%%% -*- Mode: Prolog; -*- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % ProbLog inference % % assumes probabilistic facts as Prob::Fact and clauses in normal Prolog format % % provides following inference modes (16/12/2008): % - approximation with interval width Delta (IJCAI07): problog_delta(+Query,+Delta,-Low,-High,-Status) % - bounds based on single probability threshold: problog_threshold(+Query,+Threshold,-Low,-High,-Status) % - as above, but lower bound only: problog_low(+Query,+Threshold,-Low,-Status) % - lower bound based on K most likely proofs: problog_kbest(+Query,+K,-Low,-Status) % - explanation probability (ECML07): problog_max(+Query,-Prob,-FactsUsed) % - exact probability: problog_exact(+Query,-Prob,-Status) % - sampling: problog_montecarlo(+Query,+Delta,-Prob) % % % angelika.kimmig@cs.kuleuven.be %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% :- module(problog, [problog_delta/5, problog_threshold/5, problog_low/4, problog_kbest/4, problog_kbest_save/6, problog_max/3, problog_exact/3, problog_montecarlo/3, get_fact_probability/2, set_fact_probability/2, get_fact/2, tunable_fact/2, non_ground_fact/1, export_facts/1, problog_help/0, problog_dir/1, set_problog_flag/2, problog_flag/2, problog_flags/0]). :- style_check(all). :- yap_flag(unknown,error). % problog related modules :- use_module('problog/flags',[set_problog_flag/2, problog_flag/2, problog_flags/0]). :- use_module('problog/print', [print_sep_line/0, print_inference/2]). :- use_module('problog/tptree',[init_ptree/1, delete_ptree/1, insert_ptree/2, count_ptree/2, prune_check_ptree/2, merge_ptree/3, bdd_ptree_map/4, bdd_ptree/3]). % general yap modules :- ensure_loaded(library(lists)). :- ensure_loaded(library(terms)). :- ensure_loaded(library(random)). :- ensure_loaded(library(system)). :- ensure_loaded(library(rbtrees)). % op attaching probabilities to facts :- op( 550, yfx, :: ). %%%%%%%%%%%%%%%%%%%%%%%% % control predicates on various levels %%%%%%%%%%%%%%%%%%%%%%%% % global over all inference methods, internal use only :- dynamic problog_predicate/2. % global over all inference methods, exported :- dynamic tunable_fact/2. :- dynamic non_ground_fact/1. :- dynamic problog_dir/1. % global, manipulated via problog_control/2 :- dynamic up/0. :- dynamic limit/0. :- dynamic mc/0. :- dynamic remember/0. % local to problog_delta :- dynamic low/2. :- dynamic up/2. :- dynamic stopDiff/1. % local to problog_kbest :- dynamic current_kbest/3. % local to problog_max :- dynamic max_probability/1. :- dynamic max_proof/1. % local to problog_montecarlo :- dynamic mc_prob/1. % to keep track of the groundings for non-ground facts :- dynamic grounding_is_known/2. % for fact where the proabability is a variable :- dynamic dynamic_probability_fact/1. :- dynamic dynamic_probability_fact_extract/2. % directory where ProblogBDD executable is located % automatically set during loading -- assumes it is in same place as this file (problog.yap) %:- getcwd(PD),retractall(problog_dir(_)),assert(problog_dir(PD)). :- yap_flag(shared_object_search_path,PD),retractall(problog_dir(_)),assert(problog_dir(PD)). %%%%%%%%%%%%%%%%%%%%%%%% % help %%%%%%%%%%%%%%%%%%%%%%%% problog_help :- format('~2nProbLog inference currently offers the following inference methods:~n',[]), show_inference, format('~2nThe following global parameters are available:~n',[]), problog_flags, print_sep_line, format('~n use problog_help/0 to display this information~n',[]), format('~n use problog_flags/0 to display current parameter values~2n',[]), print_sep_line, nl, flush_output. show_inference :- format('~n',[]), print_sep_line, print_inference(call,description), print_sep_line, print_inference('problog_delta(+Query,+Delta,-Low,-High,-Status)','approximation with interval width Delta (IJCAI07)'), print_inference('problog_threshold(+Query,+Threshold,-Low,-High,-Status)','bounds based on single probability