CONTENTSPreface......................................................................................................................................................... 5ABSTRACT LOGICS (by D. J. Brown and E. Suszko)Introduction.................................................................................................................................................. 9I. Elementary properties of closure systems and closure operations............................................. 10II. Some properties of closure operators and closure systems....................................................... 12III. Basic concepts of closure spaces.................................................................................................... 14IV. Galois connections and dual spaces............................................................................................... 16V. Abstract logics........................................................................................................................................ 19VI. Projective generation of abstract logics........................................................................................... 20VII. Inductive generation of abstract logics............................................................................................ 23VIII. Logical congruences and bi-logical morphisms......................................................................... 24IX. The structure of ....................................................................................................................... 26X. Logical matrices.................................................................................................................................... 28XI. Generating logics by matrices .......................................................................................................... 29XII. Structurality and invariance................................................................................................................ 31XIII. Adequacy and completeness........................................................................................................... 33XIV. Some applications to mathematical logic..................................................................................... 35References.................................................................................................................................................. 40CLASSICAL ABSTRACT LOGICS (by S.L. Bloom and D. J. Brown)1. Introduction............................................................................................................................................. 432. Preliminaries.......................................................................................................................................... 433. The category of classical logics.......................................................................................................... 454. The characterization theorems........................................................................................................... 48References.................................................................................................................................................. 52
@book{bwmeta1.element.zamlynska-4df82392-885d-44da-a717-484bfcd7da14, author = {D. J. Brown and R. Suszko and S. L. Bloom and D. J. Brown}, title = {"Abstract logics" and "Classical abstract logics"}, series = {GDML\_Books}, publisher = {Instytut Matematyczny Polskiej Akademi Nauk}, address = {Warszawa}, year = {1973}, zbl = {0317.02071}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-4df82392-885d-44da-a717-484bfcd7da14} }
D. J. Brown; R. Suszko; S. L. Bloom; D. J. Brown. "Abstract logics" and "Classical abstract logics". GDML_Books (1973), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-4df82392-885d-44da-a717-484bfcd7da14/