top
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.
Ivan Chajda, and Radomir Halaš. "Distributive implication groupoids." Open Mathematics 5.3 (2007): 484-492. <http://eudml.org/doc/269646>.
@article{IvanChajda2007, 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.}, author = {Ivan Chajda, Radomir Halaš}, journal = {Open Mathematics}, keywords = {(distributive) implication groupoid; ideal; deductive system; congruence kernel; left distributivity; variety of distributive implication groupoids; ideals; deductive systems; congruences; distributive implication algebra}, language = {eng}, number = {3}, pages = {484-492}, title = {Distributive implication groupoids}, url = {http://eudml.org/doc/269646}, volume = {5}, year = {2007}, }
TY - JOUR AU - Ivan Chajda AU - Radomir Halaš TI - Distributive implication groupoids JO - Open Mathematics PY - 2007 VL - 5 IS - 3 SP - 484 EP - 492 AB - 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. LA - eng KW - (distributive) implication groupoid; ideal; deductive system; congruence kernel; left distributivity; variety of distributive implication groupoids; ideals; deductive systems; congruences; distributive implication algebra UR - http://eudml.org/doc/269646 ER -
