continuous mathematics, logic programming
Logic programs may be construed as discrete-time and continuous-time dynamical systems with continuous states. Techniques for obtaining explicit formulations of such dynamical systems are presented and the computational performance of examples is presented. Extending 2-valued and n-valued logic to continuousvalued logic is shown to be unique, up to choosing the representations of the individual truth values as elements of a continuous field, provided that lowest degree polynomials are selected. In the case of 2-valued logic, the constraint that enables the uniqueness of the continualization is that the Jacobian matrices of the continualizations of the Boolean connectives have only affine entries. This property of the Jacobian matrix facilitates computation via gradient descent methods.
Blair, Howard A.; Dushin, Fred; Jakel, David W.; Rivera, Angel J.; and Sezgin, Metin, "Continuous Models of Computation for Logic Programs: Importing Continuous Mathematics into Logic Programming's Algorithmic Foundations" (1999). Electrical Engineering and Computer Science. Paper 94.