// negation handling inconsistency part 3: // add rules for deriving not flies // this almost restores consistency // // notice the full ruleset cannot be written in problog // NonGroundProbabilisticClause: Encountered a non-ground probabilistic clause at 10:7. /* % notice that problog does not accept %% 0.1:: flies(X) :- not bird(X). % Probabilistic facts: 0.5::bird(a). 0.5::not bird(a). 0.9:: flies(X) :- bird(X). 0.1:: not flies(X) :- bird(X). %% 0.1:: flies(X) :- not bird(X). 0.9:: not flies(X) :- not bird(X). % Queries: query(flies(_)). result: a 0.2025 */ [ {"@confidence": 0.5, "@logic": ["bird","messy"]}, {"@confidence": 0.5, "@logic": ["-bird","messy"]}, {"@confidence": 1.0, "@logic": ["bird","tweety"]}, {"@confidence": 1.0, "@logic": ["penguin","pennie"]}, {"@confidence": 1.0, "@logic": [["penguin","?:X"],"=>",["bird","?:X"]]}, {"@confidence": 0.001, "@logic": [["bird","?:X"],"=>",["penguin","?:X"]]}, {"@confidence": 0.999, "@logic": [["bird","?:X"],"=>",["-penguin","?:X"]]}, {"@confidence": 0.9, "@logic": [["bird","?:X"],"=>",["flies","?:X"]]}, {"@confidence": 0.1, "@logic": [["bird","?:X"],"=>",["-flies","?:X"]]}, {"@confidence": 0.1, "@logic": [["-bird","?:X"],"=>",["flies","?:X"]]}, {"@confidence": 0.9, "@logic": [["-bird","?:X"],"=>",["-flies","?:X"]]}, {"@confidence": 1.0, "@logic": [["penguin","?:X"],"=>",["-flies","?:X"]]}, /* {"@confidence": 0.1, "@logic": [["-penguin","?:X"],"=>",["flies","?:X"]]}, {"@confidence": 0.9999, "@logic": [["-penguin","?:X"],"=>",["-flies","?:X"]]}, */ {"@question": ["flies","?:X"]} ] /* {"result": "proof found", "answers": [ { "answer": [["$ans","?:X3"]], "confidence": -0.41105, "positive_proof": [ [1, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [2, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [3, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [4, 21, ["mp", 2, 3, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [5, 57, ["mp", 1, [4,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [6, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [7, 75, ["mp", [5,1], 6, "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X3"]]], [8, 6, ["in", "frm_7", "axiom", 0.999, 0, []], [["-penguin","?:X"], ["-bird","?:X"]]], [9, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [10, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [11, 21, ["mp", 9, 10, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [12, 5, ["in", "frm_6", "axiom", 0.001, 0, []], [["-bird","?:X"], ["penguin","?:X"]]], [13, 22, ["mp", [11,1], 12, "fromgoal", 0.0001, 0, [9,5]], [["$ans","?:X"], ["penguin","?:X"]]], [14, 33, ["mp", 8, [13,1], "fromgoal", 9.99e-05, 0, [6,9,5]], [["-bird","?:X"], ["$ans","?:X"]]], [15, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [16, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [17, 21, ["mp", 15, 16, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [18, 47, ["mp", 14, [17,1], "fromgoal", 1e-05, 0, [6,9,5]], [["$ans","?:X3"]]], [19, 170, ["cumul", 7, 18, "fromgoal", 0.0900055, 0, [7,9,6,5]], [["$ans","?:X3"]]], [20, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [21, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [22, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [23, 21, ["mp", 21, 22, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [24, 57, ["mp", 20, [23,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [25, 11, ["in", "frm_12", "axiom", 1, 0, []], [["-flies","?:X"], ["-penguin","?:X"]]], [26, 