diff --git a/explainability/src/explain/why/mod.rs b/explainability/src/explain/why/mod.rs
new file mode 100644
index 00000000..464c788f
--- /dev/null
+++ b/explainability/src/explain/why/mod.rs
@@ -0,0 +1 @@
+mod unsat;
diff --git a/explainability/src/explain/why/unsat.rs b/explainability/src/explain/why/unsat.rs
new file mode 100644
index 00000000..74a78336
--- /dev/null
+++ b/explainability/src/explain/why/unsat.rs
@@ -0,0 +1,211 @@
+use std::collections::{BTreeMap, BTreeSet};
+use std::sync::Arc;
+
+use aries::core::Lit;
+use aries::model::{Label, Model};
+
+use crate::explain::explanation::{
+    EssenceIndex, ExplEssence, ExplSubstance, Explanation, ExplanationFilter, ModelIndex, SubstanceIndex,
+};
+use crate::explain::presupposition::{check_presupposition, Presupposition, PresuppositionKind, UnmetPresupposition};
+use crate::explain::{Query, Question, Situation, Vocab};
+use crate::musmcs_enumeration::marco::simple_marco::SimpleMarco;
+use crate::musmcs_enumeration::marco::Marco;
+use crate::musmcs_enumeration::MusMcsEnumerationConfig;
+
+pub struct QwhyUnsat<Lbl> {
+    model: Arc<Model<Lbl>>,
+    situ: Situation,
+    query: Query,
+    vocab: Vocab,
+}
+
+impl<Lbl: Label> Question<Lbl> for QwhyUnsat<Lbl> {
+    fn check_presuppositions(&mut self) -> Result<(), UnmetPresupposition<Lbl>> {
+        let mut model = (*self.model).clone();
+        model.enforce_all(self.vocab.iter().cloned(), []);
+        let model = Arc::new(model);
+        check_presupposition(
+            Presupposition {
+                kind: PresuppositionKind::ModelSituUnsatWithQuery,
+                model,
+                situ: self.situ.clone(),
+                query: self.query.clone(),
+            },
+            false,
+            None,
+        )
+    }
+
+    fn compute_explanation(&mut self) -> Explanation<Lbl> {
+        let soft_constrs_reif_lits = [&self.situ[..], &self.query[..]].concat();
+        let mut model = (*self.model).clone();
+        model.enforce_all(self.vocab.iter().cloned(), []);
+        let mut simple_marco = SimpleMarco::<Lbl>::new_with_soft_constrs_reif_lits(
+            model,
+            soft_constrs_reif_lits,
+            MusMcsEnumerationConfig {
+                return_muses: true,
+                return_mcses: false,
+            },
+        );
+        let muses = simple_marco.run().muses.unwrap();
+
+        let mut essences = Vec::<ExplEssence>::new();
+        let mut substances = Vec::<ExplSubstance>::new();
+        let mut table = BTreeMap::<(EssenceIndex, SubstanceIndex), BTreeSet<ModelIndex>>::new();
+        let filter = ExplanationFilter {
+            map: None,
+            default: true,
+        };
+
+        let _situ_set = BTreeSet::from_iter(self.situ.iter().cloned());
+
+        for (mus_idx, mus) in muses.into_iter().enumerate() {
+            essences.push(ExplEssence(
+                mus.difference(&_situ_set).cloned().collect::<BTreeSet<Lit>>(),
+                mus.intersection(&_situ_set).cloned().collect::<BTreeSet<Lit>>(),
+            ));
+            let mut model = (*self.model).clone();
+            model.enforce_all(mus, []);
+            let mut simple_marco = SimpleMarco::<Lbl>::new_with_soft_constrs_reif_lits(
+                model,
+                self.vocab.clone(),
+                MusMcsEnumerationConfig {
+                    return_muses: false,
+                    return_mcses: true,
+                },
+            );
+            let mcses = simple_marco.run().mcses.unwrap();
+            for mcs in mcses {
+                let sub = ExplSubstance::Modelling(mcs);
+                let sub_idx = substances.iter().position(|s| s == &sub);
+                match sub_idx {
+                    Some(i) => table.insert((mus_idx, i), BTreeSet::from_iter([0])),
+                    None => {
+                        substances.push(sub);
+                        table.insert((mus_idx, substances.len() - 1), BTreeSet::from_iter([0]))
+                    }
+                };
+            }
+        }
+
+        Explanation {
+            models: vec![self.model.clone()],
+            essences,
+            substances,
+            table,
+            filter,
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+
+    use std::collections::{BTreeMap, BTreeSet, HashSet};
+    use std::sync::Arc;
+
+    use aries::core::{Lit, INT_CST_MAX, INT_CST_MIN};
+    use aries::model::lang::expr::{and, implies};
+    use aries::model::lang::linear::LinearSum;
+
+    use crate::explain::explanation::{ExplEssence, ExplSubstance};
+
+    use super::Question;
+
+    type Model = aries::model::Model<String>;
