Programming with logic for sophisticated applications must deal with recursion and negation, which have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a unified language, DA logic, for design and analysis logic, based on the unifying founded semantics and constraint semantics, that support the power and ease of programming with different intended semantics. The key idea is to provide meta constraints, support the use of uncertain information in the form of either undefined values or possible combinations of values, and promote the use of knowledge units that can be instantiated by any new predicates, including predicates with additional arguments.

Logic rules and inference are fundamental in computer science, especially for solving complex modeling, reasoning, and analysis problems in critical areas such as program verification, security, and decision support. The semantics of logic rules and their efficient computations have been a subject of significant study, especially for complex rules that involve recursive definitions and unrestricted negation and quantifications. Many different semantics and computation methods have been proposed. Even the two dominant semantics for logic programs, well-founded semantics (WFS) [VRS91, VG93] and stable model semantics (SMS) [GL88], are still difficult to understand intuitively, even for extremely simple rules; they also make implicit assumptions and, in some cases, do not capture common sense, especially ignorance. This paper describes a simple new semantics for logic rules, founded semantics, that extends straightforwardly to another simple new semantics, constraint semantics.