71, ["mp", [24,1], 25, "fromgoal", 0.09, 0, [7,9,11]], [["-penguin","?:X"], ["$ans","?:X"]]], [27, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [28, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [29, 21, ["mp", 27, 28, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [30, 5, ["in", "frm_6", "axiom", 0.001, 0, []], [["-bird","?:X"], ["penguin","?:X"]]], [31, 22, ["mp", [29,1], 30, "fromgoal", 0.0001, 0, [9,5]], [["$ans","?:X"], ["penguin","?:X"]]], [32, 77, ["mp", 26, [31,1], "fromgoal", 9e-06, 0, [7,9,11,5]], [["$ans","?:X3"]]], [33, 236, ["cumul", 19, 32, "fromgoal", 0.0900076, 0, [7,9,6,5,11]], [["$ans","?:X3"]]], [34, 8, ["in", "frm_9", "axiom", 0.1, 0, []], [["-flies","?:X"], ["-bird","?:X"]]], [35, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [36, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [37, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [38, 21, ["mp", 36, 37, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [39, 57, ["mp", 35, [38,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [40, 103, ["mp", 34, [39,1], "fromgoal", 0.009, 0, [8,7,9]], [["-bird","?:X"], ["$ans","?:X"]]], [41, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [42, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [43, 21, ["mp", 41, 42, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [44, 119, ["mp", 40, [43,1], "fromgoal", 0.0009, 0, [8,7,9]], [["$ans","?:X3"]]], [45, 287, ["cumul", 33, 44, "fromgoal", 0.0904171, 0, [7,9,6,5,11,8]], [["$ans","?:X3"]]] ], "negative_proof": [ [1, 11, ["in", "frm_12", "axiom", 1, 0, []], [["-flies","?:X"], ["-penguin","?:X"]]], [2, 410, ["in", "frm_13", "goal", 1, 0, []], [["flies","?:X"]]], [3, 10, ["in", "frm_11", "axiom", 0.9, 0, []], [["-flies","?:X"], ["bird","?:X"]]], [4, 420, ["mp", 3, 2, "fromgoal", 0.9, 0, [10]], [["bird","?:X"]]], [5, 5, ["in", "frm_6", "axiom", 0.001, 0, []], [["-bird","?:X"], ["penguin","?:X"]]], [6, 423, ["mp", 4, 5, "fromgoal", 0.0009, 0, [10,5]], [["penguin","?:X3"]]], [7, 425, ["mp", 1, 2, 6, "fromgoal", 0.0009, 0, [11,10,5]], false], [8, 1, ["in", "frm_2", "axiom", 0.5, 0, []], [["-bird","messy"]]], [9, 424, ["mp", 4, 8, "fromgoal", 0.45, 0, [10,1]], false], [10, 481, ["cumul", 7, 9, "fromgoal", 0.450297, 0, [11,10,5,1]], false], [11, 6, ["in", "frm_7", "axiom", 0.999, 0, []], [["-penguin","?:X"], ["-bird","?:X"]]], [12, 423, ["mp", 4, 5, "fromgoal", 0.0009, 0, [10,5]], [["penguin","?:X"]]], [13, 420, ["mp", 3, 2, "fromgoal", 0.9, 0, [10]], [["bird","?:X3"]]], [14, 426, ["mp", 11, 12, 13, "fromgoal", 0.0008092, 0, [6,10,5]], false], [15, 502, ["cumul", 10, 14, "fromgoal", 0.450488, 0, [11,10,5,1,6]], false], [16, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [17, 419, ["mp", 3, 16, "fromaxiom", 0.09, 0, [10,9]], [["bird","?:X"]]], [18, 421, ["mp", 17, 5, "fromaxiom", 9e-05, 0, [10,9,5]], [["penguin","?:X"]]], [19, 427, ["mp", 11, 18, 13, "fromgoal", 8.09e-05, 0, [6,10,9,5]], false], [20, 522, ["cumul", 15, 19, "fromgoal", 0.450503, 0, [11,10,5,1,6,9]], false], [21, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [22, 439, ["mp", 21, 4, "fromgoal", 0.81, 0, [7,10]], [["flies","?:X"]]], [23, 443, ["mp", 22, 1, 6, "fromgoal", 0.000729, 0, [7,10,11,5]], false], [24, 571, ["cumul", 20, 23, "fromgoal", 0.450663, 0, [11,10,5,1,6,9,7]], false], [25, 2, ["in", "frm_3", "axiom", 1, 0, []], [["bird","tweety"]]], [26, 442, ["mp", 21, 25, "fromaxiom", 0.9, 0, [7,2]], [["flies","tweety"]]], [27, 452, ["mp", 26, 