Abstract
Model expansion task is the task of representing the essence of search problems where we are given an instance of a problem and are searching for a solution satisfying certain properties. Such tasks are common in AI planning, scheduling, logistics, supply chain management, etc., and are inherently modular. Recently, the model expansion framework was extended to deal with multiple modules to represent e.g. the task of constructing a logistics service provider relying on local service providers. In the current paper, we study existing systems that operate in a modular way in order to obtain general principles of solving modular model expansion tasks. We introduce a general algorithm to solve model expansion tasks for modular systems. We demonstrate, through several case studies, that our algorithm closely corresponds to what is done in practice in different areas such as Satisfiability Modulo Theories (SMT), Integer Linear Programming (ILP), and Answer Set Programming (ASP). We make our framework language-independent through a model-theoretic development.
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Notes
- 1.
A more realistic example contains many more modules.
- 2.
We are equally interested in representing multi-module processes that do not require more than a polynomial number of steps to solve, as is common in some business processes such as signing a document.
- 3.
This view follows the research program started in [1].
- 4.
By “\(:=\)” we mean “is by definition” or “denotes”.
- 5.
This makes sure that \(\varOmega \) is returned only once at the beginning.
- 6.
Again \(O_T\) only returns this set when \(\mathcal{B}\) is the empty expansion of the instance structure.
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Tasharrofi, S., Wu, X.(., Ternovska, E. (2013). Solving Modular Model Expansion: Case Studies. In: Tompits, H., et al. Applications of Declarative Programming and Knowledge Management. INAP WLP 2011 2011. Lecture Notes in Computer Science(), vol 7773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41524-1_12
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