Web Information Systems (WIS) are becoming more and more ubiquitous along with the changes in information technology. There have already been several studies on modeling various aspects of WIS. This paper attempts to investigate the most recent paradigms of WIS description taking into account the Web service approaches, Service Oriented Architecture and Cloud computing. One of the modeling and analysis approaches is the Artifact Centric Business Process that unifies both the behavioral and information aspects of business processes carried out in a WIS environment. The information aspect frequently incorporates in the form of unstructured or semi-structured document that indirectly influences the content of the underlying database through several tiers of the given architecture. A business event stimulates a business process along with some set of data and triggers a process at the user interface level. The process initiates a chain of processes that goes through the tiers of architecture until the content of the database is affected. The Story Algebra, or more generally the Process Algebra approach provides a formal framework that promises a formal describing method for modeling precisely the event triggered processes coupled with data in document format.