1, "fromaxiom", 0.9, 0, [7,2,11]], [["-penguin","tweety"]]], [28, 460, ["mp", 27, 12, "fromgoal", 0.00081, 0, [7,2,11,10,5]], false], [29, 677, ["cumul", 24, 28, "fromgoal", 0.450811, 0, [11,10,5,1,6,9,7,2]], false], [30, 8, ["in", "frm_9", "axiom", 0.1, 0, []], [["-flies","?:X"], ["-bird","?:X"]]], [31, 464, ["mp", 30, 2, 13, "fromgoal", 0.09, 0, [8,10]], false], [32, 718, ["cumul", 29, 31, "fromgoal", 0.490353, 0, [11,10,5,1,6,9,7,2,8]], false], [33, 0, ["in", "frm_1", "axiom", 0.5, 0, []], [["bird","messy"]]], [34, 441, ["mp", 21, 33, "fromaxiom", 0.45, 0, [7,0]], [["flies","messy"]]], [35, 467, ["mp", 30, 34, "fromaxiom", 0.045, 0, [8,7,0]], [["-bird","messy"]]], [36, 472, ["mp", 35, 4, "fromgoal", 0.0405, 0, [8,7,0,10]], false], [37, 787, ["cumul", 32, 36, "fromgoal", 0.501467, 0, [11,10,5,1,6,9,7,2,8,0]], false] ]}, { "answer": [["$ans","messy"]], "confidence": 0.0090009, "positive_proof": [ [1, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [2, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [3, 21, ["mp", 1, 2, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [4, 1, ["in", "frm_2", "axiom", 0.5, 0, []], [["-bird","messy"]]], [5, 23, ["mp", [3,1], 4, "fromgoal", 0.05, 0, [9,1]], [["$ans","messy"]]], [6, 6, ["in", "frm_7", "axiom", 0.999, 0, []], [["-penguin","?:X"], ["-bird","?:X"]]], [7, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [8, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [9, 21, ["mp", 7, 8, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [10, 5, ["in", "frm_6", "axiom", 0.001, 0, []], [["-bird","?:X"], ["penguin","?:X"]]], [11, 22, ["mp", [9,1], 10, "fromgoal", 0.0001, 0, [9,5]], [["$ans","?:X"], ["penguin","?:X"]]], [12, 33, ["mp", 6, [11,1], "fromgoal", 9.99e-05, 0, [6,9,5]], [["-bird","?:X"], ["$ans","?:X"]]], [13, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [14, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [15, 21, ["mp", 13, 14, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [16, 47, ["mp", 12, [15,1], "fromgoal", 1e-05, 0, [6,9,5]], [["$ans","?:X3"]]], [17, 161, ["cumul", 5, 16, "fromgoal", 0.0500057, 0, [9,1,6,5]], [["$ans","messy"]]], [18, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [19, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [20, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [21, 21, ["mp", 19, 20, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [22, 57, ["mp", 18, [21,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [23, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [24, 75, ["mp", [22,1], 23, "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X3"]]], [25, 221, ["cumul", 17, 24, "fromgoal", 0.120337, 0, [9,1,6,5,7]], [["$ans","messy"]]], [26, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [27, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [28, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [29, 21, ["mp", 27, 28, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [30, 57, ["mp", 26, [29,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [31, 11, ["in", "frm_12", "axiom", 1, 0, []], [["-flies","?:X"], ["-penguin","?:X"]]], [32, 71, ["mp", [30,1], 31, "fromgoal", 0.09, 0, [7,9,11]], [["-penguin","?:X"], ["$ans","?:X"]]], [33, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [34, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [35, 21, ["mp", 33, 34, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [36, 5, ["in", "frm_6", "axiom", 0.001, 