+    type QwhyUnsat = super::QwhyUnsat<String>;
+
+    #[test]
+    fn test_qwhy_unsat() {
+        let mut model = Model::new();
+
+        let p_a = model.new_presence_variable(Lit::TRUE, "p_a").true_lit();
+        let p_b = model.new_presence_variable(Lit::TRUE, "p_b").true_lit();
+        let p_c = model.new_presence_variable(Lit::TRUE, "p_c").true_lit();
+        let p_d = model.new_presence_variable(Lit::TRUE, "p_d").true_lit();
+        let p_e = model.new_presence_variable(Lit::TRUE, "p_e").true_lit();
+
+        let a = model.new_ivar(0, INT_CST_MAX, "a");
+        let b = model.new_ivar(0, INT_CST_MAX, "b");
+        let c = model.new_ivar(0, INT_CST_MAX, "c");
+        let d = model.new_ivar(0, INT_CST_MAX, "d");
+        let e = model.new_ivar(0, INT_CST_MAX, "e");
+
+        let voc = vec![
+            model.new_presence_variable(Lit::TRUE, "a=1").true_lit(),
+            model.new_presence_variable(Lit::TRUE, "b=2").true_lit(),
+            model.new_presence_variable(Lit::TRUE, "d=3").true_lit(),
+            model.new_presence_variable(Lit::TRUE, "e=0").true_lit(),
+            model.new_presence_variable(Lit::TRUE, "cost<=5").true_lit(),
+        ];
+
+        let expr = and([model.reify(implies(p_a, a.leq(1))), model.reify(implies(p_a, a.geq(1)))]);
+        model.enforce(expr, [voc[0]]);
+        let expr = and([model.reify(implies(p_b, b.leq(2))), model.reify(implies(p_b, b.geq(2)))]);
+        model.enforce(expr, [voc[1]]);
+        let expr = and([model.reify(implies(p_c, c.leq(1))), model.reify(implies(p_c, c.geq(1)))]);
+        model.enforce(expr, []);
+        let expr = and([model.reify(implies(p_d, d.leq(3))), model.reify(implies(p_d, d.geq(3)))]);
+        model.enforce(expr, [voc[2]]);
+        let expr = and([model.reify(implies(p_e, e.leq(0))), model.reify(implies(p_e, e.geq(0)))]);
+        model.enforce(expr, [voc[3]]);
+
+        let r = model.new_ivar(INT_CST_MIN, 0, "r");
+        model.enforce(and([r.leq(-5), r.geq(-5)]), [voc[4]]);
+
+        let total_weight = LinearSum::of(vec![a, b, c, d, e, r]);
+        model.enforce(total_weight.leq(0), []);
+
+        let mut question = QwhyUnsat {
+            model: Arc::new(model),
+            situ: vec![p_d, p_e],
+            query: vec![p_a, p_b, p_c],
+            vocab: voc.clone(),
+        };
+
+        let expl = question.try_answer().unwrap();
+
+        let essences: HashSet<ExplEssence> = expl.essences.into_iter().collect::<HashSet<_>>();
+        debug_assert_eq!(
+            essences,
+            HashSet::from_iter([
+                ExplEssence(BTreeSet::from_iter([p_a, p_b]), BTreeSet::from_iter([p_d])),
+                ExplEssence(BTreeSet::from_iter([p_b, p_c]), BTreeSet::from_iter([p_d])),
+            ]),
+        );
+
+        let substances = expl.substances.into_iter().collect::<HashSet<_>>();
+        debug_assert_eq!(
+            substances,
+            HashSet::from_iter([
+                ExplSubstance::Modelling(BTreeSet::from_iter([voc[0]])),
+                ExplSubstance::Modelling(BTreeSet::from_iter([voc[1]])),
+                ExplSubstance::Modelling(BTreeSet::from_iter([voc[2]])),
+                ExplSubstance::Modelling(BTreeSet::from_iter([voc[4]])),
+            ]),
+        );
+
+        let idxe0 = essences.iter().position(|e| *e == ExplEssence(BTreeSet::from_iter([p_a, p_b]), BTreeSet::from_iter([p_d]))).unwrap();
+        let idxe1 = essences.iter().position(|e| *e == ExplEssence(BTreeSet::from_iter([p_b, p_c]), BTreeSet::from_iter([p_d]))).unwrap();
+        let idxs0 = substances.iter().position(|s| *s == ExplSubstance::Modelling(BTreeSet::from_iter([voc[0]]))).unwrap();
+        let idxs1 = substances.iter().position(|s| *s == ExplSubstance::Modelling(BTreeSet::from_iter([voc[1]]))).unwrap();
+        let idxs2 = substances.iter().position(|s| *s == ExplSubstance::Modelling(BTreeSet::from_iter([voc[2]]))).unwrap();
+        let idxs3 = substances.iter().position(|s| *s == ExplSubstance::Modelling(BTreeSet::from_iter([voc[4]]))).unwrap();
+
+        let table = expl.table;
+        debug_assert_eq!(
+            table,
+            BTreeMap::from([
+                ((idxe0, idxs0), BTreeSet::from_iter([0])),
+                ((idxe0, idxs1), BTreeSet::from_iter([0])),
+                ((idxe0, idxs2), BTreeSet::from_iter([0])),
+                ((idxe0, idxs3), BTreeSet::from_iter([0])),
+                ((idxe1, idxs1), BTreeSet::from_iter([0])),
+                ((idxe1, idxs2), BTreeSet::from_iter([0])),
+                ((idxe1, idxs3), BTreeSet::from_iter([0])),
+            ]),
+        );
+    }
+}