diff --git a/vortex-array/Cargo.toml b/vortex-array/Cargo.toml
index de3bb416985..6e8e917bf74 100644
--- a/vortex-array/Cargo.toml
+++ b/vortex-array/Cargo.toml
@@ -129,6 +129,10 @@ harness = false
 name = "binary_ops"
 harness = false
 
+[[bench]]
+name = "kleene_bool"
+harness = false
+
 [[bench]]
 name = "interleave"
 harness = false
diff --git a/vortex-array/benches/kleene_bool.rs b/vortex-array/benches/kleene_bool.rs
new file mode 100644
index 00000000000..babd859cec5
--- /dev/null
+++ b/vortex-array/benches/kleene_bool.rs
@@ -0,0 +1,230 @@
+// SPDX-License-Identifier: Apache-2.0
+// SPDX-FileCopyrightText: Copyright the Vortex contributors
+
+#![expect(clippy::unwrap_used)]
+
+use std::sync::LazyLock;
+
+use divan::Bencher;
+use divan::counter::ItemsCount;
+use vortex_array::ArrayRef;
+use vortex_array::Columnar;
+use vortex_array::IntoArray;
+use vortex_array::VortexSessionExecute;
+use vortex_array::arrays::BoolArray;
+use vortex_array::arrays::ConstantArray;
+use vortex_array::arrow::ArrowSession;
+use vortex_array::builtins::ArrayBuiltins;
+use vortex_array::dtype::DType;
+use vortex_array::dtype::Nullability;
+use vortex_array::scalar::Scalar;
+use vortex_array::scalar_fn::fns::operators::Operator;
+use vortex_array::session::ArraySession;
+use vortex_session::VortexSession;
+
+fn main() {
+    divan::main();
+}
+
+static SESSION: LazyLock<VortexSession> = LazyLock::new(|| {
+    VortexSession::empty()
+        .with::<ArraySession>()
+        .with::<ArrowSession>()
+});
+
+const LEN: usize = 65_536;
+const SHIFTED_OFFSET: usize = 1;
+
+#[divan::bench]
+fn and_bool_nonnull_arrays(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nonnull(2).into_array(),
+        bool_nonnull(3).into_array(),
+        Operator::And,
+    );
+}
+
+#[divan::bench]
+fn or_bool_nonnull_arrays(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nonnull(2).into_array(),
+        bool_nonnull(3).into_array(),
+        Operator::Or,
+    );
+}
+
+#[divan::bench]
+fn and_bool_nullable_arrays(bencher: Bencher) {
+    and_bool_nullable_arrays_aligned(bencher);
+}
+
+#[divan::bench]
+fn and_bool_nullable_arrays_aligned(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, 0),
+        bool_nullable(3, 5, 0),
+        Operator::And,
+    );
+}
+
+#[divan::bench]
+fn or_bool_nullable_arrays(bencher: Bencher) {
+    or_bool_nullable_arrays_aligned(bencher);
+}
+
+#[divan::bench]
+fn or_bool_nullable_arrays_aligned(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, 0),
+        bool_nullable(3, 5, 0),
+        Operator::Or,
+    );
+}
+
+#[divan::bench]
+fn and_bool_nullable_arrays_shifted(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, SHIFTED_OFFSET),
+        bool_nullable(3, 5, SHIFTED_OFFSET),
+        Operator::And,
+    );
+}
+
+#[divan::bench]
+fn or_bool_nullable_arrays_shifted(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, SHIFTED_OFFSET),
+        bool_nullable(3, 5, SHIFTED_OFFSET),
+        Operator::Or,
+    );
+}
+
+#[divan::bench]
+fn and_true_constant(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, 0),
+        ConstantArray::new(true, LEN).into_array(),
+        Operator::And,
+    );
+}
+
+#[divan::bench]
+fn or_false_constant(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, 0),
+        ConstantArray::new(false, LEN).into_array(),
+        Operator::Or,
+    );
+}
+
+#[divan::bench]
+fn and_false_constant(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, 0),
+        ConstantArray::new(false, LEN).into_array(),
+        Operator::And,
+    );
+}
+
+#[divan::bench]
+fn or_true_constant(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, 0),
+        ConstantArray::new(true, LEN).into_array(),
+        Operator::Or,
+    );
+}
+
+#[divan::bench]
+fn and_null_constant(bencher: Bencher) {
+    and_null_constant_aligned(bencher);
+}
+
+#[divan::bench]
+fn and_null_constant_aligned(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, 0),
+        null_bool_constant(),
+        Operator::And,
+    );
+}
+
+#[divan::bench]
+fn or_null_constant(bencher: Bencher) {
+    or_null_constant_aligned(bencher);
+}
+
+#[divan::bench]
+fn or_null_constant_aligned(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, 0),
+        null_bool_constant(),
+        Operator::Or,
+    );
+}
+
+#[divan::bench]
+fn and_null_constant_shifted(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, SHIFTED_OFFSET),
+        null_bool_constant(),
+        Operator::And,
+    );
+}
+
+#[divan::bench]
+fn or_null_constant_shifted(bencher: Bencher) {
+    bench_kleene(
+        bencher,
+        bool_nullable(2, 7, SHIFTED_OFFSET),
+        null_bool_constant(),
+        Operator::Or,
+    );
+}
+
+fn bench_kleene(bencher: Bencher, lhs: ArrayRef, rhs: ArrayRef, operator: Operator) {
+    let mut ctx = SESSION.create_execution_ctx();
+
+    bencher.counter(ItemsCount::new(LEN)).bench_local(|| {
+        lhs.clone()
+            .binary(rhs.clone(), operator)
+            .unwrap()
+            .execute::<Columnar>(&mut ctx)
+            .unwrap()
+    });
+}
+
+fn bool_nonnull(true_every: usize) -> BoolArray {
+    BoolArray::from_iter((0..LEN).map(|i| i.is_multiple_of(true_every)))
+}
+
+fn bool_nullable(true_every: usize, null_every: usize, offset: usize) -> ArrayRef {
+    let len = LEN + offset;
+    let array = BoolArray::from_iter(
+        (0..len).map(|i| (!i.is_multiple_of(null_every)).then_some(i.is_multiple_of(true_every))),
+    )
+    .into_array();
+
+    if offset == 0 {
+        array
+    } else {
+        array.slice(offset..offset + LEN).unwrap()
+    }
+}
+
+fn null_bool_constant() -> ArrayRef {
+    ConstantArray::new(Scalar::null(DType::Bool(Nullability::Nullable)), LEN).into_array()
+}