Founded Semantics and Constraint Semantics of Logic Rules
This addresses foundational issues in logic programming for computer scientists, offering a more intuitive and expressive framework, though it is incremental in unifying existing semantics.
The paper tackles the problem of subtle and non-intuitive semantics in logic rules, especially with unrestricted negation, by introducing founded semantics and constraint semantics that unify prior approaches and support unrestricted negation and quantifications. The result includes a linear-time computation for founded semantics in the size of the ground program.
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs, including in attempting to solve the well-known Russell's paradox. These semantics are often non-intuitive and hard-to-understand when unrestricted negation is used in recursion. This paper describes a simple new semantics for logic rules, founded semantics, and its straightforward extension to another simple new semantics, constraint semantics, that unify the core of different prior semantics. The new semantics support unrestricted negation, as well as unrestricted existential and universal quantifications. They are uniquely expressive and intuitive by allowing assumptions about the predicates, rules, and reasoning to be specified explicitly, as simple and precise binary choices. They are completely declarative and relate cleanly to prior semantics. In addition, founded semantics can be computed in linear time in the size of the ground program.