0, []], [["-bird","?:X"], ["penguin","?:X"]]], [37, 22, ["mp", [35,1], 36, "fromgoal", 0.0001, 0, [9,5]], [["$ans","?:X"], ["penguin","?:X"]]], [38, 77, ["mp", 32, [37,1], "fromgoal", 9e-06, 0, [7,9,11,5]], [["$ans","?:X3"]]], [39, 242, ["cumul", 25, 38, "fromgoal", 0.120339, 0, [9,1,6,5,7,11]], [["$ans","messy"]]], [40, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [41, 0, ["in", "frm_1", "axiom", 0.5, 0, []], [["bird","messy"]]], [42, 59, ["mp", 40, 41, "fromaxiom", 0.45, 0, [7,0]], [["flies","messy"]]], [43, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [44, 90, ["mp", 42, 43, "fromgoal", 0.45, 0, [7,0]], [["$ans","messy"]]], [45, 269, ["cumul", 39, 44, "fromgoal", 0.49964, 0, [9,1,6,5,7,11,0]], [["$ans","messy"]]], [46, 8, ["in", "frm_9", "axiom", 0.1, 0, []], [["-flies","?:X"], ["-bird","?:X"]]], [47, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [48, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [49, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [50, 21, ["mp", 48, 49, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [51, 57, ["mp", 47, [50,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [52, 103, ["mp", 46, [51,1], "fromgoal", 0.009, 0, [8,7,9]], [["-bird","?:X"], ["$ans","?:X"]]], [53, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [54, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [55, 21, ["mp", 53, 54, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [56, 119, ["mp", 52, [55,1], "fromgoal", 0.0009, 0, [8,7,9]], [["$ans","?:X3"]]], [57, 299, ["cumul", 45, 56, "fromgoal", 0.49991, 0, [9,1,6,5,7,11,0,8]], [["$ans","messy"]]] ], "negative_proof": [ [1, 11, ["in", "frm_12", "axiom", 1, 0, []], [["-flies","?:X"], ["-penguin","?:X"]]], [2, 858, ["in", "frm_13", "goal", 1, 0, []], [["flies","messy"]]], [3, 10, ["in", "frm_11", "axiom", 0.9, 0, []], [["-flies","?:X"], ["bird","?:X"]]], [4, 868, ["mp", 3, 2, "fromgoal", 0.9, 0, [10]], [["bird","messy"]]], [5, 5, ["in", "frm_6", "axiom", 0.001, 0, []], [["-bird","?:X"], ["penguin","?:X"]]], [6, 873, ["mp", 4, 5, "fromgoal", 0.0009, 0, [10,5]], [["penguin","messy"]]], [7, 877, ["mp", 1, 2, 6, "fromgoal", 0.0009, 0, [11,10,5]], false], [8, 868, ["mp", 3, 2, "fromgoal", 0.9, 0, [10]], [["bird","messy"]]], [9, 1, ["in", "frm_2", "axiom", 0.5, 0, []], [["-bird","messy"]]], [10, 869, ["simp", 8, 9, "fromgoal", 0.45, 0, [10,1]], false], [11, 956, ["cumul", 7, 10, "fromgoal", 0.450297, 0, [11,10,5,1]], false], [12, 6, ["in", "frm_7", "axiom", 0.999, 0, []], [["-penguin","?:X"], ["-bird","?:X"]]], [13, 873, ["mp", 4, 5, "fromgoal", 0.0009, 0, [10,5]], [["penguin","messy"]]], [14, 880, ["mp", 12, 13, 8, "fromgoal", 0.0008092, 0, [6,10,5]], false], [15, 973, ["cumul", 11, 14, "fromgoal", 0.450488, 0, [11,10,5,1,6]], false], [16, 0, ["in", "frm_1", "axiom", 0.5, 0, []], [["bird","messy"]]], [17, 860, ["mp", 5, 16, "fromaxiom", 0.0005, 0, [5,0]], [["penguin","messy"]]], [18, 883, ["mp", 12, 17, 8, "fromgoal", 0.0004496, 0, [6,5,0,10]], false], [19, 988, ["cumul", 15, 18, "fromgoal", 0.45057, 0, [11,10,5,1,6,0]], false], [20, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [21, 867, ["mp", 3, 20, "fromaxiom", 0.09, 0, [10,9]], [["bird","?:X"]]], [22, 870, ["mp", 21, 5, "fromaxiom", 9e-05, 0, [10,9,5]], [["penguin","?:X"]]], [23, 878, ["mp", 12, 22, "fromaxiom", 8.99e-05, 0, [6,10,9,5]], [["-bird","?:X"]]], [24, 887, ["mp", 23, 4, "fromgoal", 8.09e-05, 0, [6,10,9,5]], false], [25, 1009, ["cumul", 19, 24, "fromgoal", 0.450588, 