Categorical abstract algebraic logic: The largest theory system included in a theory family Export

@article{citeulike:936306, abstract = {In this note, it is shown that, given a ? -institution \ℐ = ?Sign, SEN, C ?, with N a category of natural transformations on SEN, every theory family T of \ℐ includes a unique largest theory system of \ℐ. satisfies the important property that its N -Leibniz congruence system always includes that of T . As a consequence, it is shown, on the one hand, that the relation ?N () = ?N (T ) characterizes N -protoalgebraicity inside the class of N -prealgebraic ? -institutions and, on the other, that all N -Leibniz theory families associated with theory families of a protoalgebraic ? -institution \ℐ are in fact N -Leibniz theory systems. ({\copyright} 2006 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim)}, address = {School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, USA}, author = {Voutsadakis, George}, citeulike-article-id = {936306}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/malq.200510034}, citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/112610621/ABSTRACT}, doi = {10.1002/malq.200510034}, journal = {MLQ}, keywords = {categorical-abstract-algebraic-logic, categorical-logic}, number = {3}, pages = {288--294}, posted-at = {2006-11-08 14:33:01}, priority = {2}, title = {Categorical abstract algebraic logic: The largest theory system included in a theory family}, url = {http://dx.doi.org/10.1002/malq.200510034}, volume = {52}, year = {2006} }

TY - JOUR ID - citeulike:936306 L3 - citeulike-article-id:936306 N2 - In this note, it is shown that, given a ? -institution ℐ = ?Sign, SEN, C ?, with N a category of natural transformations on SEN, every theory family T of ℐ includes a unique largest theory system of ℐ. satisfies the important property that its N -Leibniz congruence system always includes that of T . As a consequence, it is shown, on the one hand, that the relation ?N () = ?N (T ) characterizes N -protoalgebraicity inside the class of N -prealgebraic ? -institutions and, on the other, that all N -Leibniz theory families associated with theory families of a protoalgebraic ? -institution ℐ are in fact N -Leibniz theory systems. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) IS - 3 JF - MLQ AD - School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, USA EP - 294 TI - Categorical abstract algebraic logic: The largest theory system included in a theory family VL - 52 SP - 288 KW - categorical-abstract-algebraic-logic KW - categorical-logic AU - Voutsadakis, George PY - 2006/// UR - http://dx.doi.org/10.1002/malq.200510034 ER -