diff --git a/pymc/logprob/binary.py b/pymc/logprob/binary.py
index d9aeb3b57d..6ad0925025 100644
--- a/pymc/logprob/binary.py
+++ b/pymc/logprob/binary.py
@@ -19,9 +19,9 @@
 from pytensor.graph.basic import Node
 from pytensor.graph.fg import FunctionGraph
 from pytensor.graph.rewriting.basic import node_rewriter
-from pytensor.scalar.basic import GE, GT, LE, LT
+from pytensor.scalar.basic import GE, GT, LE, LT, Invert
 from pytensor.tensor import TensorVariable
-from pytensor.tensor.math import ge, gt, le, lt
+from pytensor.tensor.math import ge, gt, invert, le, lt
 
 from pymc.logprob.abstract import (
     MeasurableElemwise,
@@ -136,3 +136,57 @@ def comparison_logprob(op, values, base_rv, operand, **kwargs):
         logcdf.name = f"{base_rv_op}_logcdf"
 
     return logprob
+
+
+class MeasurableBitwise(MeasurableElemwise):
+    """A placeholder used to specify a log-likelihood for a bitwise operation RV sub-graph."""
+
+    valid_scalar_types = (Invert,)
+
+
+@node_rewriter(tracks=[invert])
+def find_measurable_bitwise(fgraph: FunctionGraph, node: Node) -> Optional[List[MeasurableBitwise]]:
+    rv_map_feature = getattr(fgraph, "preserve_rv_mappings", None)
+    if rv_map_feature is None:
+        return None  # pragma: no cover
+
+    if isinstance(node.op, MeasurableBitwise):
+        return None  # pragma: no cover
+
+    base_var = node.inputs[0]
+    if not (
+        base_var.owner
+        and isinstance(base_var.owner.op, MeasurableVariable)
+        and base_var not in rv_map_feature.rv_values
+    ):
+        return None
+
+    if not base_var.dtype.startswith("bool"):
+        raise None
+
+    # Make base_var unmeasurable
+    unmeasurable_base_var = ignore_logprob(base_var)
+
+    node_scalar_op = node.op.scalar_op
+
+    bitwise_op = MeasurableBitwise(node_scalar_op)
+    bitwise_rv = bitwise_op.make_node(unmeasurable_base_var).default_output()
+    bitwise_rv.name = node.outputs[0].name
+    return [bitwise_rv]
+
+
+measurable_ir_rewrites_db.register(
+    "find_measurable_bitwise",
+    find_measurable_bitwise,
+    "basic",
+    "bitwise",
+)
+
+
+@_logprob.register(MeasurableBitwise)
+def bitwise_not_logprob(op, values, base_rv, **kwargs):
+    (value,) = values
+
+    logprob = _logprob_helper(base_rv, invert(value), **kwargs)
+
+    return logprob
diff --git a/tests/logprob/test_binary.py b/tests/logprob/test_binary.py
index 6f2248075c..1a91abdd6f 100644
--- a/tests/logprob/test_binary.py
+++ b/tests/logprob/test_binary.py
@@ -33,7 +33,7 @@
         ((pt.gt, pt.ge), "logcdf", "logsf", (0.5, pt.random.normal(0, 1))),
     ],
 )
-def test_continuous_rv_comparison(comparison_op, exp_logp_true, exp_logp_false, inputs):
+def test_continuous_rv_comparison_bitwise(comparison_op, exp_logp_true, exp_logp_false, inputs):
     for op in comparison_op:
         comp_x_rv = op(*inputs)
 
@@ -48,6 +48,17 @@ def test_continuous_rv_comparison(comparison_op, exp_logp_true, exp_logp_false,
         assert np.isclose(logp_fn(0), getattr(ref_scipy, exp_logp_false)(0.5))
         assert np.isclose(logp_fn(1), getattr(ref_scipy, exp_logp_true)(0.5))
 
+        bitwise_rv = pt.bitwise_not(op(*inputs))
+        bitwise_vv = bitwise_rv.clone()
+
+        logprob_not = logp(bitwise_rv, bitwise_vv)
+        assert_no_rvs(logprob_not)
+
+        logp_fn_not = pytensor.function([bitwise_vv], logprob_not)
+
+        assert np.isclose(logp_fn_not(0), getattr(ref_scipy, exp_logp_true)(0.5))
+        assert np.isclose(logp_fn_not(1), getattr(ref_scipy, exp_logp_false)(0.5))
+
 
 @pytest.mark.parametrize(
     "comparison_op, exp_logp_true, exp_logp_false, inputs",
@@ -87,7 +98,7 @@ def test_continuous_rv_comparison(comparison_op, exp_logp_true, exp_logp_false,
         ),
     ],
 )
-def test_discrete_rv_comparison(inputs, comparison_op, exp_logp_true, exp_logp_false):
+def test_discrete_rv_comparison_bitwise(inputs, comparison_op, exp_logp_true, exp_logp_false):
     cens_x_rv = comparison_op(*inputs)
 
     cens_x_vv = cens_x_rv.clone()
@@ -100,6 +111,17 @@ def test_discrete_rv_comparison(inputs, comparison_op, exp_logp_true, exp_logp_f
     assert np.isclose(logp_fn(1), exp_logp_true(3))
     assert np.isclose(logp_fn(0), exp_logp_false(3))
 
+    bitwise_rv = pt.bitwise_not(comparison_op(*inputs))
+    bitwise_vv = bitwise_rv.clone()
+
+    logprob_not = logp(bitwise_rv, bitwise_vv)
+    assert_no_rvs(logprob_not)
+
+    logp_fn_not = pytensor.function([bitwise_vv], logprob_not)
+
+    assert np.isclose(logp_fn_not(1), exp_logp_false(3))
+    assert np.isclose(logp_fn_not(0), exp_logp_true(3))
+
 
 def test_potentially_measurable_operand():
     x_rv = pt.random.normal(2)