Pack pha -- readme-pha.txt

[This is the original README from David Poole's implementation - S.A.]

This directory contains an implementation of Probabilistic Horn abduction.

The implementation is written in Prolog. It has been tested with both Sicstus Prolog and Quintus Prolog. It should be very portable.

To run the program, in Prolog, do | ?- compile('pha-int.tex').

To load a rulebase "adderinf" do | ?- thconsult(adderinf).

The code is in the file 'pha-int.tex'. This can be formatted using Latex by changing one character at the beginning of the file.

The file 'pha-bn.ps' (in ftp/local/poole/papers) is a paper that describes the theory behind probabilistic Horn abduction. It is to appear in Artificial Intelligence.

The following are rule bases: 'adderinf' is a cascaded adder (as described in 'pha-bn.ps'). 'bnet' is the Bayesian network described in 'pha-bn.ps'. 'depiction' is a depiction example (as in 'pha-bn.ps'). 'inv3' is three cascaded inverters.

The following is a trace of a program (with my comments in upper case):

| ?- compile('pha-int.tex'). % compiling file /nfs/lci/ai1/poole/res/abduction/int/pha-int.tex ! Permission error: cannot redefine built-in predicate append/3 ! goal: assertz(append([],_8025,_8025)) IGNORE THIS - APPEND IS DEFINED FOR THOSE SYSTEMS THAT DON'T PREDEFINE IT % pha-int.tex compiled in module user, 1.717 sec 10,740 bytes

yes | ?- thconsult(adderinf).

yes | ?-

explain(( val(output(1,adder(1)),off,t2),
val(output(1,adder(s(1))),off,t2),
val(output(1,adder(s(s(1)))),off,t2),
val(output(2,adder(s(s(1)))),on,t2) ))

. Probability mass = [4.9403e-04,0.00397656] THIS IS THE ESTIMATE OF THE PRIOR PROBABILITY OF THE OBSERVATION Explanation: [ok(xor2(1)),ok(xor1(1)),ok(xor2(s(1))),ok(xor1(s(1))),ok(or1(1)),o k(and2(1)),ok(and1(1)),ok(xor2(s(s(1)))),ok(xor1(s(s(1)))),stuck0(or1(s(1))),

ok(
or1(s(s(1))))

,ok(and2(s(s(1)))),ok(and1(s(s(1))))] Prior = 4.9403e-04 THIS IS THE PRIOR PROBABILITY OF THE EXPLANATION Posterior = [0.124236,1.0]; THIS IS THE CURRENT ESTIMATE OF THE POSTERIOR PROBABILITY OF THE EXPLANATION Runtime: 20317 msec.

yes | ?- more. Probability mass = [9.8797e-04,0.00348238] Explanation: [ok(xor2(1)),ok(xor1(1)),ok(xor2(s(1))),ok(xor1(s(1))),ok(or1(1)),o k(and2(1)),ok(and1(1)),ok(xor2(s(s(1)))),stuck1(xor1(s(s(1)))),ok(or1(s(1))),ok( and2(s(1))),ok(or1(s(s(1)))),ok(and2(s(s(1))))] Prior = 4.9393e-04 Posterior = [0.141838,0.49995] Runtime: 833 msec.

yes | ?- more. Probability mass = [0.00148151,0.0029882] Explanation: [ok(xor2(1)),ok(xor1(1)),ok(xor2(s(1))),ok(xor1(s(1))),ok(or1(1)),o k(and2(1)),ok(and1(1)),stuck0(xor2(s(s(1)))),ok(or1(s(s(1)))),ok(and2(s(s(1)))), ok(or1(s(1))),ok(and2(s(1))),ok(xor1(s(s(1)))),ok(and1(s(s(1))))] Prior = 4.9354e-04 Posterior = [0.165163,0.333133] Runtime: 584 msec.

yes | ?- more. Probability mass = [0.00197455,0.00200112] Explanation: [ok(xor2(1)),ok(xor1(1)),ok(xor2(s(1))),ok(xor1(s(1))),ok(or1(1)),o k(and2(1)),ok(and1(1)),ok(xor2(s(s(1)))),ok(xor1(s(s(1)))),ok(or1(s(1))),stuck0( and2(s(1))),ok(and1(s(1))),ok(or1(s(s(1)))),ok(and2(s(s(1)))),ok(and1(s(s(1))))] Prior = 4.9305e-04 Posterior = [0.246384,0.2497] Runtime: 383 msec.

yes | ?- reestimate. THIS ASKS FOR A REESTIMATE OF THE PROBABILITIES Queue mass = 2.6573e-05 THIS IS AN UPPER BOUND ON THE PRIOR PROBABILITIES OF ALL OF THE EXPLANATIONS NOT YET GENERATED Probability mass = [0.00197455,0.00200112] THIS IS AN ESTIMATE OF THE POSTERIOR PROBAILITY OF THE EXPLANATIONS NOT YET GENERATED Maximum prob not found = 0.0132789 THIS IS A BOUND ON THE POSTERIOR PROBABILITY OF THE EXPLANATIONS NOT YET GENERATED (IS THE RELATIVE ERROR OF THE POSTERIOR PROBABILITIES).

Explanation: [ok(xor2(1)),ok(xor1(1)),ok(xor2(s(1))),ok(xor1(s(1))),ok(or1(1)),o k(and2(1)),ok(and1(1)),ok(xor2(s(s(1)))),ok(xor1(s(s(1)))),stuck0(or1(s(1))),ok( or1(s(s(1)))),ok(and2(s(s(1)))),ok(and1(s(s(1))))] Prior = 4.9403e-04 Posterior = [0.246878,0.2502] THIS IS A NEW ESTIMATE OF THE POSTERIOR PROBABILITY OF THE EXPLANATION

Explanation: [ok(xor2(1)),ok(xor1(1)),ok(xor2(s(1))),ok(xor1(s(1))),ok(or1(1)),o k(and2(1)),ok(and1(1)),ok(xor2(s(s(1)))),stuck1(xor1(s(s(1)))),ok(or1(s(1))),ok( and2(s(1))),ok(or1(s(s(1)))),ok(and2(s(s(1))))] Prior = 4.9393e-04 Posterior = [0.246828,0.25015]

Explanation: [ok(xor2(1)),ok(xor1(1)),ok(xor2(s(1))),ok(xor1(s(1))),ok(or1(1)),o k(and2(1)),ok(and1(1)),stuck0(xor2(s(s(1)))),ok(or1(s(s(1)))),ok(and2(s(s(1)))), ok(or1(s(1))),ok(and2(s(1))),ok(xor1(s(s(1)))),ok(and1(s(s(1))))] Prior = 4.9354e-04 Posterior = [0.246631,0.24995]

Explanation: [ok(xor2(1)),ok(xor1(1)),ok(xor2(s(1))),ok(xor1(s(1))),ok(or1(1)),o k(and2(1)),ok(and1(1)),ok(xor2(s(s(1)))),ok(xor1(s(s(1)))),ok(or1(s(1))),stuck0( and2(s(1))),ok(and1(s(1))),ok(or1(s(s(1)))),ok(and2(s(s(1)))),ok(and1(s(s(1))))] Prior = 4.9305e-04 Posterior = [0.246384,0.2497]

yes

If there are any problems please contact David Poole <poole@cs.ubc.ca>