Distributive implication groupoids

Ivan Chajda 1  and Radomir Halaš 1
  • 1 Palacký University Olomouc Tomkova 40

Abstract

We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.

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