LTLf and LDLf Monitoring: A Technical Report

Runtime monitoring is one of the central tasks to provide operational decision support to running business processes, and check on-the-fly whether they comply with constraints and rules. We study runtime monitoring of properties expressed in LTL on finite traces (LTLf) and in its extension LDLf. LDLf is a powerful logic that captures all monadic second order logic on finite traces, which is obtained by combining regular expressions and LTLf, adopting the syntax of propositional dynamic logic (PDL). Interestingly, in spite of its greater expressivity, LDLf has exactly the same computational complexity of LTLf. We show that LDLf is able to capture, in the logic itself, not only the constraints to be monitored, but also the de-facto standard RV-LTL monitors. This makes it possible to declaratively capture monitoring metaconstraints, and check them by relying on usual logical services instead of ad-hoc algorithms. This, in turn, enables to flexibly monitor constraints depending on the monitoring state of other constraints, e.g., "compensation" constraints that are only checked when others are detected to be violated. In addition, we devise a direct translation of LDLf formulas into nondeterministic automata, avoiding to detour to Buechi automata or alternating automata, and we use it to implement a monitoring plug-in for the PROM suite

LTLf/LDLf Non-Markovian Rewards

In Markov Decision Processes (MDPs), the reward obtained in a state is Markovian, i.e., depends on the last state and action. This dependency makes it difficult to reward more interesting long-term behaviors, such as always closing a door after it has been opened, or providing coffee only following a request. Extending MDPs to handle non-Markovian reward functions was the subject of two previous lines of work. Both use LTL variants to specify the reward function and then compile the new model back into a Markovian model. Building on recent progress in temporal logics over finite traces, we adopt LDLf for specifying non-Markovian rewards and provide an elegant automata construction for building a Markovian model, which extends that of previous work and offers strong minimality and compositionality guarantees