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A Simple Temporal Network (STN) consists of time points modeling temporal events and constraints modeling the minimal and maximal temporal distance between them. A Simple Temporal Network with Decisions (STND) extends an STN by adding decision time points to model temporal plans with decisions. A decision time point is a special kind of time point that once executed allows for deciding a truth value for an associated Boolean proposition. Furthermore, STNDs label time points and constraints by conjunctions of literals saying for which scenarios (i.e., complete truth value assignments to the propositions) they are relevant. Thus, an STND models a family of STNs each obtained as a projection of the initial STND onto a scenario. An STND is consistent if there exists a consistent scenario (i.e., a scenario such that the corresponding STN projection is consistent). Recently, a hybrid SAT-based consistency checking algorithm (HSCC) was proposed to check the consistency of an STND. Unfortunately, that approach lacks experimental evaluation and does not allow for the synthesis of all consistent scenarios. In this paper, we propose an incremental HSCC algorithm for STNDs that (i) is faster than the previous one and (ii) allows for the synthesis of all consistent scenarios and related early execution schedules (offline temporal planning). Then, we carry out an experimental evaluation with KAPPA, a tool that we developed for STNDs. Finally, we prove that STNDs and disjunctive temporal networks (DTNs) are equivalent.

BPMN (Business Process Model and Notation) is widely used standard modeling technique for representing Business Processes by using diagrams, but lacks in some aspects. Representing execution-dependent and time-dependent decisions in BPMN Diagrams may be a daunting challenge [Carlo Combi et al., 2017]. In many cases such constraints are omitted in order to preserve the simplicity and the readability of the process model. However, for purposes such as compliance checking, process mining, and verification, formalizing such constraints could be very useful. In this paper, we propose a novel approach for annotating BPMN Diagrams with Temporal Synchronization Rules borrowed from the timeline-based planning field. We discuss the expressivity of the proposed approach and show that it is able to capture a lot of complex temporally-related constraints without affecting the structure of BPMN diagrams. Finally, we provide a mapping from annotated BPMN diagrams to timeline-based planning problems that allows one to take advantage of the last twenty years of theoretical and practical developments in the field.

The proper handling of temporal constraints is crucial in many domains. As a particular challenge, temporal constraints must be also handled when different specific situations happen (conditional constraints) and when some event occurrences can be only observed at run time (contingent constraints). In this paper we introduce Conditional Simple Temporal Networks with Partially Shrinkable Uncertainty (CSTNPSUs), in which contingent constraints are made more flexible (guarded constraints) and they are also specified as conditional constraints. It turns out that guarded constraints require the ability to reason on both kinds of constraints in a seamless way. In particular, we discuss CSTNPSU features through a motivating example and, then, we introduce the concept of controllability for such networks and the related sound checking algorithm.

A Conditional Simple Temporal Network (CSTN) augments a Simple Temporal Network (STN) to include special time-points, called observation time-points. In a CSTN, the agent executing the network controls the execution of every time-point. However, each observation time-point has a unique propositional letter associated with it and, when the agent executes that time-point, the environment assigns a truth value to the corresponding letter. Thus, the agent observes but, does not control the assignment of truth values. A CSTN is dynamically consistent (DC) if there exists a strategy for executing its time-points such that all relevant constraints will be satisfied no matter which truth values the environment assigns to the propositional letters. Alternatively, in a Labeled Simple Temporal Network (Labeled STN) - also called a Temporal Plan with Choice - the agent executing the network controls the assignment of values to the so-called choice variables. Furthermore, the agent can make those assignments at any time. For this reason, a Labeled STN is equivalent to a Disjunctive Temporal Network. This paper incorporates both of the above extensions by augmenting a CSTN to include not only observation time-points but also decision time-points. A decision time-point is like an observation time-point in that it has an associated propositional letter whose value is determined when the decision time-point is executed. It differs in that the agent - not the environment - selects that value. The resulting network is called a CSTN with Decisions (CSTND). This paper shows that a CSTND generalizes both CSTNs and Labeled STNs, and proves that the problem of determining whether any given CSTND is dynamically consistent is PSPACE-complete. It also presents algorithms that address two sub-classes of CSTNDs: (1) those that contain only decision time-points; and (2) those in which all decisions are made before execution begins.