threshold'), print_inference('problog_low(+Query,+Threshold,-Low,-Status)','lower bound based on single probability threshold'), print_inference('problog_kbest(+Query,+K,-Low,-Status)','lower bound based on K most likely proofs'), print_inference('problog_max(+Query,-Prob,-FactsUsed)','explanation probability (ECML07)'), print_inference('problog_exact(+Query,-Prob,-Status)','exact probability'), print_inference('problog_montecarlo(+Query,+Delta,-Prob)','sampling with 95\%-confidence-interval-width Delta'), print_sep_line. %%%%%%%%%%%%%%%%%%%%%%%% % initialization of global parameters %%%%%%%%%%%%%%%%%%%%%%%% init_global_params :- set_problog_flag(bdd_time,60), set_problog_flag(first_threshold,0.1), L is 10**(-30), set_problog_flag(last_threshold,L), set_problog_flag(id_stepsize,0.5), set_problog_flag(prunecheck,off), set_problog_flag(maxsteps,1000), set_problog_flag(mc_batchsize,1000), set_problog_flag(mc_logfile,'log.txt'), set_problog_flag(bdd_file,example_bdd), set_problog_flag(dir,output), set_problog_flag(save_bdd,false), set_problog_flag(verbose,true). % problog_flags, % print_sep_line, % format('~n use problog_help/0 for information~n',[]), % format('~n use problog_flags/0 to display current parameter values~2n',[]), % print_sep_line, % nl, % flush_output. % parameter initialization to be called after returning to user's directory: :- initialization(init_global_params). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % internal control flags % if on % - up: collect stopped derivations to build upper bound % - limit: iterative deepening reached limit -> should go to next level % - mc: using problog_montecarlo, i.e. proving with current sample instead of full program % - remember: save BDD files containing script, params and mapping %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% problog_control(on,X) :- call(X),!. problog_control(on,X) :- assert(X). problog_control(off,X) :- retractall(X). problog_control(check,X) :- call(X). :- problog_control(off,up). :- problog_control(off,mc). :- problog_control(off,limit). :- problog_control(off,remember). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % nice user syntax Prob::Fact % automatic translation to internal hardware access format % % probabilities =1 are dropped -> normal Prolog fact % % internal fact representation % - prefixes predicate name with problog_ % - adds unique ID as first argument % - adds logarithm of probability as last argument % - keeps original arguments in between % % for each predicate appearing as probabilistic fact, wrapper clause is introduced: % - head is most general instance of original fact % - body is corresponding version of internal fact plus call to add_to_proof/2 to update current state during proving % example: edge(A,B) :- problog_edge(ID,A,B,LogProb), add_to_proof(ID,LogProb). % % dynamic predicate problog_predicate(Name,Arity) keeps track of predicates that already have wrapper clause %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% user:term_expansion(_P::( _Goal :- _Body ), _Error) :- throw(error('we do not support this (yet?)!')). user:term_expansion(P::Goal,Goal) :- P \= t(_), P =:= 1, !. user:term_expansion(P::Goal, problog:ProbFact) :- copy_term((P,Goal),(P_Copy,Goal_Copy)), functor(Goal, Name, Arity), atomic_concat([problog_,Name],ProblogName), Goal =.. [Name|Args], append(Args,[LProb],L1), probclause_id(ID), ProbFact =.. [ProblogName,ID|L1], ( (\+ var(P), P = t(TrueProb)) -> ( assert(tunable_fact(ID,TrueProb)), LProb is log(0.5) ); ( ground(P) -> LProb is log(P); ( % Probability is a variable... check wether it appears in the term ( variable_in_term(Goal,P) -> true; ( format(user_error,'If you use probabilisitic facts with a variable as probabilility, the variable has to appear inside the fact.~n',[]), format(user_error,'You used ~q in your program.