Algebra and Theory of OrderDeterministic Pomsets
Rensink, A. (1996) Algebra and Theory of OrderDeterministic Pomsets. Notre Dame Journal of Formal Logic, 37 (2). pp. 283320. ISSN 00294527

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Abstract:  This paper is about partially ordered multisets (pomsets for short). We investigate a particular class of pomsets that we call orderdeterministic, properly including all partially ordered sets, which satisfies a number of interesting properties: among other things, it forms a distributive lattice under pomset prefix (hence prefix closed sets of orderdeterministic pomsets are prime algebraic), and it constitutes a reflective subcategory of the category of all pomsets. For the orderdeterministic pomsets we develop an algebra with a sound and () complete equational theory. The operators in the algebra are concatenation and join, the latter being a variation on the more usual disjoint union of pomsets. This theory is then extended in order to capture refinement of pomsets by incorporating homomorphisms between models as objects in the algebra and homomorphism application as a new operator. 
Item Type:  Article 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
Research Group:  
Link to this item:  http://purl.utwente.nl/publications/66660 
Official URL:  http://dx.doi.org/10.1305/ndjfl/1040046090 
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