Problog互斥性咨询：带特殊箱子的多存储空间分配建模问题

Got it, let's walk through how to model your storage and bin scenario step-by-step in ProbLog. First, let's recap the key rules we need to enforce:

• We have 4 distinct storage spaces (I'll name them s1 to s4 for clarity)
• Bins b1-b4 can only be assigned to at most one storage space (mutually exclusive), while b5 is special and can be used across multiple storages at once
• Each bin has an assignment probability (note: you didn't finish b4's probability, so I'll use P_b4 as a placeholder—swap this with your actual value later; same for b5's probability, marked as P_b5)
• Every bin has a weight, which we can use later for queries like expected total weight

1. Define Base Facts #

First, let's lay down the foundational facts for our storages, bin weights, and assignment probabilities:

% List out all 4 storage spaces
storage(s1).
storage(s2).
storage(s3).
storage(s4).

% Define the weight for each bin
weight(b1, 4).
weight(b2, 6).
weight(b3, 5).
weight(b4, 6).
weight(b5, 5).

% Assignment probability facts: bin -> storage
% b1 has a 100% assignment chance to any storage
1.0::assign(b1, S) :- storage(S).
% b2 has a 60% assignment chance
0.6::assign(b2, S) :- storage(S).
% b3 has a 100% assignment chance
1.0::assign(b3, S) :- storage(S).
% b4: replace P_b4 with your actual probability value (e.g., 0.8)
P_b4::assign(b4, S) :- storage(S).
% b5: replace P_b5 with your actual probability value
P_b5::assign(b5, S) :- storage(S).

2. Add Mutex Constraints (For b1-b4) #

The critical part is enforcing that b1-b4 can't be assigned to multiple storages at once. We do this with ProbLog's constraint rules:

% Prevent b1 from being assigned to two different storages
:- assign(b1, S1), assign(b1, S2), S1 \= S2.

% Prevent b2 from being assigned to two different storages
:- assign(b2, S1), assign(b2, S2), S1 \= S2.

% Prevent b3 from being assigned to two different storages
:- assign(b3, S1), assign(b3, S2), S1 \= S2.

% Prevent b4 from being assigned to two different storages
:- assign(b4, S1), assign(b4, S2), S1 \= S2.

Important: We don't add this constraint for b5—that's how we let it be used across multiple storages freely.

3. Example Queries to Test the Model #

Once the model is set up, you can run all sorts of useful queries. Here are a few common ones:

Query 1: Probability that storage s1 is filled by b2 #

query(assign(b2, s1)).

Query 2: Expected total weight of all assigned bins #

First, define a rule to calculate total weight, then query its expected value:

total_weight(Total) :-
    findall(Weight, (assign(Bin, _), weight(Bin, Weight)), Weights),
    sum_list(Weights, Total).

query(total_weight(Total)).

Query 3: Probability that b1 is assigned to any storage space #

Since b1 has a 100% assignment chance, this should return 1.0, but it's a good sanity check:

query((assign(b1, s1); assign(b1, s2); assign(b1, s3); assign(b1, s4))).

Optional: Enforce "Every Storage Has At Least One Bin" #

If you need to make sure no storage is left empty, add this constraint (it filters out any scenario where a storage has no bins assigned):

:- storage(S), \+ (assign(Bin, S), member(Bin, [b1,b2,b3,b4,b5])).

Just remember to swap out the placeholder probabilities (P_b4, P_b5) with your actual values before running the model!

内容的提问来源于stack exchange，提问作者B.Cetindag