2.1 Modal logic S4 also known as KT4: axiom K + T ([]p->p:of reflexivity) + 4 ([]p->[][]p:of transitivity) Author: Lilac Team Last update: February 2009 not 1 false ~ _ 5 and 2 true _ & _ 4 or 2 true _ v _ 3 imp 2 false _ -> _ 0 mTrue 1 false mTrue _ 0 mFalse 1 false mFalse _ 0 mTrueAnd hasElement node0 mTrue and variable a variable b add node0 variable a add node0 variable b loopTest isNewNode node1 isAncestor node0 node1 contains node0 node1 mark node1 CONTAINED link node1 node0 Loop mTrueOr hasElement node mTrue or variable A variable B duplicate premodel_copy add premodel_copy.node mTrue variable B add node mTrue variable A mFalseOr hasElement node mFalse or variable A variable B add node mFalse variable A add node mFalse variable B mFalseAnd hasElement node mFalse and variable a variable b duplicate premodel_copy add premodel_copy.node mFalse variable b add node mFalse variable a mTrueImpActual hasElement node mTrue imp variable a variable b add node mFalse variable a duplicate premodel_copy add premodel_copy.node mTrue variable b mFalseImp hasElement node mFalse imp variable a variable b isNotMarked node CONTAINED createNewNode node1 add node1 mTrue variable a add node1 mFalse variable b link node node1 R mTrueImpPropagation hasElement node mTrue imp variable a variable b isLinked node node1 R add node1 mTrue imp variable a variable b mTrueNotActual hasElement node mTrue not variable a add node mFalse variable a mTrueNotPropagation hasElement node mTrue not variable a isLinked node node1 R add node1 mTrue not variable a mFalseNot hasElement node mFalse not variable a isNotMarked node CONTAINED createNewNode node1 add node1 mTrue variable a link node node1 R mTrueAtomPropagation hasElement node mTrue variable a isAtomic variable a isLinked node node1 R add node1 mTrue variable a mTrueAndFalse hasElement node mTrue variable a hasElement node mFalse variable a add node FALSE Intuit_min_Strategy repeat firstRule repeat mTrueAndFalse mTrueAnd mFalseOr mTrueNotActual mTrueImpActual mTrueNotPropagation mTrueImpPropagation mTrueAtomPropagation mTrueOr end loopTest mFalseAnd mFalseNot mFalseImp end end Intuit_min_Strategy mFalse imp not not P P mFalse imp P not not P mFalse imp imp imp P Q P P