~2n',[P::Goal]), throw(non_ground_fact_error(P::Goal)) ) ), LProb=log(P), assert(dynamic_probability_fact(ID)), assert(dynamic_probability_fact_extract(Goal_Copy,P_Copy)) ) ) ), ( ground(Goal) -> true; assert(non_ground_fact(ID)) ), problog_predicate(Name, Arity, ProblogName). % introduce wrapper clause if predicate seen first time problog_predicate(Name, Arity, _) :- problog_predicate(Name, Arity), !. problog_predicate(Name, Arity, ProblogName) :- functor(OriginalGoal, Name, Arity), OriginalGoal =.. [_|Args], append(Args,[Prob],L1), ProbFact =.. [ProblogName,ID|L1], prolog_load_context(module,Mod), assert( (Mod:OriginalGoal :- ProbFact, ( non_ground_fact(ID) -> (non_ground_fact_grounding_id(OriginalGoal,G_ID), atomic_concat([ID,'_',G_ID],ID2)); ID2=ID ), % take the log of the probability (for non ground facts with variable as probability ProbEval is Prob, add_to_proof(ID2,ProbEval) )), assert( (Mod:problog_not(OriginalGoal) :- ProbFact, ( non_ground_fact(ID) -> ( non_ground_fact_grounding_id(OriginalGoal,G_ID), atomic_concat([ID,'_',G_ID],ID2)); ID2=ID ), % take the log of the probability (for non ground facts with variable as probability ProbEval is Prob, add_to_proof_negated(ID2,ProbEval) )), assert(problog_predicate(Name, Arity)), ArityPlus2 is Arity+2, dynamic(problog:ProblogName/ArityPlus2). % generate next global identifier probclause_id(ID) :- nb_getval(probclause_counter,ID), !, C1 is ID+1, nb_setval(probclause_counter,C1), !. probclause_id(0) :- nb_setval(probclause_counter,1). non_ground_fact_grounding_id(Goal,ID) :- ( ground(Goal) -> true; ( format(user_error,'The current program uses non-ground facts.~n', []), format(user_error,'If you query those, you may only query fully-grounded versions of the fact.~n',[]), format(user_error,'Within the current proof, you queried for ~q which is not ground.~n~n', [Goal]), throw(error(non_ground_fact(Goal))) ) ), ( grounding_is_known(Goal,ID) -> true; ( nb_getval(non_ground_fact_grounding_id_counter,ID), ID2 is ID+1, nb_setval(non_ground_fact_grounding_id_counter,ID2), assert(grounding_is_known(Goal,ID)) ) ). reset_non_ground_facts :- nb_setval(non_ground_fact_grounding_id_counter,0), retractall(grounding_is_known(_,_)). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % access/update the probability of ID's fact % hardware-access version: naively scan all problog-predicates, % cut choice points if ID is ground (they'll all fail as ID is unique), % but not if it isn't (used to iterate over all facts when writing out probabilities for learning) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% get_fact_probability(ID,Prob) :- ( ground(ID) -> get_internal_fact(ID,ProblogTerm,_ProblogName,ProblogArity),! ; get_internal_fact(ID,ProblogTerm,_ProblogName,ProblogArity) ), arg(ProblogArity,ProblogTerm,Log), Prob is exp(Log). set_fact_probability(ID,Prob) :- get_internal_fact(ID,ProblogTerm,ProblogName,ProblogArity), retract(ProblogTerm), ProblogTerm =.. [ProblogName|ProblogTermArgs], nth(ProblogArity,ProblogTermArgs,_,KeepArgs), NewLogProb is log(Prob), nth(ProblogArity,NewProblogTermArgs,NewLogProb,KeepArgs), NewProblogTerm =.. [ProblogName|NewProblogTermArgs], assert(NewProblogTerm). get_internal_fact(ID,ProblogTerm,ProblogName,ProblogArity) :- problog_predicate(Name,Arity), atomic_concat([problog_,Name],ProblogName), ProblogArity is Arity+2, functor(ProblogTerm,ProblogName,ProblogArity), arg(1,ProblogTerm,ID), call(ProblogTerm). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % writing those facts with learnable parameters to File %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% export_facts(File) :- tell(File), export_facts, flush_output, told. export_facts :- tunable_fact(ID,_), once(write_tunable_fact(ID)), fail. export_facts. write_tunable_fact(ID) :- get_internal_fact(ID,ProblogTerm,ProblogName,ProblogArity), ProblogTerm =.. [_Functor,ID|Args], atomic_concat('problog_',OutsideFunctor,ProblogName), Last is ProblogArity-1, nth(Last,Args,LogProb,OutsideArgs), OutsideTerm =.. [OutsideFunctor|OutsideArgs], Prob is exp(LogProb), format('~w :: ~q.