// negation handling inconsistency part 1:
// we get a 0.45 confidence that "a" flies,
// while the inconsistency part 1 proves that
// confidence of "a" being a bird is zero.

/*

% notice that problog is consistent in its
% interpretation: 0.25*0.9=0.225 
% problog calculates bird(a) as 0.25

% Probabilistic facts:
0.5::bird(a).
0.5::not bird(a).
0.9:: flies(X) :- bird(X).

% Queries:
query(flies(_)).

result:  
a  0.225

*/

[
{"@confidence": 0.5, "@logic": ["bird","a"]},
{"@confidence": 0.5, "@logic": ["-bird","a"]},
{"@confidence": 0.9, "@logic": [["bird","?:X"],"=>",["flies","?:X"]]},
{"@question": ["flies","?:X"]}
//{"@question": ["bird","?:X"]}
]

/*

{"result": "proof found",

"answers": [
{
"answer": [["$ans","a"]],
"confidence": 0.45,
"positive_proof":
[
[1, ["in", "frm_3", "axiom", 0.9], [["-bird","?:X"], ["flies","?:X"]]],
[2, ["in", "frm_1", "axiom", 0.5], [["bird","a"]]],
[3, ["mp", 1, 2, "fromaxiom", 0.45], [["flies","a"]]],
[4, ["in", "frm_4", "goal", 1], [["-flies","?:X"], ["$ans","?:X"]]],
[5, ["mp", 3, 4, "fromgoal", 0.45], [["$ans","a"]]]
]}
]}


*/
/*

Summary of the Alchemy 2 implementation of the example.

::::::::::::::
studymln/mln/study18-lrn.mln
::::::::::::::
//predicate declarations
Obs2(c)
Obs(c)
Flies(c)
Bird(c)

// -2.77202  Obs(x) => Bird(x)
-2.77202  Bird(a1) v !Obs(a1)

// 6.8762  Obs2(x) => !Bird(x)
6.8762  !Bird(a1) v !Obs2(a1)

// 3.18368  Bird(x) => Flies(x)
3.18368  !Bird(a1) v Flies(a1)

// 5.17133  Bird(a1)
5.17133  Bird(a1)

// 0       Obs(a1)
0       Obs(a1)

// 0       Obs2(a1)
0       Obs2(a1)

// -2.86368  Flies(a1)
-2.86368  Flies(a1)

::::::::::::::
studymln/mln/study18.db
::::::::::::::
Obs(A)
Obs2(A)

::::::::::::::
studymln/RESULTS.tmp
::::::::::::::
infer:	Bird(A) 0.0030497
infer:	Flies(A) 0.0470453
liftedinfer -ptpe:	Flies(A) 0
liftedinfer -ptpe:	Bird(A) 0.330733
liftedinfer -lvg:	Flies(A) 0.98002
liftedinfer -lvg:	Bird(A) 0.337662

*/