Proving properties of states in the situation calculus
Artificial Intelligence
Artificial Intelligence
Some contributions to the metatheory of the situation calculus
Journal of the ACM (JACM)
Knowlege in action: logical foundations for specifying and implementing dynamical systems
Knowlege in action: logical foundations for specifying and implementing dynamical systems
On the progression of situation calculus basic action theories: resolving a 10-year-old conjecture
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
How to progress a database II: the STRIPS connection
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
On first-order definability and computability of progression for local-effect actions and beyond
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
On progression and query evaluation in first-order knowledge bases with function symbols
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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In a seminal paper, Lin and Reiter introduced a model-theoretic definition for the progression of a basic action theory in the situation calculus, and proved that it implies the intended properties. They also showed that this definition comes with a strong negative result, namely that for certain cases first-order logic is not expressive enough to correctly characterize the progressed theory and second-order axioms are necessary. However, they also considered an alternative simpler definition according to which the progressed theory is always first-order definable. They conjectured that this alternative definition is incorrect in the sense that the progressed theory is too weak and may sometimes lose information. This conjecture and the status of the definability of progression in first-order logic has remained open since. In this paper we present two significant results about this alternative definition of progression. First, we prove the Lin and Reiter conjecture by presenting a case where the progressed theory indeed does lose information, thus closing a question that has remained open for more than ten years. Second, we prove that the alternative definition is nonetheless correct for reasoning about a large class of sentences, including some that quantify over situations.