Reduction of Hilbert-type proof systems to the if-then-else equational logic Article

Received: 24 September 2003 Revised: 12 November 2003 DOI :
10.1007/BF02936099

Cite this article as: Jeong, J. JAMC (2004) 14: 69. doi:10.1007/BF02936099
Abstract We present a construction of the linear reduction of Hilbert type proof systems for propositional logic to if-then-else equational logic. This construction is an improvement over the same result found in [4] in the sense that the technique used in the construction can be extended to the linear reduction of first-order logic to if-then-else equational logic.

AMS Mathematics Subject Classification 03B22 03F99

Key words and phrases Proof systems reduction if-then-else equational logic This work was supported by grant No. R01-2000-00287 from the Basic Research Program of the Korea Science & Engineering Foundation.

Joohee Jeong received his BS from Seoul National University and Ph.D. at the University of California at Berkeley under the direction of Prof. R. McKenzie. His research interests focus on logic, universal algebra and their application to programming language semantics.

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Authors and Affiliations 1. Department of Mathematics Education Kyungpook National University Daegu Korea