AN INTUITIONISTIC CHARACTERIZATION OF CLASSICAL LOGIC TeX Export

@article{citeulike:2947021, abstract = {Abstract\ \ By introducing the intensional mappings and their properties, we establish a new semantical approach of characterizing intermediate logics. First prove that this new approach provides a general method of characterizing and comparing logics without changing the semantical interpretation of implication connective. Then show that it is adequate to characterize all Kripke\_complete intermediate logics by showing that each of these logics is sound and complete with respect to its (unique) 'weakest characterization property' of intensional mappings. In particular, we show that classical logic has the weakest characterization property \$\$cl\$\$, which is the strongest among all possible weakest characterization properties of intermediate logics. Finally, it follows from this result that a translation is an embedding of classical logic into intuitionistic logic, iff. its semantical counterpart has the property \$\$cl\$\$.}, author = {Hsiung, Ming}, citeulike-article-id = {2947021}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/s10992-007-9072-0}, day = {1}, doi = {10.1007/s10992-007-9072-0}, journal = {Journal of Philosophical Logic}, keywords = {kripke, logic, semantics}, number = {4}, pages = {299--317}, posted-at = {2008-07-01 09:54:13}, priority = {2}, title = {AN INTUITIONISTIC CHARACTERIZATION OF CLASSICAL LOGIC}, url = {http://dx.doi.org/10.1007/s10992-007-9072-0}, volume = {37}, year = {2008} }

TY - JOUR ID - citeulike:2947021 L3 - citeulike-article-id:2947021 N2 - Abstract  By introducing the intensional mappings and their properties, we establish a new semantical approach of characterizing intermediate logics. First prove that this new approach provides a general method of characterizing and comparing logics without changing the semantical interpretation of implication connective. Then show that it is adequate to characterize all Kripke_complete intermediate logics by showing that each of these logics is sound and complete with respect to its (unique) ‘weakest characterization property’ of intensional mappings. In particular, we show that classical logic has the weakest characterization property $$cl$$, which is the strongest among all possible weakest characterization properties of intermediate logics. Finally, it follows from this result that a translation is an embedding of classical logic into intuitionistic logic, iff. its semantical counterpart has the property $$cl$$. IS - 4 JF - Journal of Philosophical Logic EP - 317 TI - AN INTUITIONISTIC CHARACTERIZATION OF CLASSICAL LOGIC VL - 37 SP - 299 KW - kripke KW - logic KW - semantics AU - Hsiung, Ming PY - 2008//01/ UR - http://dx.doi.org/10.1007/s10992-007-9072-0 ER -