Founded Semantics and Constraint Semantics of Logic Rules

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.