A Gentzen system for conditional logic (Q1327484)

For conditional logic, a Gentzen-type formulation is given. Conditional logic is a deductive system on an algebraic system, defined by Guzmán and Squier, composed of three truth-values (true, unknown and false), three logical operations (conjunction, disjunction and negation), while implication is defined by the structural finitary consequence relation. The defined Gentzen-type system is a very natural extension of Gentzen's original. For the defined system the author proves the soundness theorem, the completeness theorem, and some other theorems. But the cut- elimination theorem is not provided.