Towards an Expressive Practical Logical Action Theory

19 pages•Published: June 22, 2012

Abstract

In the area of reasoning about actions, one of the key computational problems is the projection problem: to find whether a given logical formula is true after
performing a sequence of actions. This problem is undecidable in the general
situation calculus; however, it is decidable in some fragments. We consider
a fragment P of the situation calculus and Reiter's basic action theories (BAT)
such that the projection problem can be reduced to the satisfiability problem
in an expressive description logic $ALCO(U)$ that includes nominals ($O$),
the universal role ($U$), and constructs from the well-known logic $ALC$. It turns out
that our fragment P is more expressive than previously explored description logic
based fragments of the situation calculus. We explore some of the logical properties of our theories.
In particular, we show that the projection problem can be solved using regression
in the case where BATs include a general ``static" TBox, i.e., an ontology that has
no occurrences of fluents. Thus, we propose seamless integration of traditional
ontologies with reasoning about actions. We also show that the projection
problem can be solved using progression if all actions have only local effects on
the fluents, i.e., in P, if one starts with an incomplete initial theory that
can be transformed into an $ALCO(U)$ concept, then its progression resulting from
execution of a ground action can still be expressed in the same language. Moreover,
we show that for a broad class of incomplete initial theories progression can be computed efficiently.

Keyphrases: description logic, logics for reasoning about actions, progression, regression, reiter s basic action theories, situation calculus, the projection problem

In: Andrei Voronkov (editor). Turing-100. The Alan Turing Centenary, vol 10, pages 307-325.

Links:	https://easychair.org/publications/paper/tcmR
	https://doi.org/10.29007/2m22