Documentation

For example, >>> substitute (no p) "p" q ¬q >>> substitute (no (q ∧ no p)) "p" (q ↔ p) ¬(q ∧ ¬(q ↔ p))

For example,

>>> signify ((p ∨ q) ∧ ((no q) ∨ r)) [r]
False
>>> signify ((p ∨ q) ∧ ((no q) ∨ r)) [p,r]
True

For example,

>>> isModelForm [r]   ((p ∨ q) ∧ ((no q) ∨ r))
False
>>> isModelForm [p,r] ((p ∨ q) ∧ ((no q) ∨ r))
True

For example,

>>> propSymbolsForm (p ∧ q → p)
[p,q]

For example,

>>> interpretationsForm (p ∧ q → p)
[[],[p],[q],[p,q]]

For example,

>>> modelsForm ((p ∨ q) ∧ ((no q) ∨ r))
[[p],[p,r],[q,r],[p,q,r]]

For example,

>>> isValid (p → p)
True
>>> isValid (p → q)
False
>>> isValid ((p → q) ∨ (q → p))
True

For example,

>>> isUnsatisfiable (p ∧ (no p))
True
>>> isUnsatisfiable ((p → q) ∧ (q → r))
False

For example,

>>> isSatisfiable (p ∧ (no p))
False
>>> isSatisfiable ((p → q) ∧ (q → r))
True

For example,

>>> propSymbolsKB (S.fromList [p ∧ q → r, p → r])
[p,r,q]

For example,

>>> interpretationsKB (S.fromList [p → q, q → r])
[[],[p],[q],[p,q],[r],[p,r],[q,r],[p,q,r]]

For example,

>>> isModelKB [r] (S.fromList [q,no p ,r])
False
>>> isModelKB [q,r] (S.fromList [q,no p ,r])
True

For example,

>>> modelsKB $ S.fromList [(p ∨ q) ∧ ((no q) ∨ r), q → r]
[[p],[p,r],[q,r],[p,q,r]]
>>> modelsKB $ S.fromList [(p ∨ q) ∧ ((no q) ∨ r), r → q]
[[p],[q,r],[p,q,r]]

For example,

>>> isConsistent $ S.fromList [(p ∨ q) ∧ ((no q) ∨ r), p → r]
True
>>> isConsistent $ S.fromList [(p ∨ q) ∧ ((no q) ∨ r), p → r, no r]
False

For example,

>>> isInconsistent $ S.fromList [(p ∨ q) ∧ ((no q) ∨ r), p → r]
False
>>> isInconsistent $ S.fromList [(p ∨ q) ∧ ((no q) ∨ r), p → r, no r]
True

For example,

>>> isConsequence (S.fromList [p → q, q → r]) (p → r)
True
>>> isConsequence (S.fromList [p]) (p ∧ q)
False

>>> quickCheck prop_isValid
+++ OK, passed 100 tests.

>>> quickCheck prop_isConsequence
+++ OK, passed 100 tests.

For example, >>> isConsequenceKB (S.fromList [p → q, q → r]) (S.fromList [p → q, p → r]) True >>> isConsequenceKB (S.fromList [p]) (S.fromList [p ∧ q]) False

For example, >>> equivalent (p → q) (no p ∨ q) True >>> equivalent (p) (no (no p)) True

For example, >>> equivalentKB (S.fromList [p → q,r ∨ q]) (S.fromList [no p ∨ q, q ∨ r]) True >>> equivalentKB (S.fromList [p ∧ q]) (S.fromList [q,p]) True

>>> quickCheck prop_equivalent
+++ OK, passed 100 tests.