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updated comments in lattice with single quotes

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carmenchui committed Jun 20, 2018
1 parent 7996301 commit 3a60eba7735067b922bdf580a51e92b29b81f049
Showing with 76 additions and 76 deletions.
  1. +1 −1 ontologies/lattices/Atom.clif
  2. +1 −1 ontologies/lattices/atomless_boolean_lattice.clif
  3. +2 −2 ontologies/lattices/boolean_ortho_lattice.clif
  4. +1 −1 ontologies/lattices/boolean_p_ortho_lattice.clif
  5. +3 −3 ontologies/lattices/bounded_lattice.clif
  6. +2 −2 ontologies/lattices/complemented_lattice.clif
  7. +1 −1 ontologies/lattices/definitions/complement.clif
  8. +2 −2 ontologies/lattices/definitions/joincomplement.clif
  9. +2 −2 ontologies/lattices/definitions/meetcomplement.clif
  10. +2 −2 ontologies/lattices/definitions/one.clif
  11. +2 −2 ontologies/lattices/definitions/zero.clif
  12. +2 −2 ontologies/lattices/distributive_lattice.clif
  13. +2 −2 ontologies/lattices/dual_stone_lattice.clif
  14. +3 −3 ontologies/lattices/join_semilattice.clif
  15. +4 −4 ontologies/lattices/lattice.clif
  16. +3 −3 ontologies/lattices/meet_semilattice.clif
  17. +2 −2 ontologies/lattices/modular_lattice.clif
  18. +4 −4 ontologies/lattices/ortho_complemented_lattice.clif
  19. +4 −4 ontologies/lattices/ortho_complemented_lattice_meet_join.clif
  20. +4 −4 ontologies/lattices/ortho_lattice.clif
  21. +2 −2 ontologies/lattices/ortho_modular_lattice.clif
  22. +1 −1 ontologies/lattices/pseudo_complemented_distributive_lattice.clif
  23. +3 −3 ontologies/lattices/pseudo_complemented_lattice.clif
  24. +1 −1 ontologies/lattices/quasi_complemented_distributive_lattice.clif
  25. +4 −4 ontologies/lattices/quasi_complemented_lattice.clif
  26. +2 −2 ontologies/lattices/stone_lattice.clif
  27. +2 −2 ontologies/lattices/stonian_p_ortho_lattice.clif
  28. +12 −12 ontologies/lattices/stonian_p_ortho_lattice_meet.clif
  29. +2 −2 ontologies/lattices/uni_complemented_lattice.clif
@@ -1,5 +1,5 @@

(cl-comment " Contributors: Torsten Hahmann - initial implementation")
(cl-comment ' Contributors: Torsten Hahmann - initial implementation')

(cl-text http://colore.oor.net/lattices/Atom.clif

@@ -14,7 +14,7 @@

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

(cl-comment "AB1: Non-atomicity")
(cl-comment 'AB1: Non-atomicity')

(forall (x)
(exists (y)
@@ -12,9 +12,9 @@

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

(cl-comment "Defining a Boolean lattice as extension of Beran's Ortholattice")
(cl-comment 'Defining a Boolean lattice as extension of Beran's Ortholattice')

(cl-comment "O2.4 (B21v from Padmanabhan and Rudeanu 2008")
(cl-comment 'O2.4 (B21v from Padmanabhan and Rudeanu 2008')

(forall (x y)
(= x (join (meet x y) (meet x (oc y))))
@@ -12,7 +12,7 @@

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

(cl-comment "ortho- and pseudocomplement are identical")
(cl-comment 'ortho- and pseudocomplement are identical')

(forall (x)
(= (oc x) (pc x))
@@ -18,14 +18,14 @@

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

(cl-comment "Bounded lattice axioms")
(cl-comment 'Bounded lattice axioms')

(cl-comment "L5: Bottom (zero)")
(cl-comment 'L5: Bottom (zero)')

(exists (zero))


(cl-comment "L6: Top (one)")
(cl-comment 'L6: Top (one)')

(exists (one))

