کاربرد منطق پیشنهادی برای تجزیه و تحلیل جریان کار

In this paper our main goal is to describe the structure of workflows. A workflow is an abstraction of a business process that consists of one or more tasks to be executed to reach a final objective. In our approach we describe a workflow as a graph whose vertices represent workflow tasks and the arcs represent workflow transitions. Moreover, every arc (tk,tltk,tl) (i.e., a transition) has attributed a Boolean value to specify the execution/non-execution of tasks tk,tltk,tl. With this attribution we are able to identify the natural flow in the workflow. Finally, we establish a necessary and sufficient condition for the termination of workflows. In other words, we identify conditions under which a business process will be complete.

In this paper, we use graph theory and propositional logic to describe and analyze workflows. In particular, the use of propositional logic is a fundamental instrument to determine if a workflow has been correctly designed by an end user from the termination point of view. A workflow is an abstraction of a business process that consists of one or more tasks that need to be executed to complete a process (for example, hiring process, sales order processing, article reviewing, member registration, etc.), that can include human activity and/or software applications to carry out activities. A workflow can be represented by a graph, whose tasks are represented with vertices and the tasks are modeled with arcs, known as transitions. Each task represents a unit of work to be executed either by humans or application programs. A workflow describes all of the tasks needed to achieve each step in a business process. Workflows may involve many distinct, heterogeneous, autonomous, and distributed tasks that are interrelated in complex ways. The complexity of large workflows requires a precise modeling to ensure that they perform according to initial specifications. A vast number of formal frameworks have been proposed to allow workflow modeling verification and analysis, such as State and Activity Charts [1], Graphs [2], Event-Condition-Action rules [3] and [4], Petri Nets [5], [6], [7] and [8], Temporal Logic [9] and Markov chains [10]. Other approaches can be found in [11], [12] and [13]. In this paper our formalism is based on graph theory and propositional logic. One relevant aspect of our approach is the use of propositional logic. In particular, the attribution of Boolean values to each arc of the workflow is very important, since it allows us to identify the natural flow in the workflow. Finally, we identify conditions under which a workflow logically terminates. In other words, we are able to verify if a business process will be complete

In this paper we provide a theoretical mathematical foundation, based on graph theory and propositional logic, that can describe the structure of workflows. One relevant aspect of our approach is the use of propositional logic. In particular the attribution of Boolean values to each transition is one highlight of our study. This attribution allows to identify the natural flow in the workflow. Finally, our approach allows us to determine under which conditions a workflow will be completed, i.e., a workflow logically terminates. Indeed, we prove that a workflow logically terminates, if and only if, for any materialized workflow instance, all its compound EAEA models are positive.