From Classical to Normal Modal Logics

Classical modal logics (Segerberg [27], Chellas [2]) are weaker than the well-known normal modal logics: The only rule that is common to all classical modal logics is % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiaadw % eacaGG6aWaaSaaaeaacaWGgbGaeyiLHSQaam4raaqaaiablgAjxjaa % dAeacqGHugYQcqWIHwYvcaWGhbaaaaaa!42C5! ]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$ RE:\frac{{F \leftrightarrow G}}{{\square F \leftrightarrow \square G}} $$ (We nevertheless note that this principle raises problems in systems containing equality (Hughes and Cresswell [14]).)