Temporal semantics of compositional task models
and problem solving methods
Frances M.T. Brazier, Jan Treur*, Niek J.E. Wijngaards, Mark Willems
Abstract
I. Introduct ion
Complex tasks in which reasoning plays an important role, such as design or diagnostic tasks, are
most often extremely dynamic. The aim in knowledge ngineering is to model such complex

18 F. Brazier et al. / Data & Knowledge Engineering 29 (1999) 17-42
provide a means to formally describe a complex task thereby providing a common ground for
informal models of the same complex task.
A framework that allows conceptual and formal specification of such models should be powerful
enough to capture such behaviour in an explicit and transparent manner. Early work on formalisation
of task models and problem solving methods can be found in \[5,24,38\]. These formalisations only
address the syntax of the models. A number of the current approaches to modelling complex
reasoning tasks, in which formal specification plays an important role, are MIKE/V,~ARL \[3,16\],
CommonKADS/(ML) 2 \[2,19\], VITAL \[34\], TASK \[28\] and MILORD \[1\]. Also, these approaches include a
formal syntax for the specification language, but the formal semantics of such systems from a
dynamic perspective are often not defined in detail; for a description that is detailed, see \[16\].
Both a conceptual nd formal definition of the temporal semantics of behaviour are especially of
importance for dynamic tasks. Formal semantics not only provides a basis for validation and
verification of system behaviour \[32\], but specifications of components at different levels of
abstraction with well-defined semantics also provide a means to enable automated support for
re-design of task models and components. Automated support for re-design, for example, often
requires explicit formulation of requirements on system behaviour, based on well-defined semantics.
The temporal approach to semantics described in this paper assumes equential processing, as do all
other approaches to modelling of tasks and problem solving methods mentioned above (in contrast to
multi-agent systems, where parallel processing is assumed; e.g. \[7\]).
Temporal modelling and temporal reasoning is often applied in the context of reasoning about a
dynamic world (e.g. patient data) \[35\]. Another application of temporal modelling is reasoning about
the order in which certain operators need to be applied \[13,14\]. In contrast his paper addresses
temporal semantics of reasoning tasks themselves.
Section 2 provides an overview of the knowledge modelled and specified in task models. In Section
3 the perspective on temporal semantics i introduced and the basic concepts are defined. In Section 4
definitions of the concepts required to formalise compositional information states are introduced,
followed by definitions of concepts directly related to transitions between (compositional) component
information states in Section 5. The formalisation of the resulting compositional behaviour is defined
(in terms of the temporal approach) in Section 5 and discussed in Section 6. Further discussion of
applications for which this approach as been successfully applied extends beyond the scope of this
paper: see, for example \[21\].
2. Compositional modelling of tasks and problem solving methods
Using the development method DESIRE \[11,25\], problem solving behaviour in complex tasks in
knowledge-intensive domains is modelled explicitly in a compositional manner. The resulting
products are specifications of reflective (knowledge based) compositional rchitectures (including task
and domain knowledge) and specifications of problem description and design rationale. To this end a
problem description, a design rationale, and three levels of design are distinguished: conceptual
design, detailed esign and operational design, as shown in Fig. 1.
The relations between these levels of design are well defined. The detailed specification, for
example, always preserves the structures defined at the conceptual level of specification. However, at
the detailed level of design, additional structures (and details) are added. At the level of operational