~n',[Prob,OutsideTerm]). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % recover fact for given id % list version not exported (yet?) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % ID of ground fact get_fact(ID,OutsideTerm) :- get_internal_fact(ID,ProblogTerm,ProblogName,ProblogArity), !, ProblogTerm =.. [_Functor,ID|Args], atomic_concat('problog_',OutsideFunctor,ProblogName), Last is ProblogArity-1, nth(Last,Args,_LogProb,OutsideArgs), OutsideTerm =.. [OutsideFunctor|OutsideArgs]. % ID of instance of non-ground fact: get fact from grounding table get_fact(ID,OutsideTerm) :- recover_grounding_id(ID,GID), grounding_is_known(OutsideTerm,GID). recover_grounding_id(Atom,ID) :- name(Atom,List), reverse(List,Rev), recover_number(Rev,NumRev), reverse(NumRev,Num), name(ID,Num). recover_number([95|_],[]) :- !. % name('_',[95]) recover_number([A|B],[A|C]) :- recover_number(B,C). get_fact_list([],[]). get_fact_list([ID|IDs],[Fact|Facts]) :- (ID=not(X) -> Fact=not(Y); Fact=Y, ID=X), get_fact(X,Y), get_fact_list(IDs,Facts). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % ProbLog inference, core methods % % state of proving saved in two backtrackable global variables % - problog_current_proof holds list of IDs of clauses used % - problog_probability holds the sum of their log probabilities %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % called "inside" probabilistic facts to update current state of proving % if number of steps exceeded, fail % if fact used before, succeed and keep status as is % if not prunable, calculate probability and % if threshold exceeded, add stopped derivation to upper bound and fail % else update state and succeed add_to_proof(ID,Prob) :- montecarlo_check(ID), b_getval(problog_steps,MaxSteps), b_getval(problog_probability, CurrentP), nb_getval(problog_threshold, CurrentThreshold), b_getval(problog_current_proof, IDs), %%%% Bernd, changes for negated ground facts \+ memberchk(not(ID),IDs), %%%% Bernd, changes for negated ground facts ( MaxSteps =< 0 -> fail ; ( memberchk(ID, IDs) -> true ; \+ prune_check([ID|IDs],1), multiply_probabilities(CurrentP, Prob, NProb), ( NProb < CurrentThreshold -> upper_bound([ID|IDs]), fail ; b_setval(problog_probability, NProb), b_setval(problog_current_proof, [ID|IDs]) ) ), Steps is MaxSteps-1, b_setval(problog_steps,Steps) ). %%%% Bernd, changes for negated ground facts add_to_proof_negated(ID,Prob) :- ( problog_control(check,mc) -> % the sample has to fail if the fact is negated \+ montecarlo_check(ID); true ), b_getval(problog_steps,MaxSteps), b_getval(problog_probability, CurrentP), nb_getval(problog_threshold, CurrentThreshold), b_getval(problog_current_proof, IDs), \+ memberchk(ID,IDs), ( MaxSteps =< 0 -> fail ; ( memberchk(not(ID), IDs) -> true ; % \+ prune_check([ID|IDs],1), InverseProb is log(1 - exp(Prob)), multiply_probabilities(CurrentP, InverseProb, NProb), ( NProb < CurrentThreshold -> upper_bound([not(ID)|IDs]), %% checkme fail ; b_setval(problog_probability, NProb), b_setval(problog_current_proof, [not(ID)|IDs]) ) ), Steps is MaxSteps-1, b_setval(problog_steps,Steps) ). %%%% Bernd, changes for negated ground facts % if in monte carlo mode, check array to see if fact can be used montecarlo_check(ID) :- ( problog_control(check,mc) -> ( array_element(mc_sample,ID,V), ( V == 1 -> true ; V == 2 -> fail ; new_sample(ID) ) ) ; true ). new_sample(ID) :- get_fact_probability(ID,Prob), random(R), R=1 -> don't need []=true-case for tries upper_bound(List) :- problog_control(on,limit), problog_control(check,up), reverse(List,R), (prune_check(R,2) -> true; insert_ptree(R,2)). multiply_probabilities(CurrentLogP, LogProb, NLogProb) :- NLogProb is CurrentLogP+LogProb. % this is called by all inference methods before the actual ProbLog goal % to set up environment for proving init_problog(Threshold) :- reset_non_ground_facts, LT is