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updated comments in contact_algebras Hierarchy with single quotes

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carmenchui committed Jun 20, 2018
1 parent b66712d commit e2b105166c81aa5422cfaf99e25b20b34ef3a721
@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/C-Ext.clif (cl-text http://colore.oor.net/contact_algebras/C-Ext.clif


(cl-comment "C-Ext") (cl-comment 'C-Ext')


(forall (x y) (forall (x y)
(if (if
@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/C4.clif (cl-text http://colore.oor.net/contact_algebras/C4.clif


(cl-comment "C4") (cl-comment 'C4')


(forall (x y z) (forall (x y z)
(if (if
@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/C5prime.clif (cl-text http://colore.oor.net/contact_algebras/C5prime.clif


(cl-comment "C5prime") (cl-comment 'C5prime')


(forall (x z) (forall (x z)
(if (if
@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/Conn.clif (cl-text http://colore.oor.net/contact_algebras/Conn.clif


(cl-comment "Con: Connection axiom (connection of an entity with its complement)") (cl-comment 'Con: Connection axiom (connection of an entity with its complement)')


(forall (x) (forall (x)
(if (and (if (and
@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/Dis.clif (cl-text http://colore.oor.net/contact_algebras/Dis.clif


(cl-comment "Dis") (cl-comment 'Dis')


(forall (x) (forall (x)
(if (if
@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/atomless_boolean_contact_algebra.clif (cl-text http://colore.oor.net/contact_algebras/atomless_boolean_contact_algebra.clif


(cl-comment "atomless Boolean Contact algebra axioms") (cl-comment 'atomless Boolean Contact algebra axioms')


(cl-imports http://colore.oor.net/contact_algebras/boolean_contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/boolean_contact_algebra.clif)


@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/boolean_contact_algebra.clif (cl-text http://colore.oor.net/contact_algebras/boolean_contact_algebra.clif


(cl-comment "Boolean Contact algebra axioms") (cl-comment 'Boolean Contact algebra axioms')


(cl-imports http://colore.oor.net/contact_algebras/contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/contact_algebra.clif)


@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/contact_algebra.clif (cl-text http://colore.oor.net/contact_algebras/contact_algebra.clif


(cl-comment "axioms of a (pseudocomplemented) contact algebra") (cl-comment 'axioms of a (pseudocomplemented) contact algebra')


(cl-imports http://colore.oor.net/contact_algebras/distributive_contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/distributive_contact_algebra.clif)


@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/distributive_contact_algebra.clif (cl-text http://colore.oor.net/contact_algebras/distributive_contact_algebra.clif


(cl-comment "Axioms of a distributive contact algebra which satifies the sum axiom C4") (cl-comment 'Axioms of a distributive contact algebra which satifies the sum axiom C4')


(cl-imports http://colore.oor.net/contact_algebras/weak_contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/weak_contact_algebra.clif)


@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/ewbca.clif (cl-text http://colore.oor.net/contact_algebras/ewbca.clif


(cl-comment "Extensionsal Weak Boolean Contact algebra axioms (as defined in Hahmann and Gruninger, Notre Dame J. Formal Logic 2013)") (cl-comment 'Extensionsal Weak Boolean Contact algebra axioms (as defined in Hahmann and Gruninger, Notre Dame J. Formal Logic 2013)')


(cl-imports http://colore.oor.net/contact_algebras/wbca.clif) (cl-imports http://colore.oor.net/contact_algebras/wbca.clif)


@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/extensional_weak_boolean_contact_algebra.clif (cl-text http://colore.oor.net/contact_algebras/extensional_weak_boolean_contact_algebra.clif


(cl-comment "Extensional Weak Boolean Contact algebra axioms") (cl-comment 'Extensional Weak Boolean Contact algebra axioms')


(cl-imports http://colore.oor.net/contact_algebras/extensional_weak_contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/extensional_weak_contact_algebra.clif)


@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/extensional_weak_contact_algebra.clif (cl-text http://colore.oor.net/contact_algebras/extensional_weak_contact_algebra.clif


(cl-comment "axioms for extensional weak contact algebras") (cl-comment 'axioms for extensional weak contact algebras')


(cl-imports http://colore.oor.net/contact_algebras/weak_contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/weak_contact_algebra.clif)


@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/gbca.clif (cl-text http://colore.oor.net/contact_algebras/gbca.clif


(cl-comment "Generalized Weak Boolean Contact algebra axioms (as defined in Hahmann and Gruninger, Notre Dame J. Formal Logic 2013)") (cl-comment 'Generalized Weak Boolean Contact algebra axioms (as defined in Hahmann and Gruninger, Notre Dame J. Formal Logic 2013)')


(cl-imports http://colore.oor.net/contact_algebras/wbca.clif) (cl-imports http://colore.oor.net/contact_algebras/wbca.clif)


@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/generalized_boolean_contact_algebra.clif (cl-text http://colore.oor.net/contact_algebras/generalized_boolean_contact_algebra.clif


(cl-comment "Generalized Boolean Contact algebra axioms") (cl-comment 'Generalized Boolean Contact algebra axioms')


(cl-imports http://colore.oor.net/contact_algebras/contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/contact_algebra.clif)


@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/notC4.clif (cl-text http://colore.oor.net/contact_algebras/notC4.clif


(cl-comment "notC4") (cl-comment 'notC4')


(exists (x y z) (exists (x y z)
(and (and
@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/NotTriv.clif (cl-text http://colore.oor.net/contact_algebras/NotTriv.clif


(cl-comment "non-trivial model") (cl-comment 'non-trivial model')


