A description logic based situation calculus

Abstract

We consider a modified version of the situation calculus built using a two-variable fragment of the first-order logic extended with counting quantifiers. We mention several additional groups of axioms that can be introduced to capture taxonomic reasoning. We show that the regression operator in this framework can be defined similarly to regression in Reiter's version of the situation calculus. Using this new regression operator, we show that the projection and executability problems (the important reasoning tasks in the situation calculus) are decidable in the modified version even if an initial knowledge base is incomplete. We also discuss the complexity of solving the projection problem via regression in this modified language in general. Furthermore, we define description logic based sublanguages of our modified situation calculus. They are based on the description logics ALCO(U) (or ALCQO(U), respectively). We show that in these sub-languages solving the projection problem via regression has better computational complexity than in the general modified situation calculus. We mention possible applications to formalization of Semantic Web services and some connections with reasoning about actions based on description logics.

Towards an Expressive Practical Logical Action Theory

“…This lemma is proved using the standard translation between DLs and FOL; the proof is similar to the proof of Lemma 1 in [11]. Using the fluents Loaded(box, s), At(box, city, s), and In(box, vehicle, s) from Logistics as an example, after suppressing…”

“…A BAT D that satisfies all of the above requirements is called an action theory P. We note that BATs proposed in [11] are less general than P, because their axioms should be written using formulas from FO DL , but FO DL is a proper subset of L . Sometimes, for clarity, when we talk about P, we say that it is an L -based BAT, in contrast to FO DL -based BATs considered in [11].…”

“…On the other hand, there are several proposals regarding the integration of DLs and reasoning about actions [19,3,17,4,11]. In [11], it is shown that the projection problem is decidable in a proposed fragment of the situation calculus (SC).…”

“…In [11], it is shown that the projection problem is decidable in a proposed fragment of the situation calculus (SC). However, the logical languages developed in these papers are not expressive enough to represent some of the action theories popular in AI or to solve the projection problem in a general case.…”

“…However, the logical languages developed in these papers are not expressive enough to represent some of the action theories popular in AI or to solve the projection problem in a general case. For example, Gu& Soutchanski propose a DL based situation calculus [11], where the projection problem is reduced to the satisfiability problem in ALCO(U), a DL that adds nominals O and the universal (global) role U to the well known description logic ALC. The universal role links any two individuals in the domain; it is introduced to add the usual unguarded ∀-and ∃-quantifiers which are handy to represent incomplete knowledge about an initial state and about conditional effects.…”