Date of Award


Degree Name

Doctor of Philosophy


Computer Science

First Advisor

Rahimi, Shahram


The Generalized Constraint Language (GCL), introduced by Zadeh, is the essence of Computing with Words (CW). It provides an genda to represent the meaning of imprecise words and phrases in natural language and introduces advanced techniques to perform reasoning on imprecise knowledge. Despite its fundamental role, the definition of GCL has remained informal since its introduction by Zadeh and, to our knowledge, no attempt has been made to formalize GCL or to build a working GCL deduction system. In this dissertation, two main interrelated objectives are pursued: First, the syntax and semantics of GCL are formalized in a logical setting. The notion of soundness of a GCL argument is defined and Zadeh's inference rules are proven sound in the defined language. Second, a CW Expert System Shell (CWSHELL) is implemented for the realization of a GCL deduction system. The CWSHELL software allows users to express their knowledge in terms of GCL formulas and pose queries to a GCL knowledge base. The richness of GCL language allows CWSHELL to greatly surpass current fuzzy logic expert systems both in its knowledge representation and reasoning capabilities. While many available fuzzy logic toolboxes can only represent knowledge in terms of fuzzy-if-then rules, CWShell goes beyond simple fuzzy conditional statements and performs a chain of reasoning on complex fuzzy propositions containing generalized constraints, fuzzy arithmetic expressions, fuzzy quantifiers, and fuzzy relations. To explore the application of CWSHELL, a realistic case study is developed to compute the auto insurance premium based on an imprecise knowledge base. The alpha version of CWSHELL along with the case study and documentation is available for download at




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