@@ -14,10 +14,10 @@

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

(cl-comment "Complemented lattice axioms")
(cl-comment 'Complemented lattice axioms')


(cl-comment "C1: Existence of a complement (C1 in terms of D6)")
(cl-comment 'C1: Existence of a complement (C1 in terms of D6)')

(forall (x)
(exists (y)
@@ -17,7 +17,7 @@
(cl-imports http://colore.oor.net/lattices/definitions/joincomplement.clif)


(cl-comment "D6: Definition of a complement (binary relation, not unique) as join- and meet-complement")
(cl-comment 'D6: Definition of a complement (binary relation, not unique) as join- and meet-complement')

(forall (x y)
(iff
@@ -14,10 +14,10 @@

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

(cl-comment "Complemented lattice axioms")
(cl-comment 'Complemented lattice axioms')


(cl-comment "D5: Definition of a join-complement")
(cl-comment 'D5: Definition of a join-complement')

(forall (x y)
(iff
@@ -14,10 +14,10 @@

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

(cl-comment "Complemented lattice axioms")
(cl-comment 'Complemented lattice axioms')


(cl-comment "D4: Definition of a meet-complement")
(cl-comment 'D4: Definition of a meet-complement')

(forall (x y)
(iff
@@ -12,10 +12,10 @@

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

(cl-comment "Complemented lattice axioms")
(cl-comment 'Complemented lattice axioms')


(cl-comment "Definition of a one (top element); doesn't require it to exist")
(cl-comment 'Definition of a one (top element); doesn't require it to exist')

(forall (x)
(iff
@@ -12,10 +12,10 @@

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

(cl-comment "Complemented lattice axioms")
(cl-comment 'Complemented lattice axioms')


(cl-comment "D4: Definition of a zero")
(cl-comment 'D4: Definition of a zero')

(forall (x)
(iff
@@ -12,9 +12,9 @@

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

(cl-comment "Distributive lattice axioms")
(cl-comment 'Distributive lattice axioms')

(cl-comment "L8: Distributivity")
(cl-comment 'L8: Distributivity')

(forall (x y z)
(= (meet (x (join y z)))
@@ -12,9 +12,9 @@

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

(cl-comment "Defining the dual Stone lattices as quasicomplemented (dual pseudocomplemented) distributive lattices satisfying the Stone identity")
(cl-comment 'Defining the dual Stone lattices as quasicomplemented (dual pseudocomplemented) distributive lattices satisfying the Stone identity')

(cl-comment "S1: Stone identity")
(cl-comment 'S1: Stone identity')

(forall (x y)
(= (pc (join x y)) (meet (qc x) (qc y)))
@@ -11,18 +11,18 @@
(cl-text http://colore.oor.net/lattices/join_semilattice.clif


(cl-comment "L1: Idempotency")
(cl-comment 'L1: Idempotency')

(forall (x)
(= x (join x x)))

(cl-comment "L2: Commutativity")
(cl-comment 'L2: Commutativity')

(forall (x y)
(= (join x y)
(join y x)))

(cl-comment "L3: Associativity")
(cl-comment 'L3: Associativity')

(forall (x y z)
(= (join x (join y z))
@@ -11,7 +11,7 @@
(cl-text http://colore.oor.net/lattices/lattice.clif


(cl-comment "L1: Idempotency")
(cl-comment 'L1: Idempotency')

(forall (x)
(= x (meet x x)))
@@ -20,7 +20,7 @@
(= x (join x x)))


(cl-comment "L2: Commutativity")
(cl-comment 'L2: Commutativity')

(forall (x y)
(= (meet x y)
@@ -31,7 +31,7 @@
(join y x)))


(cl-comment "L3: Associativity")
(cl-comment 'L3: Associativity')

(forall (x y z)
(= (meet x (meet y z))
@@ -43,7 +43,7 @@



(cl-comment "L4: Absorption Laws")
(cl-comment 'L4: Absorption Laws')

(forall (x y)
(= (meet x (join x y))
@@ -9,19 +9,19 @@
(cl-text http://colore.oor.net/lattices/meet_semilattice.clif


