The Expressive Power of Unique Total Stable Model Semantics

This paper investigates the expressive power of DATALOG queries under unique T-stable model semantics, i.e., a query on a given database yields an answer if and only if there exists a unique T-stable model. Under this semantics DATALOG queries are shown to express exactly all decision problems with unique solutions. Obviously, unique Testable model semantics is the 'natural' semantics for queries with at most one T-stable model or with exactly one T-stable model for every database. The expressive powers of of these two classes of queries are investigated as well but it turns out that any practical language for such queries cannot get to an expressive power higher than DATALOG with stratified negation.