol 167 ◽  
pp. 15-24 ◽  
Author(s):  
Tamon Stephen ◽  
Timothy Yusun

2010 ◽  
Vol 310 (8) ◽  
pp. 1401-1402
Author(s):  
Demetres Christofides

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