Resin — Reactive Signal Inference

Reactive Knowledge Representation and Asynchronous Reasoning
Simon Kohaut, Benedict Flade, Julian Eggert, Kristian Kersting, Devendra Singh Dhami
Paper · Project Page · Citation

Resin is a probabilistic first-order logic programming language for building reactive inference pipelines over continuous, asynchronous data streams. Resin programs are compiled via Answer Set Programming (ASP) into Reactive Circuits: vectorised, self-adapting computation graphs that perform Algebraic Model Counting (AMC) in real time.

Highlights

• Resin merges probabilistic first-order logic with reactive programming: programs declare asynchronous data streams as sources and query targets over them.
• Reactive Circuits are time-dynamic DAGs over Algebraic Circuits that adapt their own structure to the estimated Frequency of Change of each input, as in the animation above.
• Exact and incremental: inference is partitioned into individually memoized sub-problems, so a new input only re-evaluates the parts of the model it affects.

The core library is written in Rust. A Python package (pyresin) is published to PyPI and built with Maturin.

Installation

For employing Resin with Python, you can install the pre-compiled package via PyPI:

pip install pyresin

To use Resin with Rust, you may clone this repository and build locally with cargo.

The Resin language

A Resin program declares sources (incoming signals), rules (first-order logic), and targets (the quantities to infer).

Source types

Type	Declared with	ASP encoding
Probability	a value in [0, 1]	choice atom {name}.
Boolean	true/false	choice atom {name}.
Density	a continuous distribution	exactly-one choice over the intervals induced by the source's thresholds
Number	a scalar value	exactly-one choice over the intervals induced by the source's thresholds
Categorical	a vector of class probabilities	1 { c₀ ; c₁ ; … } 1. exactly-one constraint

Syntax

Here is an example Resin program for an autonomous aircraft system navigating an urban environment.

# Source declarations
over(park)         <- source("/map/over/park", Probability).
distance(hospital) <- source("/map/distance/hospital", Density).
distance(airport)  <- source("/map/distance/airport", Density).
speed              <- source("/sensor/speed", Number).
flight_hours(w1)   <- source("/metrics/flight_hours/wing_1", Number).
flight_hours(w2)   <- source("/metrics/flight_hours/wing_2", Number).
flight_hours(w3)   <- source("/metrics/flight_hours/wing_3", Number).
flight_hours(w4)   <- source("/metrics/flight_hours/wing_4", Number).
{sunny, raining}   <- source("/weather", Categorical).

# Propositional rules
permitted if over(park) and speed < 25.

# First-order rules
critical_infrastructure(hospital).
critical_infrastructure(airport).
safety_distance(T) if critical_infrastructure(T) and distance(T) > 100.

# Conditional probabilities and Noisy-OR over first-order instantiations
wing(w1). wing(w2). wing(w3). wing(w4).
needs_checkup(W) <- P(0.9) if flight_hours(W) > 100 and wing(W).
any_wing_needs_checkup if needs_checkup(W).

# Target that the program will be constrained on
safe if permitted and safety_distance(T) and not any_wing_needs_checkup and not raining.
safe -> target("/output/safe").

A program may declare several targets, each with its own channel. Every target is solved separately into a DNF over the shared source leaves, and all targets live in one reactive circuit, where adaptation lets them share sub-circuits (see Reactive Circuit adaptation).

Rules supports variables (uppercase arguments, in the example above W, T) and conjunctions (and); disjunctions are implemented through multiple clauses. Comparison literals (<, >) on Number and Density sources (ground atom left, constant literal value right) are derived from the exactly-one interval choice of their source: all thresholds registered for a source partition it into mutually exclusive intervals, so two comparisons on the same source (e.g. s < 20 and s < 30) are never treated as independent. Categorical sources provide probabilities for mutually exclusive ground atoms that are assumed to sum up to 1.

In Python, using the Resin code from above, inference can be run over one of the supported commutative semirings:

from resin import Resin
semiring = "LogProb"  # default, otherwise use boolean, fuzzy, maxproduct, probgradient, or criticalexplanation
resin = Resin.compile(code, value_size=1, semiring=semiring)
result = resin.get_reactive_circuit().update()
# result["/output/safe"] contains resulting value

Semirings

Resin's inference algebra, and thereby the value which is computed per target, is selectable at runtime.
Every Resin program can be evaluated under a different semiring by changing the type parameter S in Resin::<S>::compile(...).

