Skip to content
A repository for paper submission
Branch: master
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Type Name Latest commit message Commit time
Failed to load latest commit information.

Academic Citation

Please cite the following paper when using this tool.

Ibrahim, A., Rehwald, S., Pretschner, A.: Efficiently checking actual causality with sat solving. In: Dependable Software Systems Engineering (2019),

@incollection{ibrahim2019, author={Ibrahim, Amjad and Rehwald, Simon and Pretschner, Alexander}, title = {Efficiently Checking Actual Causality with SAT Solving}, booktitle = {Dependable Software Systems Engineering}, year = {2019}, url ={}, }


Build Status


This library allows to determine actual causality according to the modified Halpern-Pearl definition of causality [1] . The used examples in the unit test cases (specifically in CausalitySolverInstanceTest) are described here.


Currently, this library is not published in a Maven repository. Please build it manually from source:

$ mvn install

Then, you can import it using Maven:


Alternatively, a pre-built .jar is offered in the release section of this repository.



Creation of a causal model

// instantiate a new FormulaFactory
FormulaFactory f = new FormulaFactory();

// create exogenous variables; using _exo is not required, but used to distinguish them
Variable BTExo = f.variable("BT_exo");
Variable STExo = f.variable("ST_exo");

// create endogenous variables; technically, there is no difference to exogenous ones
Variable BT = f.variable("BT");
Variable ST = f.variable("ST");
Variable BH = f.variable("BH");
Variable SH = f.variable("SH");
Variable BS = f.variable("BS");

// create the formula/function for each endogenous variable
Formula BTFormula = BTExo;
Formula STFormula = STExo;
Formula SHFormula = ST;
Formula BHFormula = f.and(BT, f.not(SH));
Formula BSFormula = f.or(SH, BH);

// create the equations of the causal model: each endogenous variable and its formula form an equation
Equation BTEquation = new Equation(BT, BTFormula);
Equation STEquation = new Equation(ST, STFormula);
Equation SHEquation = new Equation(SH, SHFormula);
Equation BHEquation = new Equation(BH, BHFormula);
Equation BSEquation = new Equation(BS, BSFormula);

Set<Equation> equations = new HashSet<>(Arrays.asList(BTEquation, STEquation, SHEquation,
    BHEquation, BSEquation));
Set<Variable> exogenousVariables = new HashSet<>(Arrays.asList(BTExo, STExo));

// instantiate the CausalModel
CausalModel causalModel = new CausalModel("RockThrowing", equations, exogenousVariables, f);

Check whether ST = 1 is a cause of BS = 1 in the previously created causal model given ST_exo, BT_exo = 1 as context

// IMPORTANT: Use the same FormulaFactory instance as in the above!

 * Create positive literals for ST_exo and BT_exo. If ST_exo, BT_exo = 0, we would create negative ones,
 * e.g. f.literal("ST_exo", false). Using f.variable("ST_exo") would be a shortcut for f.literal("ST_exo", true)
Set<Literal> context = new HashSet<>(Arrays.asList(f.literal("BT_exo", true),
    f.literal("ST_exo", true)));

 * Similar as for the context, we specify f.literal("ST", true) as cause and f.variable("BS") as phi, as we 
 * want to express ST = 1 and BS = 1, respectively.
Set<Literal> cause = new HashSet<>(Collections.singletonList(f.literal("ST", true)));
Formula phi = f.variable("BS");

// finally, call isCause on the causal model using the SAT-based algorithm
CausalitySolverResult causalitySolverResult =
    CauscausalModel.isCause(context, phi, cause, SolvingStrategy.SAT);

Use other algorithms

The SolvingStrategy enum contains all currently supported algorithms/strategies:

public enum SolvingStrategy {

Just call the isCause-method with the respective SolvingStrategy:

// Brute-Force
CausalitySolverResult causalitySolverResult =
    CauscausalModel.isCause(context, phi, cause, SolvingStrategy.BRUTE_FORCE);

// SAT-based
CausalitySolverResult causalitySolverResult =
    CauscausalModel.isCause(context, phi, cause, SolvingStrategy.SAT);

// SAT-based returning a minimal W for AC2
CausalitySolverResult causalitySolverResult =
    CauscausalModel.isCause(context, phi, cause, SolvingStrategy.SAT_MINIMAL);

// SAT-based where checking AC2 and AC3 is combined
CausalitySolverResult causalitySolverResult =
    CauscausalModel.isCause(context, phi, cause, SolvingStrategy.SAT_COMBINED);

// SAT-based where AC3 check does not require ALL-SAT
CausalitySolverResult causalitySolverResult =
    CauscausalModel.isCause(context, phi, cause, SolvingStrategy.SAT_OPTIMIZED_AC3);

Important Notes

  • When working with a causal model, always use the same FormulaFactory instance. If not, an exception might occur.
  • When creating a CausalModel, it is checked whether the latter is valid. It needs to fulfill the following characteristics; otherwise an exception is thrown:
    • Each variable needs to be either exogenous or defined by exactly one equation.
    • The causal model must be acyclic. That is, no variables are allowed to mutually depend on each other (directly and indirectly)
    • Variables must not be named with "_dummy".


[1] J. Y. Halpern. "A Modification of the Halpern-Pearl Definition of Causality." In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015. 2015, pp. 3022–3033.

You can’t perform that action at this time.