(exists (y) (exists (y)
(and (and
@@ -11,7 +11,7 @@


(cl-text http://colore.oor.net/contact_algebras/oca.clif (cl-text http://colore.oor.net/contact_algebras/oca.clif


(cl-comment "equational axiomatization of orthocomplemented contact algebra (as defined in Hahmann and Gruninger, Notre Dame J. Formal Logic 2013)") (cl-comment 'equational axiomatization of orthocomplemented contact algebra (as defined in Hahmann and Gruninger, Notre Dame J. Formal Logic 2013)')


(cl-imports http://colore.oor.net/contact_algebras/weakest_contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/weakest_contact_algebra.clif)


@@ -10,11 +10,11 @@


(cl-text http://colore.oor.net/contact_algebras/proximity_boolean_contact_algebra.clif (cl-text http://colore.oor.net/contact_algebras/proximity_boolean_contact_algebra.clif


(cl-comment "Proximity Boolean Contact algebra (PBCA) axioms") (cl-comment 'Proximity Boolean Contact algebra (PBCA) axioms')


(cl-imports http://colore.oor.net/contact_algebras/boolean_contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/boolean_contact_algebra.clif)


(cl-comment "Nor: Normality axiom ") (cl-comment 'Nor: Normality axiom ')


(forall (x y) (forall (x y)
(if (not (c x y)) (if (not (c x y))
@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/region_boolean_contact_algebra.clif (cl-text http://colore.oor.net/contact_algebras/region_boolean_contact_algebra.clif


(cl-comment "Region Boolean Contact algebra (RBCA) axioms") (cl-comment 'Region Boolean Contact algebra (RBCA) axioms')


(cl-imports http://colore.oor.net/contact_algebras/boolean_contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/boolean_contact_algebra.clif)


@@ -11,11 +11,11 @@


(cl-text http://colore.oor.net/contact_algebras/spoca.clif (cl-text http://colore.oor.net/contact_algebras/spoca.clif


(cl-comment "Stonian p-ortocomplemented contact algebra (as defined in Hahmann and Gruninger, Notre Dame J. Formal Logic 2013)") (cl-comment 'Stonian p-ortocomplemented contact algebra (as defined in Hahmann and Gruninger, Notre Dame J. Formal Logic 2013)')


(cl-imports http://colore.oor.net/contact_algebras/oca.clif) (cl-imports http://colore.oor.net/contact_algebras/oca.clif)


(cl-comment "PC1") (cl-comment 'PC1')


(forall (x y) (forall (x y)
(= (=
@@ -25,15 +25,15 @@
) )




(cl-comment "PC2prime") (cl-comment 'PC2prime')


(= (pc zero) one) (= (pc zero) one)


(cl-comment "PC2primeprime") (cl-comment 'PC2primeprime')


(= (pc one) zero) (= (pc one) zero)


(cl-comment "S: Stone property") (cl-comment 'S: Stone property')


(forall (x y) (forall (x y)
(= (=
@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/wbca.clif (cl-text http://colore.oor.net/contact_algebras/wbca.clif


(cl-comment "Weak Boolean Contact algebra axioms (as defined in Hahmann and Gruninger, Notre Dame J. Formal Logic 2013)") (cl-comment 'Weak Boolean Contact algebra axioms (as defined in Hahmann and Gruninger, Notre Dame J. Formal Logic 2013)')


(cl-imports http://colore.oor.net/contact_algebras/spoca.clif) (cl-imports http://colore.oor.net/contact_algebras/spoca.clif)


@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/weak_boolean_contact_algebra.clif (cl-text http://colore.oor.net/contact_algebras/weak_boolean_contact_algebra.clif


(cl-comment "Weak Boolean Contact algebra axioms") (cl-comment 'Weak Boolean Contact algebra axioms')


(cl-imports http://colore.oor.net/contact_algebras/weak_contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/weak_contact_algebra.clif)


@@ -10,7 +10,7 @@


(cl-text http://colore.oor.net/contact_algebras/weak_contact_algebra.clif (cl-text http://colore.oor.net/contact_algebras/weak_contact_algebra.clif


(cl-comment "Weak Contact Algebra (WCA, according to Duentsch and Winter 2006: Topological representations of contact lattices)") (cl-comment 'Weak Contact Algebra (WCA, according to Duentsch and Winter 2006: Topological representations of contact lattices)')


(cl-imports http://colore.oor.net/contact_algebras/weakest_contact_algebra.clif) (cl-imports http://colore.oor.net/contact_algebras/weakest_contact_algebra.clif)


@@ -12,24 +12,24 @@


(cl-imports http://colore.oor.net/lattices/bounded_lattice_meet_join.clif) (cl-imports http://colore.oor.net/lattices/bounded_lattice_meet_join.clif)


(cl-comment "C0: Disconnected null region") (cl-comment 'C0: Disconnected null region')


(forall (x) (forall (x)
(not (c 0 x))) (not (c 0 x)))


(cl-comment "C1: Reflexivity") (cl-comment 'C1: Reflexivity')


(forall (x) (forall (x)
(if (not (= x 0)) (if (not (= x 0))
(c x x))) (c x x)))


(cl-comment "C2: Symmetry") (cl-comment 'C2: Symmetry')


(forall (x y) (forall (x y)
(if (c x y) (if (c x y)
(c y x))) (c y x)))


(cl-comment "C3: Closure (using rewriting of lattice operation leq)") (cl-comment 'C3: Closure (using rewriting of lattice operation leq)')


(forall (x y z) (forall (x y z)
(if (and (c x y) (if (and (c x y)

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