MoL-2011-16: Completing partial algebra models of term rewriting systems

MoL-2011-16: Nesin, Gabriela Asli Rino (2011) Completing partial algebra models of term rewriting systems. [Report]

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The study of partial algebras is the part of universal algebra which deals with structures whose operations are not defined everywhere. A natural question to ask if faced with a partial algebra is whether or not it can be completed, i.e. embedded into a total algebra. If furthermore we take partial algebras modelling a certain theory T , the question of finding a completion also modelling T may be very hard, depending on the strength of T . In this thesis we investigate a special case of the difficult problem stated above. In particular, we show that partial algebras which model an orthogonal term rewriting system and which satisfy a certain condition on head-normal forms can be completed. Our result generalizes a previous result by Inge Bethke, Jan Willem Klop and Roel de Vrijer presented in [BKdV96]. In the process, we will prove an abstract confluence theorem which is independent from our particular choice of term rewriting system and therefore can be taken separately. Our proof is preceded by a section on completions of partial algebras, describing the construction of the one-point completion and free completion of a given partial algebra, and showing the relations between these completions in category-theoretic terms.

Item Type: Report
Report Nr: MoL-2011-16
Series Name: Master of Logic Thesis (MoL) Series
Year: 2011
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38

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