0, [11,10,5,1,6,0,9]], false], [26, 8, ["in", "frm_9", "axiom", 0.1, 0, []], [["-flies","?:X"], ["-bird","?:X"]]], [27, 922, ["mp", 26, 2, 8, "fromgoal", 0.09, 0, [8,10]], false], [28, 1059, ["cumul", 25, 27, "fromgoal", 0.489047, 0, [11,10,5,1,6,0,9,8]], false], [29, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [30, 893, ["mp", 29, 21, "fromaxiom", 0.081, 0, [7,10,9]], [["flies","?:X"]]], [31, 916, ["mp", 26, 30, "fromaxiom", 0.0081, 0, [8,7,10,9]], [["-bird","?:X"]]], [32, 924, ["mp", 31, 4, "fromgoal", 0.00729, 0, [8,7,10,9]], false], [33, 1101, ["cumul", 28, 32, "fromgoal", 0.490909, 0, [11,10,5,1,6,0,9,8,7]], false] ]}, { "answer": [["$ans","tweety"]], "confidence": 0.811421, "positive_proof": [ [1, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [2, 2, ["in", "frm_3", "axiom", 1, 0, []], [["bird","tweety"]]], [3, 60, ["mp", 1, 2, "fromaxiom", 0.9, 0, [7,2]], [["flies","tweety"]]], [4, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [5, 95, ["mp", 3, 4, "fromgoal", 0.9, 0, [7,2]], [["$ans","tweety"]]], [6, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [7, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [8, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [9, 21, ["mp", 7, 8, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [10, 57, ["mp", 6, [9,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [11, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [12, 75, ["mp", [10,1], 11, "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X3"]]], [13, 6, ["in", "frm_7", "axiom", 0.999, 0, []], [["-penguin","?:X"], ["-bird","?:X"]]], [14, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [15, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [16, 21, ["mp", 14, 15, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [17, 5, ["in", "frm_6", "axiom", 0.001, 0, []], [["-bird","?:X"], ["penguin","?:X"]]], [18, 22, ["mp", [16,1], 17, "fromgoal", 0.0001, 0, [9,5]], [["$ans","?:X"], ["penguin","?:X"]]], [19, 33, ["mp", 13, [18,1], "fromgoal", 9.99e-05, 0, [6,9,5]], [["-bird","?:X"], ["$ans","?:X"]]], [20, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [21, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [22, 21, ["mp", 20, 21, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [23, 47, ["mp", 19, [22,1], "fromgoal", 1e-05, 0, [6,9,5]], [["$ans","?:X3"]]], [24, 170, ["cumul", 12, 23, "fromgoal", 0.0900055, 0, [7,9,6,5]], [["$ans","?:X3"]]], [25, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [26, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [27, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [28, 21, ["mp", 26, 27, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [29, 57, ["mp", 25, [28,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [30, 11, ["in", "frm_12", "axiom", 1, 0, []], [["-flies","?:X"], ["-penguin","?:X"]]], [31, 71, ["mp", [29,1], 30, "fromgoal", 0.09, 0, [7,9,11]], [["-penguin","?:X"], ["$ans","?:X"]]], [32, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [33, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [34, 21, ["mp", 32, 33, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [35, 5, ["in", "frm_6", "axiom", 0.001, 0, []], [["-bird","?:X"], ["penguin","?:X"]]], [36, 22, ["mp", [34,1], 35, "fromgoal", 0.0001, 0, [9,5]], [["$ans","?:X"], ["penguin","?:X"]]], [37, 77, ["mp", 31, [36,1], "fromgoal", 9e-06, 0, [7,9,11,5]], [["$ans","?:X3"]]], [38, 236, ["cumul", 24, 37, "fromgoal", 0.0900076, 0, [7,9,6,5,11]], [["$ans","?:X3"]]], [39, 