Pure-Past Linear Temporal and Dynamic Logic on Finite Traces

LTLf and LDLf are well-known logics on finite traces. We review PLTLf and PLDLf, their pure- past versions. These are interpreted backward from the end of the trace towards the beginning. Because of this, we can exploit a foundational result on reverse languages to get an exponential improvement, wrt LTLf /LDLf, in computing the corresponding DFA. This exponential improvement is reflected in several forms sequential decision making involving temporal specifications, such as planning and decision problems in non-deterministic and non-Markovian domains. Interestingly, PLTLf (resp. PLDLf ) has the same expressive power as LTLf (resp. LDLf ), but transforming a PLTLf (resp. PLDLf ) formula into its equivalent in LTLf (resp. LDLf ) is quite expensive. Hence, to take advantage of the exponential improvement, properties of interest must be directly expressed in PLTLf /PLTLf

Planning for LTLF/LDLF goals in non-Markovian fully observable nondeterministic domains

In this paper, we investigate non-Markovian Nondeterministic Fully Observable Planning Domains (NMFONDs), variants of Nondeterministic Fully Observable Planning Domains (FONDs) where the next state is determined by the full history leading to the current state. In particular, we introduce TFONDs which are NMFONDs where conditions on the history are succinctly and declaratively specified using the linear-time temporal logic on finite traces LTLf and its extension LDLf. We provide algorithms for planning in TFONDs for general LTLf/LDLf goals, and establish tight complexity bounds w.r.t. the domain representation and the goal, separately. We also show that TFONDs are able to capture all NMFONDs in which the dependency on the history is “finite state”. Finally, we show that TFONDs also capture Partially Observable Nondeterministic Planning Domains (PONDs), but without referring to unobservable variables