Incorporating measurement uncertainty into OCL/UML primitive datatypes

Abstract

The correct representation of the relevant properties of a system is an essential requirement for the effective use and wide adoption of model-based practices in industry. Uncertainty is one of the inherent properties of any measurement or estimation that is obtained in any physical setting; as such, it must be considered when modeling software systems that deal with real data. Although a few modeling languages enable the representation of measurement uncertainty, these aspects are not normally incorporated into their type systems. Therefore, operating with uncertain values and propagating their uncertainty become cumbersome processes, which hinder their realization in real environments. This paper proposes an extension of OCL/UML primitive datatypes that enables the representation of the uncertainty that comes from physical measurements or user estimates into the models, together with an algebra of operations that are defined for the values of these types.

Extending OCL with Subjective Logic.

“…The result can be expressed by the probability that one is in fact less than the other: in this case, 0.383, cf. (Bertoa et al 2019). On the other hand, epistemic uncertainty happens, for example, when somebody is asked whether it will rain tomorrow or not.…”

“…In (Bertoa et al 2019), we proposed an extension of all UML and OCL primitive datatypes (Boolean, Real, String, Integer) able to deal with uncertainty. Type embedding was used to define the extensions, and subtyping ensured safe replaceability of values and operations.…”

“…Similar to the embedding relationship Boolean → UBoolean that lifts Boolean values to their corresponding probabilities (Bertoa et al 2019), we also define the embedding relationship UBoolean → SBoolean that lifts probabilities to opinions-hence obtaining the complete embedding chain Boolean → UBoolean → SBoolean.…”

“…Despite the success of UML (Object Management Group 2015) and OCL (Object Management Group 2014) for modeling information systems, the birth of new paradigms such as the Internet of Things (IoT), Cyber-physical Systems (CPS), the advances in Robotics and Artificial Intelligence (AI), have raised the need to model systems that represent or interact with new environments (i.e., physical factors), which is challenging these notations. In particular, the basic datatypes and mechanisms that they provide are falling short for expressing behavioral aspects which are essential to these kinds of systems such as concurrency, units, precision, uncertainty or social behavior (Lee 2008;Selic 2015;Zhang et al 2016;Bertoa et al 2019;Burgueño, Mayerhofer, et al 2019;Bucchiarone et al 2020).…”

“…In other words, they let Boolean values or predicates to be partially true. In (Bertoa et al 2019), we proposed an extension of UML and OCL type Boolean, called UBoolean (Uncertain Boolean), which adds to each Boolean value a real number in the range [0,1] that represents the likelihood that such a value is true. This datatype provides a probabilistic extension to binary logic.…”