273, ["cumul", 5, 38, "fromgoal", 0.906429, 0, [7,2,9,6,5,11]], [["$ans","tweety"]]], [40, 8, ["in", "frm_9", "axiom", 0.1, 0, []], [["-flies","?:X"], ["-bird","?:X"]]], [41, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [42, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [43, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [44, 21, ["mp", 42, 43, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [45, 57, ["mp", 41, [44,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [46, 103, ["mp", 40, [45,1], "fromgoal", 0.009, 0, [8,7,9]], [["-bird","?:X"], ["$ans","?:X"]]], [47, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [48, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [49, 21, ["mp", 47, 48, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [50, 119, ["mp", 46, [49,1], "fromgoal", 0.0009, 0, [8,7,9]], [["$ans","?:X3"]]], [51, 301, ["cumul", 39, 50, "fromgoal", 0.906476, 0, [7,2,9,6,5,11,8]], [["$ans","tweety"]]] ], "negative_proof": [ [1, 8, ["in", "frm_9", "axiom", 0.1, 0, []], [["-flies","?:X"], ["-bird","?:X"]]], [2, 1134, ["in", "frm_13", "goal", 1, 0, []], [["flies","tweety"]]], [3, 10, ["in", "frm_11", "axiom", 0.9, 0, []], [["-flies","?:X"], ["bird","?:X"]]], [4, 1144, ["mp", 3, 2, "fromgoal", 0.9, 0, [10]], [["bird","tweety"]]], [5, 1197, ["mp", 1, 2, 4, "fromgoal", 0.09, 0, [8,10]], false], [6, 11, ["in", "frm_12", "axiom", 1, 0, []], [["-flies","?:X"], ["-penguin","?:X"]]], [7, 1144, ["mp", 3, 2, "fromgoal", 0.9, 0, [10]], [["bird","tweety"]]], [8, 5, ["in", "frm_6", "axiom", 0.001, 0, []], [["-bird","?:X"], ["penguin","?:X"]]], [9, 1148, ["mp", 7, 8, "fromgoal", 0.0009, 0, [10,5]], [["penguin","tweety"]]], [10, 1151, ["mp", 6, 2, 9, "fromgoal", 0.0009, 0, [11,10,5]], false], [11, 1233, ["cumul", 5, 10, "fromgoal", 0.0904914, 0, [8,10,11,5]], false], [12, 6, ["in", "frm_7", "axiom", 0.999, 0, []], [["-penguin","?:X"], ["-bird","?:X"]]], [13, 1148, ["mp", 7, 8, "fromgoal", 0.0009, 0, [10,5]], [["penguin","tweety"]]], [14, 1154, ["mp", 12, 13, 4, "fromgoal", 0.0008092, 0, [6,10,5]], false], [15, 1238, ["cumul", 11, 14, "fromgoal", 0.0908068, 0, [8,10,11,5,6]], false], [16, 2, ["in", "frm_3", "axiom", 1, 0, []], [["bird","tweety"]]], [17, 1137, ["mp", 8, 16, "fromaxiom", 0.001, 0, [5,2]], [["penguin","tweety"]]], [18, 1155, ["mp", 12, 17, 4, "fromgoal", 0.0008991, 0, [6,5,2,10]], false], [19, 1246, ["cumul", 15, 18, "fromgoal", 0.0910793, 0, [8,10,11,5,6,2]], false], [20, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [21, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [22, 1143, ["mp", 3, 21, "fromaxiom", 0.09, 0, [10,9]], [["bird","?:X"]]], [23, 1168, ["mp", 20, 22, "fromaxiom", 0.081, 0, [7,10,9]], [["flies","?:X"]]], [24, 1191, ["mp", 1, 23, "fromaxiom", 0.0081, 0, [8,7,10,9]], [["-bird","?:X"]]], [25, 1199, ["mp", 24, 7, "fromgoal", 0.00729, 0, [8,7,10,9]], false], [26, 1287, ["cumul", 19, 25, "fromgoal", 0.0950549, 0, [8,10,11,5,6,2,7,9]], false] ]}, { "answer": [["$ans","pennie"]], "confidence": 0.00399041, "positive_proof": [ [1, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [2, 4, ["in", "frm_5", "axiom", 1, 0, []], [["-penguin","?:X"], ["bird","?:X"]]], [3, 3, ["in", "frm_4", "axiom", 1, 0, []], [["penguin","pennie"]]], [4, 19, ["mp", 2, 3, "fromaxiom", 1, 0, [4,3]], [["bird","pennie"]]], [5, 58, ["mp", 1, 4, "fromaxiom", 0.9, 0, [7,4,3]], [["flies","pennie"]]], [6, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [7, 85, ["mp", 