LogProb — standard probabilistic inference (default)

Computes the sum of probabilities of all satisfying worlds.

⊗ = product of probabilities  (log-space: addition)
⊕ = sum of probabilities      (log-space: numerically-stable logsumexp)

MaxProduct — Most Probable Explanation

Computes the single most-likely world.
The sum over minterms becomes a max, so the circuit returns the probability of the highest-weight satisfying assignment rather than the marginal.

⊗ = product   
⊕ = max

Fuzzy — degree of truth

Evaluates the program under Łukasiewicz / Zadeh fuzzy logic, treating input probabilities as membership grades.

⊗ = min (fuzzy AND)   
⊕ = max (fuzzy OR)

The result is the degree to which the target condition holds, dominated by the strongest single conjunction. For the same proximity model: max(min(0.8, 0.7), min(0.2, 0.7), min(0.8, 0.3)) = 0.7.

Boolean — satisfiability

Answers "is the target satisfiable?" by snapping all input probabilities to {0, 1} and evaluating with classical AND/OR. Returns 1.0 if any world satisfies the target, 0.0 otherwise.

⊗ = AND   ⊕ = OR   encode: p > 0 → 1, else 0

ProbGradient — forward-mode autodiff

Computes probabilistic inference and all partial derivatives using forward-mode automatic differentiation. The result vector for a circuit with n leaves has layout:

[WMC, ∂WMC/∂x₀, ∂WMC/∂x₁, …, ∂WMC/∂xₙ₋₁]

Currently, no batched operations are supported, hence the value_size parameter is ignored and automatically set to 1 + n_parameters. Because ProbGradient returns the full Jacobian, it enables gradient-based learning of leaf probabilities directly inside Resin.
With each gradient_update() call , the probability of the target is evaluated together with all gradients and can be used to tune program internal parameters:

import time
from resin import Resin

# An example program for the safe deployment of a quadcopter
code = """
flight_hours(w1)   <- source("/metrics/flight_hours/wing_1", Number).
flight_hours(w2)   <- source("/metrics/flight_hours/wing_2", Number).
flight_hours(w3)   <- source("/metrics/flight_hours/wing_3", Number).
flight_hours(w4)   <- source("/metrics/flight_hours/wing_4", Number).

wing(w1). wing(w2). wing(w3). wing(w4).
needs_checkup(W) <- P(0.9) if flight_hours(W) > 100 and wing(W).
any_wing_needs_checkup if needs_checkup(W).

safe if any_wing_needs_checkup.
safe -> target("/output/safety").
"""

# Setup training for simple example program
# Make sure to use ProbGradient semiring for computing gradients alongside probabilities
resin = Resin.compile(code, semiring="ProbGradient")
reactive_circuit = resin.get_reactive_circuit()

# Set all wings' flight_hours above 100 so the condition is active
for channel in [
    "/metrics/flight_hours/wing_1",
    "/metrics/flight_hours/wing_2",
    "/metrics/flight_hours/wing_3",
    "/metrics/flight_hours/wing_4",
]:
    writer = resin.make_writer(channel)
    writer.write([200.0], timestamp=None)
time.sleep(0.05)

# Training parameters
ground_truth = 0.5
learning_rate = 0.1
for timestep in range(500):
    result = reactive_circuit.gradient_update()

    # Updated weights was not enough to invalidate any circuit
    # -> Training converged
    if not result:
        break

    # Get inference and gradient results
    # Gradients are dictionary from leaf_name -> gradient
    probability = result["/output/safety"]["probability"]
    gradients = result["/output/safety"]["gradients"]

    # Finish once Man Squared Error (MSE) is small enough
    if abs(probability - ground_truth) < 1e-3:
        print(f"Converged at step {timestep}: P(safe) = {probability:.4f}")
        break

    # Compute MSE and perform gradient descent step
    # We set parameters to "needs_checkup#0" to only fit the conditional 
    # probability of the first clause with that head
    mse = 2.0 * (probability - ground_truth)
    resin.fit_parameters(
        gradients, learning_rate, mse,
        parameters=["needs_checkup#0"], timestamp=float(timestep),
    )

Gradient mapping for network outputs

When leaf probabilities come from a neural network, the gradients dict provides the upstream values to feed into the network's own backward pass. You can access all gradients related to your source channel via resin.source_gradients(channel_name) or resin.source_gradients_for(atom_name).

