Categorical abstract algebraic logic: The criterion for deductive equivalence Export

@article{citeulike:878977, abstract = {Equivalent deductive systems were introduced in [4] with the goal of treating 1-deductive systems and algebraic 2-deductive systems in a uniform way. Results of [3], appropriately translated and strengthened, show that two deductive systems over the same language type are equivalent if and only if their lattices of theories are isomorphic via an isomorphism that commutes with substitutions. Deductive equivalence of ?-institutions [14, 15] generalizes the notion of equivalence of deductive systems. In [15, Theorem 10.26] this criterion for the equivalence of deductive systems was generalized to a criterion for the deductive equivalence of term ?-institutions, forming a subclass of all ?-institutions that contains those ?-institutions directly corresponding to deductive systems. This criterion is generalized here to cover the case of arbitrary ?-institutions.}, address = {School of Mathematics and Computer Science, Lake Superior State University, 650 W. Easterday Avenue, Sault Sainte Marie, MI 49783, U. S. A.}, author = {Voutsadakis, George}, citeulike-article-id = {878977}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/malq.200310036}, citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/104531731/ABSTRACT}, doi = {10.1002/malq.200310036}, journal = {MLQ}, keywords = {algebraic, categorical-logic, category-of-theories, lattice-of-theories}, number = {4}, pages = {347--352}, posted-at = {2006-09-30 15:04:48}, priority = {2}, title = {Categorical abstract algebraic logic: The criterion for deductive equivalence}, url = {http://dx.doi.org/10.1002/malq.200310036}, volume = {49}, year = {2003} }

TY - JOUR ID - citeulike:878977 L3 - citeulike-article-id:878977 N2 - Equivalent deductive systems were introduced in [4] with the goal of treating 1-deductive systems and algebraic 2-deductive systems in a uniform way. Results of [3], appropriately translated and strengthened, show that two deductive systems over the same language type are equivalent if and only if their lattices of theories are isomorphic via an isomorphism that commutes with substitutions. Deductive equivalence of ?-institutions [14, 15] generalizes the notion of equivalence of deductive systems. In [15, Theorem 10.26] this criterion for the equivalence of deductive systems was generalized to a criterion for the deductive equivalence of term ?-institutions, forming a subclass of all ?-institutions that contains those ?-institutions directly corresponding to deductive systems. This criterion is generalized here to cover the case of arbitrary ?-institutions. IS - 4 JF - MLQ AD - School of Mathematics and Computer Science, Lake Superior State University, 650 W. Easterday Avenue, Sault Sainte Marie, MI 49783, U. S. A. EP - 352 TI - Categorical abstract algebraic logic: The criterion for deductive equivalence VL - 49 SP - 347 KW - algebraic KW - categorical-logic KW - category-of-theories KW - lattice-of-theories AU - Voutsadakis, George PY - 2003/// UR - http://dx.doi.org/10.1002/malq.200310036 ER -