Abstract: New methods to represent variables as parts of the classical truth table lead to complete evaluation methods that generate a compiled, efficient version of logical expressions. The new methods are suitable for use in, e.g., relational database applications in which both, efficient query times as well as logical completeness and consistency are required in the context of general constraint treatments. Input/output operations remain linear in the length of the input character strings regardless of the complexity of the logical theory. A new processing method of formulas is described as the basis for the efficiency increase. In order to find a specific truth-value, pattern trees are used representing the extension of the logical theory.

Abstract: In relational database concepts, query procedures suffer either from logically incomplete query results or lack of query time efficiency. The present invention provides efficient methods that optimize relational database systems in their query procedures so that the response procedure experiences an increase in efficiency in terms of speed and memory requirements without sacrificing logical conditions. In order to increase the efficiency of the query methods, a logically complete and at the same time efficient ontological level is introduced, which makes it possible to derive and/or evaluate application-specific constraints both, deductively and inductively.

Abstract: New methods to represent variables as parts of the classical truth table lead to complete evaluation methods that generate a compiled, efficient version of logical expressions. The new methods are suitable for use in, e.g., relational database applications in which both, efficient query times as well as logical completeness and consistency are required in the context of general constraint treatments. Input/output operations remain linear in the length of the input character strings regardless of the complexity of the logical theory. A new processing method of formulas is described as the basis for the efficiency increase. In order to find a specific truth-value, pattern trees are used representing the extension of the logical theory.