%%% -*- Mode: Prolog; -*- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % $Date: 2010-08-24 15:14:21 +0200 (Di, 24. Aug 2010) $ % $Revision: 4671 $ % % This file is part of ProbLog % http://dtai.cs.kuleuven.be/problog % % ProbLog was developed at Katholieke Universiteit Leuven % % Copyright 2008, 2009, 2010 % Katholieke Universiteit Leuven % % Main authors of this file: % Guy Van den Broeck % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Artistic License 2.0 % % Copyright (c) 2000-2006, The Perl Foundation. % % Everyone is permitted to copy and distribute verbatim copies of this % license document, but changing it is not allowed. Preamble % % This license establishes the terms under which a given free software % Package may be copied, modified, distributed, and/or % redistributed. 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If you institute patent litigation % (including a cross-claim or counterclaim) against any party alleging % that the Package constitutes direct or contributory patent % infringement, then this Artistic License to you shall terminate on the % date that such litigation is filed. % % (14) Disclaimer of Warranty: THE PACKAGE IS PROVIDED BY THE COPYRIGHT % HOLDER AND CONTRIBUTORS "AS IS' AND WITHOUT ANY EXPRESS OR IMPLIED % WARRANTIES. THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A % PARTICULAR PURPOSE, OR NON-INFRINGEMENT ARE DISCLAIMED TO THE EXTENT % PERMITTED BY YOUR LOCAL LAW. UNLESS REQUIRED BY LAW, NO COPYRIGHT % HOLDER OR CONTRIBUTOR WILL BE LIABLE FOR ANY DIRECT, INDIRECT, % INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING IN ANY WAY OUT OF THE USE % OF THE PACKAGE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % DECISION-THEORETIC PROBLOG %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% :- module(dtproblog, [ 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, problog_dnf_sampling/3, problog_answers/2, problog_kbest_answers/3, problog_table/1, clear_retained_tables/0, problog_neg/1, get_fact_probability/2, set_fact_probability/2, get_continuous_fact_parameters/2, set_continuous_fact_parameters/2, get_fact/2, tunable_fact/2, continuous_fact/1, non_ground_fact/1, export_facts/1, problog_help/0, show_inference/0, problog_dir/1, set_problog_flag/2, problog_flag/2, problog_flags/0, reset_problog_flags/0, problog_assert/1, problog_assert/2, problog_retractall/1, problog_statistics/2, problog_statistics/0, grow_atom_table/1, problog_exact_nested/3, problog_tabling_negated_synonym/2, build_trie/2, build_trie/3, problog_infer/2, problog_infer/3, problog_infer_forest/2, write_bdd_struct_script/3, problog_bdd_forest/1, require/1, unrequire/1, '::'/2, probabilistic_fact/3, problog_real_kbest/4, in_interval/3, below/2, above/2, op( 550, yfx, :: ), op( 550, fx, ?:: ), op( 1150, fx, problog_table ), % DTProbLog set_strategy/1, unset_strategy/1, dtproblog_utility_facts/1, dtproblog_utility_attributes/1, dtproblog_ev/2, dtproblog_ev/3, dtproblog_ev/4, dtproblog_decisions/1, dtproblog_decision_ids/1, dtproblog_decision_ids/2, dtproblog_solve/2, dtproblog_solve_specialized/2, dtproblog_solve_general/2, dtproblog_solve_local/4, dtproblog_solve_naive/2, op( 550, yfx, => ) ]). :- style_check(all). :- yap_flag(unknown,error). % problog-related modules :- use_module('problog'). :- use_module('problog/flags',[ problog_define_flag/4, problog_define_flag/5, problog_define_flag/6, set_problog_flag/2, reset_problog_flags/0, problog_flag/2 ]). :- use_module('problog/os', [convert_filename_to_working_path/2, convert_filename_to_problog_path/2]). :- use_module('problog/ptree', [delete_ptree/1]). :- use_module('problog/tabling', [clear_tabling/0]). % general yap modules :- use_module(library(system), [delete_file/2, shell/2]). :- initialization(( problog_define_flag(optimization, problog_flag_validate_atom, 'optimization algorithm [local/global]', global, dtproblog), problog_define_flag(forest_type, problog_flag_validate_atom, 'type of BDD forest [dependent/independent]', dependent, dtproblog) )). init_dtproblog :- problog_control(off,find_decisions), problog_control(off,internal_strategy). :- initialization(init_dtproblog). :- op( 550, yfx, :: ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Utility Attributes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % op for utility attributes :- op( 550, yfx, => ). % SETOF DOESNT WORK!!! BUT all/3 is A LOT slower because it doesn't sort the solutions? dtproblog_utility_facts(Facts) :- all((Attr => Util),user:(Attr => Util),Facts). dtproblog_utility_attributes(Attrs) :- dtproblog_utility_facts(Facts), facts_to_attributes(Facts,Attrs). facts_to_attributes([],[]). facts_to_attributes([A => _|FR],[A|AR]) :- facts_to_attributes(FR,AR). conditioned_utility_facts([],_,[],[]). conditioned_utility_facts([(Attr => Reward)|Facts],Condition,[(Condition,Attr)|Attrs],[Reward|Rewards]):- conditioned_utility_facts(Facts,Condition,Attrs,Rewards). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Strategies (getting/setting/transforming) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Internal strategy representation % for GROUND strategies (one can specify a ground strategy for a non-ground decision clause) % e.g. 1 :: market(guy) for ? :: market(P). set_ground_strategy(GID,LogProb) :- bb_put(GID,LogProb). get_ground_strategy(GID,LogProb) :- bb_get(GID,LogProb),!. get_ground_strategy(_,never). % Internal strategy representation % for NON-GROUND strategies % e.g. 1 :: market(guy) for ? :: market(P) :- dynamic(non_ground_strategy/2). % Get Strategy strategy(_,_,_) :- \+ problog_control(check,internal_strategy), throw(error('Trying to get a strategy that is not set.')). strategy(ID,Decision,Prob) :- grounding_id(ID,Decision,GID), bb_get(GID,LogProb), % because we don't want the default, maybe there is a non-ground strategy !, logprob_prob(LogProb, Prob). strategy(_,Decision,Prob) :- non_ground_strategy(Decision,LogProb), !, logprob_prob(LogProb, Prob). strategy(_,_,never). strategy_log(ID,Decision,LogProb) :- strategy(ID,Decision,Prob), logprob_prob(LogProb, Prob). % convert from/to probabilities and their logarithms logprob_prob(always,always) :- !. logprob_prob(never,never) :- !. logprob_prob(0,always) :- !. logprob_prob(-inf,never) :- !. logprob_prob(always,1) :- !. logprob_prob(never,0) :- !. logprob_prob(LogP,P) :- number(LogP), !, P is exp(LogP). logprob_prob(LogP,P) :- number(P), !, LogP is log(p). % Set Strategy % expects a list of (p :: decision) terms % - (decision) is interpreted as (1 :: decision) % - decisions that are not set will evaluate to (0 :: decision) set_strategy(_) :- problog_control(check,internal_strategy), throw(error('A strategy is already set, unset first.')). set_strategy([]) :- problog_control(on,internal_strategy). set_strategy([Term|R]) :- strategy_entry(Term,LogProb,Decision), (user:problog_user_ground(Decision)-> decision_fact(ID,Decision), grounding_id(ID,Decision,ID2), %format("Setting ~q/~q to ~q~n",[Decision,ID2,Prob]), set_ground_strategy(ID2,LogProb) ; copy_term(Decision, Decision2), assertz(non_ground_strategy(Decision2,LogProb)) ), set_strategy(R). unset_strategy(_) :- \+ problog_control(check,internal_strategy), throw(error('Cannot unset a strategy when no strategy is set.')). unset_strategy([]) :- retractall(non_ground_strategy(_,_)), problog_control(off,internal_strategy). unset_strategy([Term|R]) :- strategy_entry(Term,LogProb,Decision), (user:problog_user_ground(Decision)-> decision_fact(ID,Decision), grounding_id(ID,Decision,ID2), %format("Unsetting ~q/~q to ~q~n",[Decision,ID2,Prob]), bb_delete(ID2,LogProb) ; true ), unset_strategy(R). strategy_entry('::'(Prob,Decision),LogProb,Decision) :- !,logprob_prob(LogProb, Prob). strategy_entry(Decision,always,Decision). % Get strategy for a list of decision IDs % only use when grounding ids are known and strategy is stored internally! strategy_as_term_list(IDs,List) :- strategy_as_term_list(IDs,[],List). strategy_as_term_list([],In,In). strategy_as_term_list([ID|R],In,Out) :- strategy_as_term(ID,In,In2), strategy_as_term_list(R,In2,Out). % Get