log(Threshold), b_setval(problog_probability, 0.0), b_setval(problog_current_proof, []), nb_setval(problog_threshold, LT), problog_flag(maxsteps,MaxS), b_setval(problog_steps, MaxS), problog_control(off,limit). % idea: proofs that are refinements of known proof can be pruned as they don't add probability mass % note that current ptree implementation doesn't provide the check as there's no efficient method known so far... prune_check(Proof,TreeID) :- problog_flag(prunecheck,on), prune_check_ptree(Proof,TreeID). % to call a ProbLog goal, patch all subgoals with the user's module context % (as logical part is there, but probabilistic part in problog) problog_call(Goal) :- yap_flag(typein_module,Module), %%% if user provides init_db, call this before proving goal (current_predicate(_,Module:init_db) -> call(Module:init_db); true), put_module(Goal,Module,ModGoal), call(ModGoal). put_module((Mod:Goal,Rest),Module,(Mod:Goal,Transformed)) :- !, put_module(Rest,Module,Transformed). put_module((Goal,Rest),Module,(Module:Goal,Transformed)) :- !, put_module(Rest,Module,Transformed). put_module((Mod:Goal),_Module,(Mod:Goal)) :- !. put_module(Goal,Module,Module:Goal). % end of core %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % evaluating a DNF given as trie using BDD % input: ID of trie to be used % output: probability and status (to catch potential failures/timeouts from outside) % % with internal BDD timeout (set using problog flag bdd_time) % % bdd_ptree/3 constructs files for ProblogBDD from the trie % % if calling ProblogBDD doesn't exit successfully, status will be timeout % % writes number of proofs in trie and BDD time to standard user output % % if remember is on, input files for ProblogBDD will be saved %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% eval_dnf(ID,Prob,Status) :- ((ID = 1, problog_flag(save_bdd,true)) -> problog_control(on,remember); problog_control(off,remember)), count_ptree(ID,NX), ( problog_flag(verbose,true) -> ( NX=1 -> format(user,'1 proof~n',[]); format(user,'~w proofs~n',[NX]) ); true ), problog_flag(dir,DirFlag), problog_flag(bdd_file,BDDFileFlag), atomic_concat([DirFlag,BDDFileFlag],BDDFile), problog_flag(bdd_par_file,BDDParFileFlag), atomic_concat([DirFlag,BDDParFileFlag],BDDParFile), (problog_control(check,remember) -> bdd_ptree_map(ID,BDDFile,BDDParFile,Mapping), atomic_concat([DirFlag,'save_map'],MapFile), tell(MapFile), format('mapping(~q).~n',[Mapping]), flush_output, told ; bdd_ptree(ID,BDDFile,BDDParFile) ), problog_flag(bdd_time,BDDTime), problog_flag(bdd_result,ResultFileFlag), atomic_concat([DirFlag,ResultFileFlag],ResultFile), problog_dir(PD), atomic_concat([PD,'/ProblogBDD -l ',BDDFile,' -i ',BDDParFile,' -m p -t ', BDDTime,' > ', ResultFile],Command), statistics(walltime,_), shell(Command,Return), ( Return =\= 0 -> Status = timeout ; ( statistics(walltime,[_,E3]), (problog_flag(verbose,true) -> format(user,'~w ms BDD processing~n',[E3]);true), see(ResultFile), read(probability(Prob)), seen, delete_file(ResultFile), Status = ok ) ), (problog_control(check,remember) -> atomic_concat([DirFlag,'save_script'],SaveBDDFile), rename_file(BDDFile,SaveBDDFile), atomic_concat([DirFlag,'save_params'],SaveBDDParFile), rename_file(BDDParFile,SaveBDDParFile) ; true ), problog_control(off,remember). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % different inference methods %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % approximate inference: bounds based on single probability threshold % problog_threshold(+Goal,+Threshold,-LowerBound,-UpperBound,-Status) % % use backtracking over problog_call to get all solutions % % trie 1 collects proofs, trie 2 collects stopped derivations, trie 3 is used to unit them for the upper bound %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% problog_threshold(Goal, Threshold, _, _, _) :- problog_control(on,up), init_problog_threshold(Threshold), problog_call(Goal), add_solution, fail. problog_threshold(_, _, LP, UP, Status) :- compute_bounds(LP, UP, Status). init_problog_threshold(Threshold) :- init_ptree(1), init_ptree(2), init_problog(Threshold). add_solution :- b_getval(problog_current_proof, IDs), (IDs == [] -> R = true ; reverse(IDs,R)), insert_ptree(R,1). compute_bounds(LP, UP, Status) :- eval_dnf(1,LP,StatusLow), (StatusLow \== ok -> Status = StatusLow ; merge_ptree(1,2,3), eval_dnf(3,UP,Status)), delete_ptree(1), delete_ptree(2), delete_ptree(3). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % approximate inference: lower bound based on all proofs above probability threshold % problog_low(+Goal,+Threshold,-LowerBound,-Status) % % same as problog_threshold/5, but lower bound only (no stopped derivations stored) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% problog_low(Goal, Threshold, _, _) :- problog_control(off,up), init_problog_low(Threshold), problog_call(Goal), add_solution, fail. problog_low(_, _, LP, Status) :- eval_dnf(1,LP,Status), delete_ptree(1). init_problog_low(Threshold) :- init_ptree(1), init_problog(Threshold). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % approximate inference: bounds by iterative deepening up to interval width Delta % problog_delta(+Goal,+Delta,-LowerBound,-UpperBound,-Status) % % wraps iterative deepening around problog_threshold, i.e. % - starts with threshold given by first_threshold flag % - if Up-Low >= Delta, multiply threshold by factor given in id_stepsize flag and iterate % (does not use problog_threshold as trie 1 is kept over entire search) % % local dynamic predicates low/2, up/2, stopDiff/1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% problog_delta(Goal, Delta, Low, Up, Status) :- problog_control(on,up), problog_flag(first_threshold,InitT), init_problog_delta(InitT,Delta), problog_delta_id(Goal,Status), delete_ptree(1), delete_ptree(2), (retract(low(_,Low)) -> true; true), (retract(up(_,Up)) -> true; true). init_problog_delta(Threshold,Delta) :- retractall(low(_,_)), retractall(up(_,_)), retractall(stopDiff(_)), init_ptree(1), init_ptree(2), assert(low(0,0.0)), assert(up(0,1.0)), assert(stopDiff(Delta)), init_problog(Threshold). problog_delta_id(Goal, _) :- problog_call(Goal), add_solution, % reused from problog_threshold fail. problog_delta_id(Goal, Status) :- evaluateStep(Ans,StatusE), problog_flag(last_threshold_log,Stop), nb_getval(problog_threshold,Min), (StatusE \== ok -> Status = StatusE ; ( Ans = 1 -> Status = ok ; Min =< Stop -> Status = stopreached ; problog_control(check,limit) -> problog_control(off,limit), problog_flag(id_stepsize_log,Step), New is Min+Step, nb_setval(problog_threshold,New), problog_delta_id(Goal, Status) ; true )). % call the dnf evaluation where needed evaluateStep(Ans,Status) :- once(evalStep(Ans,Status)). evalStep(Ans,Status) :- stopDiff(Delta), count_ptree(1,NProofs), count_ptree(2,NCands), (problog_flag(verbose,true) -> format(user,'~w proofs, ~w stopped derivations~n',[NProofs,NCands]);true), flush_output(user), eval_lower(NProofs,Low,StatusLow), (StatusLow \== ok -> Status = StatusLow ; up(_,OUP), IntDiff is OUP-Low, ((IntDiff < Delta; IntDiff =:= 0) -> Up=OUP, StatusUp = ok ; eval_upper(NCands,Up,StatusUp), delete_ptree(2), init_ptree(2), delete_ptree(3) ), (StatusUp \== ok -> Status = StatusUp ; Diff is Up-Low, (problog_flag(verbose,true) -> format(user,'difference: ~6f~n',[Diff]);true), flush_output(user), ((Diff < Delta; Diff =:= 0) -> Ans = 1; Ans = 0), Status = ok)). % no need to re-evaluate if no new proofs found on this level eval_lower(N,P,ok) :- low(N,P). % evaluate if there are proofs eval_lower(N,P,Status) :- N > 0, low(OldN,_), N \= OldN, eval_dnf(1,P,Status), (Status = ok -> retract(low(_,_)), assert(low(N,P)), (problog_flag(verbose,true) -> format(user,'lower bound: ~6f~n',[P]);true), flush_output(user) ; true). % if no stopped derivations, up=low eval_upper(0,P,ok) :- retractall(up(_,_)), low(N,P), assert(up(N,P)). % else merge proofs and stopped derivations to get upper bound % in case of timeout or other problems, skip and use bound from last level eval_upper(N,UpP,ok) :- N > 0, merge_ptree(1,2,3), eval_dnf(3,UpP,StatusUp), (StatusUp = ok -> retract(up(_,_)), assert(up(N,UpP)) ; (problog_flag(verbose,true) -> format(user,'~w - continue using old up~n',[StatusUp]);true), flush_output(user), up(_,UpP)). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % explanation probability - returns list of facts used or constant 'unprovable' as third argument % problog_max(+Goal,-Prob,-Facts) % % uses iterative deepening with samw parameters as bounding algorithm % threshold gets adapted whenever better proof is found % % uses local dynamic predicates max_probability/1 and max_proof/1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% problog_max(Goal, Prob, Facts) :- problog_control(off,up), problog_flag(first_threshold,InitT), init_problog_max(InitT), problog_max_id(Goal, Prob, FactIDs), ( FactIDs = [_|_] -> get_fact_list(FactIDs,Facts); Facts = FactIDs). init_problog_max(Threshold) :- retractall(max_probability(_)), retractall(max_proof(_)), assert(max_probability(-999999)), assert(max_proof(unprovable)), init_problog(Threshold). update_max :- b_getval(problog_probability,CurrP), max_probability(MaxP), (CurrP =< MaxP -> fail ; b_getval(problog_current_proof, IDs), reverse(IDs,R), retractall(max_proof(_)), assert(max_proof(R)), nb_setval(problog_threshold, CurrP), retractall(max_probability(_)), assert(max_probability(CurrP))). problog_max_id(Goal, _Prob, _Clauses) :- problog_call(Goal), update_max, fail. problog_max_id(Goal, Prob, Clauses) :- max_probability(MaxP), nb_getval(problog_threshold, LT), problog_flag(last_threshold_log,ToSmall), ((MaxP >= LT ; \+ problog_control(check,limit); LT < ToSmall) -> ((max_proof(unprovable), problog_control(check,limit), LT < ToSmall) -> problog_flag(last_threshold,Stopping), Clauses = unprovable(Stopping) ; max_proof(Clauses)), Prob is exp(MaxP) ; problog_flag(id_stepsize_log,Step), NewLT is LT+Step, nb_setval(problog_threshold, NewLT), problog_control(off,limit), problog_max_id(Goal, Prob, Clauses)). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % lower bound using k best proofs % problog_kbest(+Goal,+K,-Prob,-Status) % % does iterative deepening search similar to problog_max, but for k(>=1) most likely proofs % afterwards uses BDD evaluation to calculate probability (also for k=1 -> uniform treatment in learning) % % uses dynamic local predicate current_kbest/3 to collect proofs, % only builds trie at the end (as probabilities of single proofs are important here) % % note: >k proofs will be used if the one at position k shares its probability with others, % as all proofs with that probability will be included % % version with _save at the end renames files for ProblogBDD to keep them %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% problog_kbest_save(Goal, K, Prob, Status, BDDFile, ParamFile) :- problog_kbest(Goal, K, Prob, Status), ( Status=ok -> problog_flag(bdd_file,InternBDDFlag), problog_flag(bdd_par_file,InternParFlag), problog_flag(dir,DirFlag), atomic_concat([DirFlag,InternBDDFlag],InternBDD), atomic_concat([DirFlag,InternParFlag],InternPar), rename_file(InternBDD,BDDFile), rename_file(InternPar,ParamFile) ; true). problog_kbest(Goal, K, Prob, Status) :- problog_control(off,up), problog_flag(first_threshold,InitT), init_problog_kbest(InitT), problog_kbest_id(Goal, K), retract(current_kbest(_,ListFound,_NumFound)), build_prefixtree(ListFound), eval_dnf(1,Prob,Status), delete_ptree(1). init_problog_kbest(Threshold) :- retractall(current_kbest(_,_,_)), assert(current_kbest(-999999,[],0)), %(log-threshold,proofs,num_proofs) init_ptree(1), init_problog(Threshold). problog_kbest_id(Goal, K) :- problog_call(Goal), update_kbest(K), fail. problog_kbest_id(Goal, K) :- current_kbest(CurrentBorder,_,Found), nb_getval(problog_threshold, Min), problog_flag(last_threshold_log,ToSmall), ((Found>=K ; \+ problog_control(check,limit) ; Min < CurrentBorder ; Min < ToSmall) -> true ; problog_flag(id_stepsize_log,Step), NewLT is Min+Step, nb_setval(problog_threshold, NewLT), problog_control(off,limit), problog_kbest_id(Goal, K)). update_kbest(K) :- b_getval(problog_probability,NewLogProb), current_kbest(LogThreshold,_,_), (NewLogProb>=LogThreshold -> b_getval(problog_current_proof,RevProof), reverse(RevProof,Proof), update_current_kbest(K,NewLogProb,Proof) ; fail). update_current_kbest(_,NewLogProb,Cl) :- current_kbest(_,List,_), memberchk(NewLogProb-Cl,List), !. update_current_kbest(K,NewLogProb,Cl) :- retract(current_kbest(OldThres,List,Length)), sorted_insert(NewLogProb-Cl,List,NewList), NewLength is Length+1, (NewLength < K -> assert(current_kbest(OldThres,NewList,NewLength)) ; (NewLength>K -> First is NewLength-K+1, cutoff(NewList,NewLength,First,FinalList,FinalLength) ; FinalList=NewList, FinalLength=NewLength), FinalList=[NewThres-_|_], nb_setval(problog_threshold,NewThres), assert(current_kbest(NewThres,FinalList,FinalLength))). sorted_insert(A,[],[A]). sorted_insert(A-LA,[B1-LB1|B], [A-LA,B1-LB1|B] ) :- A =< B1. sorted_insert(A-LA,[B1-LB1|B], [B1-LB1|C] ) :- A > B1, sorted_insert(A-LA,B,C). % keeps all entries with lowest probability, even if implying a total of more than k cutoff(List,Len,1,List,Len) :- !. cutoff([P-L|List],Length,First,[P-L|List],Length) :- nth(First,[P-L|List],PF-_), PF=:=P, !. cutoff([_|List],Length,First,NewList,NewLength) :- NextFirst is First-1, NextLength is Length-1, cutoff(List,NextLength,NextFirst,NewList,NewLength). build_prefixtree([]). build_prefixtree([_-[]|_List]) :- !, insert_ptree(true,1). build_prefixtree([_-L|List]) :- insert_ptree(L,1), build_prefixtree(List). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % exact probability % problog_exact(+Goal,-Prob,-Status) % % using all proofs = using all proofs with probability > 0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% problog_exact(Goal,Prob,Status) :- problog_low(Goal,0,Prob,Status). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % probability by sampling: % running another N samples until 95percentCI-width format('search for ~q~n',[Goal]);true), montecarlo(Goal,Delta,K,0,File,0,T1), problog_control(off,mc), delete_ptree(1). % calculate values after K samples montecarlo(Goal,Delta,K,SamplesSoFar,File,PositiveSoFar,InitialTime) :- SamplesNew is SamplesSoFar+1, SamplesNew mod K =:= 0, !, copy_term(Goal,GoalC), (mc_prove(GoalC) -> Next is PositiveSoFar+1; Next=PositiveSoFar), Prob is Next/SamplesNew, Epsilon is 2*sqrt(Prob*(1-Prob)/SamplesNew), Low is Prob-Epsilon, High is Prob+Epsilon, Diff is 2*Epsilon, statistics(walltime,[T2,_]), Time is (T2-InitialTime)/1000, count_ptree(1,CacheSize), (problog_flag(verbose,true) -> format('~n~w samples~nestimated probability ~w~n95 percent confidence interval [~w,~w]~n',[SamplesNew,Prob,Low,High]);true), open(File,append,Log), format(Log,'~w ~8f ~8f ~8f ~8f ~3f ~w ~w~n',[SamplesNew,Prob,Low,High,Diff,Time,CacheSize,Next]), close(Log), ((Diff (problog_flag(verbose,true) -> format('Runtime ~w sec~2n',[Time]);true),assert(mc_prob(Prob)) ; montecarlo(Goal,Delta,K,SamplesNew,File,Next,InitialTime)). % continue until next K samples done montecarlo(Goal,Delta,K,SamplesSoFar,File,PositiveSoFar,InitialTime) :- SamplesNew is SamplesSoFar+1, copy_term(Goal,GoalC), (mc_prove(GoalC) -> Next is PositiveSoFar+1; Next=PositiveSoFar), montecarlo(Goal,Delta,K,SamplesNew,File,Next,InitialTime). mc_prove(A) :- !, (get_some_proof(A) -> clean_sample ; clean_sample,fail ). clean_sample :- reset_static_array(mc_sample), fail. clean_sample. % find new proof get_some_proof(Goal) :- init_problog(0), problog_call(Goal), b_getval(problog_current_proof,Used), (Used == [] -> Proof=true; reverse(Used,Proof)), insert_ptree(Proof,1).