Toward a mathematical theory of plan synthesis
Toward a mathematical theory of plan synthesis
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)
Non-Markovian control in the situation calculus
Eighteenth national conference on Artificial intelligence
Existential assertions and quantum levels on the tree of the situation calculus
Artificial Intelligence
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Reasoning about Movement in Two-Dimensions
Canadian AI '09 Proceedings of the 22nd Canadian Conference on Artificial Intelligence: Advances in Artificial Intelligence
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
Property persistence in the situation calculus
Artificial Intelligence
A semantic characterization of a useful fragment of the situation calculus with knowledge
Artificial Intelligence
Artificial Intelligence
On the progression of knowledge in the situation calculus
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
How to progress a database III
Artificial Intelligence
A classification of first-order progressable action theories in situation calculus
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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In a seminal paper, Lin and Reiter introduced a model-theoretic definition for the progression of the initial knowledge base of a basic action theory. This definition comes with a strong negative result, namely that for certain kinds of action theories, first-order logic is not expressive enough to correctly characterize this form of progression, and second-order axioms are necessary. However, Lin and Reiter also considered an alternative definition for progression which 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 first-order definable progression, has remained open since then. 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. Second, we prove that the alternative definition is nonetheless correct for reasoning about a large class of sentences, including some that quantify over situations. In this case the alternative definition is a preferred option due to its simplicity and the fact that it is always first-order.