We define the robustness of a sequential plan as the probability that it will execute successfully despite uncertainty in the execution environment. We consider a rich notion of uncertainty over continuous domains that includes stochastic action effects, and changes to state variables due to unpredictable exogenous events. Given a characterization of this uncertainty in terms of probability dis...

Recently Lakemeyer and Levesque proposed the logic AOL, which amalgamates both the situation calculus and Levesque’s logic of only knowing. While very expressive the practical relevance of the formalism is unclear because it heavily relies on second-order logic. In this paper we demonstrate that the picture is not as bleak as it may seem. In particular, we show that for large classes of AOL kno...

A situation calculus is presented that provides a solution to the frame problem for hierarchical situations, that is, situations that have a modular structure in which parts of the situation behave in a relatively independent manner. This situation calculus is given in a relational, functional, and modal logic form. Each form permits both a single level hierarchy or a multiple level hierarchy, ...

In this work we study action theories of the situation calculus such that the initial KB is a generalized database with equality constraints (GFDBs). We show that GFDBs characterize the class of definitional KBs and that they are closed under progression. We also show that, under conditions, generalized projection queries can be decided based on an induced transition system and evaluation of lo...

Flat transactions with savepoints are a variation of the classical flat transactions that allows the user to go undo work done so far back to a certain point within the transaction. This is as opposed to pure classical flat transactions that either commit to whole work done so far or undo it. Recently, this mechanism is being offered by some major database products. Their semantics, however, se...

In many real-world applications, temporal information is often imprecise about the temporal location of events (indeterminacy) and comes at different granularities. Formalisms for reasoning about events and change, such as the Event Calculus (EC) and the Situation Calculus, do not usually provide mechanisms for handling such data, and very little research has been devoted to the goal of extendi...

The Situation Calculus and the Fluent Calculus are successful action formalisms that share many concepts. But until now there is no formal relation between the two calculi that would allow to formally analyze the relationship between the two approaches as well as between the programming languages based on them, Golog and FLUX. Furthermore, such a formal relation would allow to combine Golog and...

The Situation Calculus is a logic of time and change in which there is a distinguished initial situation S0 and all other situations arise from the different sequences of actions that might be performed starting in the initial one. Within this framework, it is difficult to incorporate the notion of an occurrence, since all situations after the initial one are hypothetical. These occurrences are...