Belnap's logic and conditional composition

Authors:
Alban Ponse;Mark B. van der Zwaag
Affiliations:
Department of Computer Science, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands;Department of Computer Science, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

We study two alternative bases for Belnap's four-valued logic and provide complete equational axiomatizations for them. One is called conditional composition logic. It has a single, ternary if-then-else connective with a sequential, operational reading, and four constants for the truth values. The other logic is called guard logic. The main motivation for this logic lies in its technical properties. It admits a useful type of canonical form (term representation), and a relatively simple strategy for equational reasoning.