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In the car industry you have thousand of different variants of components available to choose from when you buy a car. Not every component is combinable, so for each car there exist a lot of rules that are expressed in propositional logic. In my case each car has between 2000 and 4000 rules.

They look like this:

  1. A → B ∨ C ∨ D
  2. C → ¬F
  3. F ∧ G → D
  4. ...

where "∧" = "and" / "∨" = "or" / "¬" = "not" / "→" = "implication".

With the tool "limboole" (http://fmv.jku.at/limboole/) I am able to to convert the propositional logic expressions into conjunctive normal form (CNF). This is needed in case I have to use a SAT solver.

Now, I would like to check the buildability feasibility for specific components within the rule set. For example, for each of the following expressions or combinations, I would like to check if the are feasible within the rule set.

  1. (A) ∧ (B)
  2. (A) ∧ (C ∨ F)
  3. (B ∨ G)
  4. ...

My question is how to solve this problem. I asked a similar questions before (Tool to solve propositional logic / boolean expressions (SAT Solver?)), but with a different focus and now I am stuck again. Or I just do not understand it.

One option is to calculate all solutions with an ALLSAT approach of the rule set. Then I could check if each combination is part of any solution. If yes, I can derive that this specific combination is feasible.

Another option would be, that I add the combination to the rule set and then run a normal SAT solver. But I would have to do it for each expression I want to check.

What do you think is the most elegant or rather easiest way to solve this problem?

Olaf_SQL
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  • Have you tried using an SMT solver out of the box? They present a much nicer interface to program with, and in your case they should perform just about as good as a SAT solver. – alias Mar 10 '18 at 18:51

1 Answers1

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The best method which is known to me is to use "incremental solving under assumptions" technique. It was motivated by the same problem you have: multiple SAT instances (CNF formulae) which have some common subformulae. Formally, you have some core Boolean formula C in CNF. And you have a set of assumptions {A_i}, i=1..n, where A_i is a Boolean formula in CNF also.

On the step 0 you provide to the solver your core formula C. It tries to solve it, says a result to you and save its state (lets call this state as core-state). If formula C is satisfiable, on the step i you provide assumption A_i to the solver and it continues its execution from the core-state. Actually, it tries to solve a formula C ∧ A_i but not from the beginning.

You can find a bunch of papers related to this topic easily, where much information is located. Also, you can check you favorite SAT-solver for the support of this technique.

Ilya Zakirzyanov
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  • I had a quick look and it is exactly what I was looking for! Thank you! But a short question, just to be sure. Using "incremental solving under assumptions" means that each A_i is checked individually with the core formula c, right? – Olaf_SQL Feb 01 '18 at 16:03
  • @Olaf_SQL at each `(check-sat-assuming A_0 ... A_N)` call, the solver checks the satisfiability of the conjunction of all `A_i` for `i` in `0..N` with the core formula `C`. **e.g.** to check `(A) ∧ (C ∨ F)`, you would assign a Boolean label `L_cf` to the clause `C v F`, and then issue the command `(check-sat-assuming A L_cf)`. – Patrick Trentin Feb 01 '18 at 21:57