strategy for a decision ID strategy_as_term(ID,In,Out) :- %findall(grounding_is_known(D,I),grounding_is_known(D,I),LGround), %findall(decision_fact(D,I),decision_fact(D,I),LBasic), %format("Known IDs: ~q~n",[LGround]), %format("Known IDs: ~q~n",[LBasic]), ((recover_grounding_id(ID,GID),grounding_is_known(Decision,GID)) -> %original fact was non-ground true ; % original fact was ground decision_fact(ID,Decision) ), strategy(ID,Decision,Prob), strategy_as_term_entry(Decision,Prob,In,Out). % Convert strategy for a decision to term representation strategy_as_term_entry(_,0,In,In) :- !. strategy_as_term_entry(Decision,1,In,[Decision|In]) :- !. strategy_as_term_entry(_,never,In,In) :- !. strategy_as_term_entry(Decision,always,In,[Decision|In]) :- !. strategy_as_term_entry(Decision,P,In,[P'::'Decision|In]). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Utility inference %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Unconditional expected value for all utilities dtproblog_ev(Strategy,Ev) :- dtproblog_ev(Strategy,true,Ev). % Conditional expected value for a given strategy and all utility attributes dtproblog_ev(Strategy,Condition,Ev) :- (dtproblog_utility_facts(UtilFacts) -> dtproblog_ev(Strategy,Condition,UtilFacts,Ev) ; format('There are no utility facts in the program.~n',[]), Ev = 0 ). % Conditional expected value for a given strategy and utility attributes dtproblog_ev(Strategy,Condition,UtilFacts,Ev) :- require(keep_ground_ids), set_strategy(Strategy), ev_for_internal_strategy(Condition,UtilFacts,Ev), unset_strategy(Strategy), unrequire(keep_ground_ids), reset_non_ground_facts. % Conditional expected value for internal strategy and given utility attributes % assumes that problog_control(on,internal_strategy) ev_for_internal_strategy(Condition,UtilFacts,Ev) :- require(keep_ground_ids), (problog_infer_forest_supported -> % specialized version for inference using forests conditioned_utility_facts(UtilFacts,Condition,Goals,Utilities), problog_infer_forest([Condition|Goals],[CondProb|GoalProbs]), !, % forest inference was supported, don't try general purpose summed_utils(Utilities,GoalProbs,0,EvUncond), Ev is EvUncond/CondProb ; % general-purpose version ev_loop(Condition, UtilFacts, 0, EvUnnormalized), problog_infer(Condition, Prob), %format("Dividing the utilities by the conditional probability ~q~n",[Prob]), (Prob > 0.000001 -> Ev is EvUnnormalized/Prob ; format('Impossible condition: ~q has probability ~q.~n', [Condition,Prob]), %throw(error(improbable_condition(Condition))) Ev = -inf ) ), unrequire(keep_ground_ids), reset_non_ground_facts. summed_utils([],[],Ev,Ev). summed_utils([Util|Utils],[Prob|Probs],Acc,Ev) :- Acc2 is Acc + (Util * Prob), summed_utils(Utils,Probs,Acc2,Ev). ev_loop(_, [],Acc,Acc). ev_loop(Condition,[(Attr => Util)|R],Acc,Ev) :- problog_infer((Condition,Attr), Prob), Acc2 is Acc + (Prob * Util), %format('The probability of ~q is ~q, yielding a utility of ~q.~n', [(Condition,Attr),Prob,Prob * Util]), ev_loop(Condition,R,Acc2,Ev). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Finding all decisions used in proofs %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Finding all decisions used in proofs dtproblog_decisions(Decisions) :- require(keep_ground_ids), dtproblog_decision_ids(IDs), ids_as_decisions(IDs,Decisions), unrequire(keep_ground_ids), reset_non_ground_facts. % Get decisions for a list of IDs ids_as_decisions(IDs,List) :- ids_as_decisions(IDs,[],List). ids_as_decisions([],In,In). ids_as_decisions([ID|R],In,Out) :- id_as_decision(ID,In,In2), ids_as_decisions(R,In2,Out). id_as_decision(ID,In,[Decision|In]) :- %findall(grounding_is_known(D,I),grounding_is_known(D,I),LGround), %findall(decision_fact(D,I),decision_fact(D,I),LBasic), %format("Known IDs: ~q~n",[LGround]), %format("Known IDs: ~q~n",[LBasic]), ((recover_grounding_id(ID,GID),grounding_is_known(Decision,GID)) -> % original fact was non-ground true ; % original fact was ground decision_fact(ID,Decision) ). % Finding all