Logica Universalis

, Volume 9, Issue 1, pp 1–26 | Cite as

Existence of Finite Total Equivalence Systems for Certain Closed Classes of 3-Valued Logic Functions

Article

Abstract

The article deals with finding finite total equivalence systems for formulas based on an arbitrary closed class of functions of several variables defined on the set {0, 1, 2} and taking values in the set {0,1} with the property that the restrictions of its functions to the set {0, 1} constitutes a closed class of Boolean functions. We consider all classes whose restriction closure is either the set of all functions of two-valued logic or the set Ta of functions preserving \({a, a\in\{0, 1\}}\). In each of these cases, we find a finite total equivalence system, construct a canonical type for formulas, and present a complete algorithm for determining whether any two formulas are equivalent.

Keywords

Many-valued logic closed class finite total equivalence system 

Mathematics Subject Classification

03B50 06E30 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Data Analysis and Artificial IntelligenceNational Research University Higher School of EconomicsMoscowRussia

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