5, 6, "fromgoal", 0.9, 0, [7,4,3]], [["$ans","pennie"]]], [8, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [9, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [10, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [11, 21, ["mp", 9, 10, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [12, 57, ["mp", 8, [11,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [13, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [14, 75, ["mp", [12,1], 13, "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X3"]]], [15, 6, ["in", "frm_7", "axiom", 0.999, 0, []], [["-penguin","?:X"], ["-bird","?:X"]]], [16, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [17, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [18, 21, ["mp", 16, 17, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [19, 5, ["in", "frm_6", "axiom", 0.001, 0, []], [["-bird","?:X"], ["penguin","?:X"]]], [20, 22, ["mp", [18,1], 19, "fromgoal", 0.0001, 0, [9,5]], [["$ans","?:X"], ["penguin","?:X"]]], [21, 33, ["mp", 15, [20,1], "fromgoal", 9.99e-05, 0, [6,9,5]], [["-bird","?:X"], ["$ans","?:X"]]], [22, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [23, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [24, 21, ["mp", 22, 23, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [25, 47, ["mp", 21, [24,1], "fromgoal", 1e-05, 0, [6,9,5]], [["$ans","?:X3"]]], [26, 170, ["cumul", 14, 25, "fromgoal", 0.0900055, 0, [7,9,6,5]], [["$ans","?:X3"]]], [27, 254, ["cumul", 7, 26, "fromgoal", 0.906429, 0, [7,4,3,9,6,5]], [["$ans","pennie"]]], [28, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [29, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [30, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [31, 21, ["mp", 29, 30, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [32, 57, ["mp", 28, [31,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [33, 11, ["in", "frm_12", "axiom", 1, 0, []], [["-flies","?:X"], ["-penguin","?:X"]]], [34, 71, ["mp", [32,1], 33, "fromgoal", 0.09, 0, [7,9,11]], [["-penguin","?:X"], ["$ans","?:X"]]], [35, 3, ["in", "frm_4", "axiom", 1, 0, []], [["penguin","pennie"]]], [36, 80, ["mp", 34, 35, "fromgoal", 0.09, 0, [7,9,11,3]], [["$ans","pennie"]]], [37, 8, ["in", "frm_9", "axiom", 0.1, 0, []], [["-flies","?:X"], ["-bird","?:X"]]], [38, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [39, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [40, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [41, 21, ["mp", 39, 40, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [42, 57, ["mp", 38, [41,1], "fromgoal", 0.09, 0, [7,9]], [["$ans","?:X"], ["flies","?:X"]]], [43, 103, ["mp", 37, [42,1], "fromgoal", 0.009, 0, [8,7,9]], [["-bird","?:X"], ["$ans","?:X"]]], [44, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [45, 12, ["in", "frm_13", "goal", 1, 0, []], [["-flies","?:X"], ["$ans","?:X"]]], [46, 21, ["mp", 44, 45, "fromgoal", 0.1, 0, [9]], [["$ans","?:X"], ["bird","?:X"]]], [47, 119, ["mp", 43, [46,1], "fromgoal", 0.0009, 0, [8,7,9]], [["$ans","?:X3"]]], [48, 244, ["cumul", 36, 47, "fromgoal", 0.090351, 0, [7,9,11,3,8]], [["$ans","pennie"]]], [49, 408, ["cumul", 27, 48, "fromgoal", 0.910272, 0, [7,4,3,9,6,5,11,8]], [["$ans","pennie"]]] ], "negative_proof": [ [1, 6, ["in", "frm_7", "axiom", 0.999, 0, []], [["-penguin","?:X"], ["-bird","?:X"]]], [2, 3, ["in", "frm_4", "axiom", 1, 0, []], [["penguin","pennie"]]], [3, 10, ["in", "frm_11", "axiom", 0.9, 0, []], [["-flies","?:X"], ["bird","?:X"]]], [4, 