decision IDs used in proofs dtproblog_decision_ids(Decisions) :- (dtproblog_utility_attributes(UtilityAttrs) -> dtproblog_decision_ids(UtilityAttrs,Decisions) ; Decisions = [] ). dtproblog_decision_ids(UtilityAttrs,Decisions) :- require(keep_ground_ids), problog_control(on,find_decisions), reset_decisions, add_decisions_all(UtilityAttrs), unrequire(keep_ground_ids), reset_non_ground_facts, get_decisions(Decisions), problog_control(off,find_decisions), reset_decisions. % TODO generalize so that it works with every inference method, not just exact. add_decisions_all([]) :- clear_tabling. add_decisions_all([Goal|R]) :- add_decisions(Goal), add_decisions_all(R). % UGLY - needs to actually build tries for tabling to work. % TODO change tabling.yap to do nothing when problog_control(on,find_decisions) % then, simplify this predicate so that it doesn't build tries % setting problog_control(on,mc) might work, but will maybe prune some decisions away? add_decisions(Goal) :- problog_control(on, exact), build_trie(exact, Goal, Trie), delete_ptree(Trie), problog_control(off, exact). reset_decisions :- bb_put(problog:decisions,[]). get_decisions(D) :- bb_get(problog:decisions,D). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Strategy optimization % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dtproblog_solve(Strategy,EV) :- (dtproblog_solve_specialized_supported -> % try to go specialized dtproblog_solve_specialized(Strategy,EV) ; format('Flag settings not supported by specialized solution algorithm.~nTrying general purpose version.~n',[]), (dtproblog_solve_general_supported -> % try to go general dtproblog_solve_general(Strategy,EV) ; throw(error('Flag settings not supported by dtproblog_solve/2.')) ) ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Strategy optimization (specialized in BDD) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dtproblog_solve_specialized(Strategy,EV) :- (dtproblog_solve_specialized_supported -> require(keep_ground_ids), dtproblog_utility_facts(UtilFacts), conditioned_utility_facts(UtilFacts,true,Goals,Utilities), write_util_file(Utilities), problog_bdd_forest(Goals), length(Goals,N), bdd_optimization(N,EV,DecisionIDs,ok), (problog_flag(save_bdd,true) -> true ; delete_util_file ), strategy_as_term_list(DecisionIDs,Strategy), unset_strategy(Strategy), % was set by bdd_optimization/4 require(keep_ground_ids), reset_non_ground_facts ; throw(error('Flag settings not supported by dtproblog_solve_specialized/2.')) ). dtproblog_solve_specialized_supported :- problog_bdd_forest_supported, ( problog_flag(forest_type, dependent) ; problog_flag(optimization, local) ). % Write a utility file, with for every utility attribute BDD, its reward value on a new line write_util_file(Utils) :- bdd_util_file(UtilFile), open(UtilFile,'write',UtilFileStream), tell(UtilFileStream), length(Utils,N), format("~w~n",[N]), write_util_file_line(Utils), flush_output, told. write_util_file_line([]). write_util_file_line([U|R]) :- format("~w~n",[U]), write_util_file_line(R). bdd_util_file(UtilFile) :- problog_flag(bdd_file,BDDFileFlag), atomic_concat([BDDFileFlag,'_',utils],UtilFileName), convert_filename_to_working_path(UtilFileName, UtilFile). delete_util_file :- bdd_util_file(UtilFile), delete_file(UtilFile,[]). bdd_optimization(N,EV,Decisions,Status) :- bdd_files(BDDFile,BDDParFile), problog_flag(bdd_time,BDDTime), (problog_flag(dynamic_reorder, true) -> ParamD = '' ; ParamD = ' -dreorder'), (problog_flag(bdd_static_order, true) -> problog_flag(static_order_file, FileName), convert_filename_to_working_path(FileName, SOFileName), atomic_concat([ParamD, ' -sord ', SOFileName], Param) ; Param = ParamD ), convert_filename_to_problog_path('problogbdd', ProblogBDD), problog_flag(bdd_result,ResultFileFlag), convert_filename_to_working_path(ResultFileFlag, ResultFile), bdd_util_file(UtilFile), (problog_flag(optimization,local) -> LocalPar = ' -lo';LocalPar = ''), (problog_flag(forest_type,independent) -> Forest = ' -if';Forest = ''), %(problog_flag(verbose,true) -> Debug = ' -d';Debug = ''), % messes up result parsing atomic_concat([ProblogBDD, Param, ' -l ',BDDFile,' -i ',BDDParFile,' -u ',UtilFile,' -m s',LocalPar,Forest,' -t ', BDDTime,' > ', ResultFile],Command), statistics(walltime,_), % format(user,'$ ~w~n',[Command]), 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(expected_value(EV)), read_strategy(Decisions), seen, Status = ok, % cleanup (problog_flag(save_bdd,true) -> true ; delete_file(BDDFile,[]), delete_file(BDDParFile,[]), delete_file(ResultFile,[]), delete_bdd_forest_files(N) ) ). % set the strategy in the internal format and returns a list of all decisions read_strategy(_) :- problog_control(check,internal_strategy), throw(error('A strategy is already set, unset first.')). read_strategy(DecisionIDs) :- problog_control(on,internal_strategy), read_strategy_intern(DecisionIDs). read_strategy_intern(DecisionIDs) :- read(T), (T = end_of_file -> DecisionIDs = [] ; T = strategy(ID,Prob), logprob_prob(LProb,Prob), set_ground_strategy(ID,LProb), DecisionIDs = [ID|Rest], read_strategy_intern(Rest) ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Strategy optimization (general purpose) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dtproblog_solve_general(Strategy,EV) :- (dtproblog_solve_general_supported -> dtproblog_utility_facts(UtilFacts), dtproblog_solve_local(true,UtilFacts,Strategy,EV) ; throw(error('Flag settings not supported by dtproblog_solve_specialized/2.')) ). dtproblog_solve_general_supported :- problog_flag(optimization, local). dtproblog_solve_local(Condition,Utils,Strategy,EV) :- require(keep_ground_ids), facts_to_attributes(Utils,Attrs), dtproblog_decision_ids(Attrs,DecisionIDs), problog_control(on,internal_strategy), % consider strategy set, even though everything is default ev_for_internal_strategy(Condition,Utils,EvStart), optimization_iteration_loop(DecisionIDs,Condition,Utils,EvStart,EV), strategy_as_term_list(DecisionIDs,Strategy), unset_strategy(Strategy), unrequire(keep_ground_ids), reset_non_ground_facts. optimization_iteration_loop(Decisions,Condition,Utils,EVIn,EVOut) :- optimization_decision_loop(Decisions,Condition,Utils,EVIn,EVTemp), strategy_as_term_list(Decisions,Strategy), (problog_flag(verbose,true) -> format("Found strategy ~q with EV=~q~n",[Strategy,EVTemp]);true), (EVIn == EVTemp -> EVOut = EVTemp ; optimization_iteration_loop(Decisions,Condition,Utils,EVTemp,EVOut) ). optimization_decision_loop([],_,_,Ev,Ev). optimization_decision_loop([ID|Rest],Condition,Utils,EvIn,EvOut) :- get_ground_strategy(ID,ProbBefore), flip(ProbBefore, ProbAfter), set_ground_strategy(ID,ProbAfter), ev_for_internal_strategy(Condition,Utils,EvTest), (EvTest>EvIn -> EvTemp = EvTest, (problog_flag(verbose,true) -> format("Changing strategy for #~q to ~q for EV of ~q~n",[ID,ProbAfter,EvTest]);true) ; EvTemp = EvIn, set_ground_strategy(ID,ProbBefore), (problog_flag(verbose,true) -> format("Keeping strategy for #~q at ~q because EV is ~q~n",[ID,ProbBefore,EvTest]);true) ), optimization_decision_loop(Rest,Condition,Utils,EvTemp,EvOut). flip(always,never) :- !. flip(never,always) :- !. flip(P,always) :- P<1, !. flip(_,never). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Naive Search %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dtproblog_solve_naive(Strategy,EV) :- require(keep_ground_ids), dtproblog_decisions(Decisions), all_subsets(Decisions,Strategies), max_strategy(Strategies,[],-inf,Strategy,EV), unrequire(keep_ground_ids), reset_non_ground_facts. max_strategy([],Strategy,EV,Strategy,EV). max_strategy([S1|Rest],S2,U2,S3,U3) :- dtproblog_ev(S1,true,U1), %format("EV of ~q is ~q~n",[S1,U1]), (U1>U2 -> max_strategy(Rest,S1,U1,S3,U3) ; max_strategy(Rest,S2,U2,S3,U3) ). % List of all sublists all_subsets([], [[]]). all_subsets([X|Xs], Subsets) :- all_subsets(Xs, Subsets1), attach_first_element(Subsets1, X, Subsets, Subsets1). attach_first_element([], _, S, S). attach_first_element([Sub|Subs], X, [[X|Sub]|XSubs], S) :- attach_first_element(Subs, X, XSubs, S).