pl-files/diagnosis.pl

   1 :- [tp].
   2
   3 % Definition of logical gates, used in the examples below.
   4 and_gate(all X:(and(X) , ~ab(X) => (in1(X), in2(X) <=> out(X)))).
   5 or_gate( all X:(or(X)  , ~ab(X) => (in1(X) ; in2(X) <=> out(X)))).
   6 xor_gate(all X:(xor(X) , ~ab(X) => (out(X) <=> in1(X),~in2(X);~in1(X),in2(X)))).
   7
   8 % Two unconnected AND gates with two inputs. It is observed that the
   9 % inputs are true and the outputs are false.
  10 problem1(SD, COMP, OBS) :-
  11   and_gate(AND),
  12   SD = [ AND, and(a1), and(a2) ],
  13   COMP = [a1, a2],
  14   OBS = [in1(a1), in2(a1), ~out(a1), in1(a2), in2(a2), ~out(a2)].
  15
  16 % Example of wwo AND gates where the output of the first gate (a1) is
  17 % connected to the first input (in1) of the second gate (a2). It is
  18 % easy to see that the observations are inconsistent with the
  19 % specification.
  20 problem2(SD, COMP, OBS) :-
  21   and_gate(AND),
  22   SD = [ AND, and(a1), and(a2), out(a1) <=> in1(a2) ],
  23   COMP = [a1, a2],
  24   OBS = [in1(a1), ~in2(a1), out(a2)].
  25
  26 % Another wiring example, now with two AND gates and an OR gate.
  27 problem3(SD, COMP, OBS) :-
  28   and_gate(AND), or_gate(OR),
  29   SD = [ AND, OR, and(a1), and(a2), or(o1),
  30          out(a1) <=> in1(o1), out(a2) <=> in2(o1)],
  31   COMP = [a1, a2, o1],
  32   OBS = [in1(a1), in2(a1), in1(a2), in2(a2), ~out(o1)].
  33
  34 % The following represents a (one-bit) full adder: a
  35 % circuit that can be used for the addition of two bits with
  36 % carry-in and carry-out bits.
  37 %
  38 % in1(fa), in2(fa): input bits
  39 % carryin(fa):      carry-in bit
  40 % out(fa):          output bit
  41 % carryout(fa):     carry-out bit
  42 %
  43 % returns the sum of in1(fa) + in2(fa) + carryin(fa)
  44 % as 2 * carryout(fa) + out(fa) (i.e., as 2 bits)
  45 fulladder(SD, COMP, OBS) :-
  46   and_gate(AND), or_gate(OR), xor_gate(XOR),
  47   SD = [AND, OR, XOR,
  48         and(a1), and(a2), xor(x1), xor(x2), or(r1),
  49         in1(fa) <=> in1(x1), in2(fa) <=> in1(a1),
  50         carryin(fa) <=> in1(a2), carryin(fa) <=> in2(x2),
  51         out(fa) <=> out(x2), carryout(fa) <=> out(r1),
  52         in2(fa) <=> in2(x1), in2(fa) <=> in2(a1),
  53         out(x1) <=> in2(a2), out(x1) <=> in1(x2),
  54         out(a2) <=> in1(r1), out(a1) <=> in2(r1) ],
  55   COMP = [a1, a2, x1, x2, r1],
  56   OBS = [in1(fa), ~in2(fa), carryin(fa), out(fa), ~carryout(fa)]. %1+1=1?
  57