1303, ["in", "frm_13", "goal", 1, 0, []], [["flies","pennie"]]], [5, 1313, ["mp", 3, 4, "fromgoal", 0.9, 0, [10]], [["bird","pennie"]]], [6, 1328, ["mp", 1, 2, 5, "fromgoal", 0.8991, 0, [6,3,10]], false], [7, 11, ["in", "frm_12", "axiom", 1, 0, []], [["-flies","?:X"], ["-penguin","?:X"]]], [8, 1313, ["mp", 3, 4, "fromgoal", 0.9, 0, [10]], [["bird","pennie"]]], [9, 5, ["in", "frm_6", "axiom", 0.001, 0, []], [["-bird","?:X"], ["penguin","?:X"]]], [10, 1317, ["mp", 8, 9, "fromgoal", 0.0009, 0, [10,5]], [["penguin","pennie"]]], [11, 1320, ["mp", 7, 4, 10, "fromgoal", 0.0009, 0, [11,10,5]], false], [12, 1385, ["cumul", 6, 11, "fromgoal", 0.899161, 0, [6,3,10,11,5]], false], [13, 9, ["in", "frm_10", "axiom", 0.1, 0, []], [["flies","?:X"], ["bird","?:X"]]], [14, 1312, ["mp", 3, 13, "fromaxiom", 0.09, 0, [10,9]], [["bird","?:X"]]], [15, 1314, ["mp", 14, 9, "fromaxiom", 9e-05, 0, [10,9,5]], [["penguin","?:X"]]], [16, 1321, ["mp", 1, 15, "fromaxiom", 8.99e-05, 0, [6,10,9,5]], [["-bird","?:X"]]], [17, 1330, ["mp", 16, 8, "fromgoal", 8.09e-05, 0, [6,10,9,5]], false], [18, 1406, ["cumul", 12, 17, "fromgoal", 0.899163, 0, [6,3,10,11,5,9]], false], [19, 8, ["in", "frm_9", "axiom", 0.1, 0, []], [["-flies","?:X"], ["-bird","?:X"]]], [20, 1367, ["mp", 19, 4, 5, "fromgoal", 0.09, 0, [8,10]], false], [21, 1434, ["cumul", 18, 20, "fromgoal", 0.90597, 0, [6,3,10,11,5,9,8]], false], [22, 7, ["in", "frm_8", "axiom", 0.9, 0, []], [["-bird","?:X"], ["flies","?:X"]]], [23, 1337, ["mp", 22, 14, "fromaxiom", 0.081, 0, [7,10,9]], [["flies","?:X"]]], [24, 1361, ["mp", 19, 23, "fromaxiom", 0.0081, 0, [8,7,10,9]], [["-bird","?:X"]]], [25, 1369, ["mp", 24, 8, "fromgoal", 0.00729, 0, [8,7,10,9]], false], [26, 1454, ["cumul", 21, 25, "fromgoal", 0.906281, 0, [6,3,10,11,5,9,8,7]], false] ]} ]} */ /* Summary of the Alchemy 2 implementation of the example. :::::::::::::: studymln/mln/study23-lrn.mln :::::::::::::: //predicate declarations Obs2(c) Obs(c) Penguin(c) Flies(c) Bird(c) // -4.53941 Obs(x) => Bird(x) -4.53941 Bird(a1) v !Obs(a1) // 8.10784 Obs2(x) => !Bird(x) 8.10784 !Bird(a1) v !Obs2(a1) // Penguin(x) => Bird(x). Bird(a1) v !Penguin(a1). // -2.48726 Bird(x) => Penguin(x) -2.48726 !Bird(a1) v Penguin(a1) // 2.17445 Bird(x) => !Penguin(x) 2.17445 !Bird(a1) v !Penguin(a1) // -0.844797 Bird(x) => Flies(x) -0.844797 !Bird(a1) v Flies(a1) // Penguin(x) => !Flies(x). !Penguin(a1) v !Flies(a1). // 1.63321 Bird(a1) 1.63321 Bird(a1) // -2.17445 Penguin(a1) -2.17445 Penguin(a1) // -1.75495 Flies(a1) -1.75495 Flies(a1) // 0 Obs(a1) 0 Obs(a1) // 0 Obs2(a1) 0 Obs2(a1) :::::::::::::: studymln/mln/study23.db :::::::::::::: Obs(Messy) Obs2(Messy) Bird(Tweety) Penguin(Pennie) :::::::::::::: studymln/RESULTS.tmp :::::::::::::: infer: Bird(Messy) 4.9995e-05 infer: Bird(Pennie) 0.99995 infer: Flies(Messy) 0.149035 infer: Flies(Tweety) 0.0720428 infer: Flies(Pennie) 4.9995e-05 infer: Penguin(Messy) 4.9995e-05 infer: Penguin(Tweety) 4.9995e-05 liftedinfer -ptpe: Penguin(Messy) 0 liftedinfer -ptpe: Penguin(Tweety) 0 liftedinfer -ptpe: Flies(Messy) 0 liftedinfer -ptpe: Flies(Tweety) 0 liftedinfer -ptpe: Flies(Pennie) 0 liftedinfer -ptpe: Bird(Messy) 0.913007 liftedinfer -ptpe: Bird(Pennie) 0.913007 liftedinfer -lvg: Penguin(Messy) 0 liftedinfer -lvg: Penguin(Tweety) 0 liftedinfer -lvg: Flies(Messy) 0.745255 liftedinfer -lvg: Flies(Tweety) 0 liftedinfer -lvg: Flies(Pennie) 0 liftedinfer -lvg: Bird(Messy) 0 liftedinfer -lvg: Bird(Pennie) 0.805195 */