BASIC CONCEPTS OF CONTINUOUS LOGIC
Irwin P. Levin · Studies in Logic Grammar and Rhetoric · 2007
In this paper, a general description of a continuous (-valued) logic is given and some problems and particulars of their solutions are discussed. Firstly, we define algebra of continuous logic and enumerate its basic unary, binary and ternary functions. All laws of continuous logic are compared to laws of discrete binary logic. We discuss how to enumerate all the functions of continuous logic with a specified number of variables and how to represent such functions in a standard form. Procedures of minimization regarding continuous logical functions and their decomposition into functions with less clarity are exploited. The procedures are compared to their counterparts from binary logic. We also tackle problems of the analysis and synthesis of continuous logical functions, and show that the problem of synthesis may not have a solution. Basics of differential and integral calculus are applied to continuous-valued logic. We demonstrate that any continuous logical function has the points where a derivative does not exist. To conclude, we briefly discuss a problem of incompleteness regarding continuous logic, application of continuous logic in mathematics, engineering and economy, give examples, draw a perspective of further development and supply an extensive bibliography of Russian works in the field.