(cl-comment "L1: Idempotency")
(cl-comment 'L1: Idempotency')

(forall (x)
(= x (meet x x)))


(cl-comment "L2: Commutativity")
(cl-comment 'L2: Commutativity')

(forall (x y)
(= (meet x y)
(meet y x)))

(cl-comment "L3: Associativity")
(cl-comment 'L3: Associativity')

(forall (x y z)
(= (meet x (meet y z))
@@ -12,9 +12,9 @@

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

(cl-comment "Modular lattice axioms")
(cl-comment 'Modular lattice axioms')

(cl-comment "M: Modularity")
(cl-comment 'M: Modularity')

(forall (x y z)
(= (join (meet x y) (meet x z))
@@ -14,20 +14,20 @@

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

(cl-comment "Orthocomplemented lattice axioms")
(cl-comment 'Orthocomplemented lattice axioms')

(cl-comment "OC1: Orthocomplement is complement")
(cl-comment 'OC1: Orthocomplement is complement')

(forall (x)
(complement x (oc x)))

(cl-comment "OC2: Orthocomplement is involutary")
(cl-comment 'OC2: Orthocomplement is involutary')

(forall (x)
(= x (oc (oc x)))
)

(cl-comment "OC3: Orthocomplement is order-reversing")
(cl-comment 'OC3: Orthocomplement is order-reversing')


(forall (x y)
@@ -12,15 +12,15 @@

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

(cl-comment "Orthocomplemented lattice axioms")
(cl-comment 'Orthocomplemented lattice axioms')

(cl-comment "O1prime: Orthocomplement is complement")
(cl-comment 'O1prime: Orthocomplement is complement')

(forall (x)
(= x (oc (oc x)))
)

(cl-comment "O2prime: Orthocomplement is involutary")
(cl-comment 'O2prime: Orthocomplement is involutary')

(forall (x)
(=
@@ -30,7 +30,7 @@
)


(cl-comment "O3prime: Orthocomplement is order-reversing")
(cl-comment 'O3prime: Orthocomplement is order-reversing')


(forall (x y)
@@ -10,22 +10,22 @@

(cl-text http://colore.oor.net/lattices/ortho_lattice.clif

(cl-comment "Orthocomplemented lattice axioms according to Beran 1976")
(cl-comment 'Orthocomplemented lattice axioms according to Beran 1976')

(cl-comment "O2.1")
(cl-comment 'O2.1')

(forall (x y z)
(= (join (join x y) z)
(join (meet (oc z) (oc y)) x))
)

(cl-comment "O2.2")
(cl-comment 'O2.2')

(forall (x y)
(= x (meet x (join x y)))
)

(cl-comment "O2.3")
(cl-comment 'O2.3')

(forall (x y)
(= x (join x (meet y (oc y))))
@@ -12,9 +12,9 @@

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

(cl-comment "Orthomodular lattice axioms")
(cl-comment 'Orthomodular lattice axioms')

(cl-comment "OM: Orthomodular law")
(cl-comment 'OM: Orthomodular law')

(forall (x)
(if
@@ -14,6 +14,6 @@

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

(cl-comment "Pseudocomplemented distributive lattices")
(cl-comment 'Pseudocomplemented distributive lattices')

)
@@ -12,17 +12,17 @@

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

(cl-comment "Pseudocomplemented lattice axioms")
(cl-comment 'Pseudocomplemented lattice axioms')


(cl-comment "PC1: Pseudocomplements are meet-complements")
(cl-comment 'PC1: Pseudocomplements are meet-complements')

(forall (x)
(meetcomplement x (pc x)))



(cl-comment "PC2: Behaviour of a pseudocomplement")
(cl-comment 'PC2: Behaviour of a pseudocomplement')

(forall (x y)
(iff
@@ -14,6 +14,6 @@

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

(cl-comment "Quasicomplemented (dual seudocomplemented) distributive lattices")
(cl-comment 'Quasicomplemented (dual seudocomplemented) distributive lattices')

)
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