Note that you may have to combine gradients depending on your networks output layer, e.g., for a single output neuron that was used to provide a probability you need to compute full_gradient = gradient[atom] - gradient[-atom] to include the gradient on the negation.

CriticalExplanation — weakest link of the most probable explanation

Computes the marginal probability together with the most probable explanation and its least-probable fact. Sources are written with value_size probabilities as usual, and the result vector has four blocks of value_size values each:

[P | v | tag | w]

• P: probability of the target (as in LogProb)
• v: probability of the most probable explanation (as in MaxProduct)
• tag: index of the least-probable circuit leaf within that explanation
• w: probability of that leaf

Because ⊕ decides by v alone, ⊗ distributes over ⊕ and the result is independent of how the circuit is restructured by adaptation.

Python API

Compiling a model

from resin import Resin

model = """
active <- source("/sensors/active", Boolean).
alarm if active.
alarm -> target("/output/alarm").
"""

resin = Resin.compile(model, value_size=1, verbose=False)

value_size sets the width of the internal value-space vector (e.g. number of particles or grid cells for vectorised evaluation). This is helpful for running the same Resin program for many problem instances in parallel.

Writing signals

Both make_writer(channel) and make_writer_for(atom) return a correctly typed writer for the declared source — the former looks up by IPC channel name, the latter by source atom name.

# Boolean source — by channel name
bool_writer = resin.make_writer("/sensors/active")
bool_writer.write([True], timestamp=None)

# Probability source — by atom name
prob_writer = resin.make_writer_for("over(park)")
prob_writer.write([0.73], timestamp=None)

# Density source — pass distribution name and parameters
# Every time parameters are written, the density function may change
density_writer = resin.make_writer("/map/distance/hospital")
density_writer.write("normal", [[25.0], [5.0]], timestamp=None)
# Supported distributions: "normal", "lognormal", "exponential", "uniform"

# Number source for scalar comparison
number_writer = resin.make_writer_for("speed")
number_writer.write([12.5], timestamp=None)

# Categorical source — flat vector of class probabilities
cat_writer = resin.make_categorical_writer("/classifier/digit")
cat_writer.write([0.1, 0.6, 0.3], timestamp=None)

Reactive Circuit adaptation

The underlying circuit can adapt its structure in response to changing signal frequencies: For example, to group source leafs in 0.1Hz wide bins, each bin being separated into its own group of circuits, you can run:

rc.adapt(bin_size=0.1, number_bins=10)

Alternatively, leaves can be lifted or dropped at runtime, meaning we may manually indicate that a leaf's value changes more or less often than others:

names = resin.get_names()
rc.lift_leaf(names.index("alarm"))
rc.drop_leaf(names.index("raining"))

By default, adaptation builds a DAG: sub-circuits with identical formulas are merged, so targets of the same program grow into one another and share computation. Pass dag=False to adapt, lift_leaf or drop_leaf to keep a separate tree per target instead, e.g., for comparison.

Building from source

Requirements: Rust toolchain, Clingo, Python ≥ 3.9, Maturin.

macOS

brew install clingo
export CLINGO_LIBRARY_PATH=$(brew --prefix clingo)/lib
maturin develop --release  # Optional for building the Python package

Linux

pip install clingo
CLINGO_DIR=$(python3 -c "import clingo, os; print(os.path.dirname(clingo.__file__))")
export CLINGO_LIBRARY_PATH="$CLINGO_DIR"
maturin develop --release  # Optional for building the Python package

Run tests

cargo test

Update the Python type stub after changing the Python API (fails if resin.pyi and the module disagree):

maturin develop --release
python scripts/generate_stub.py

License

See LICENSE.md.

Citation

If you find our work useful, please consider citing the paper Reactive Knowledge Representation and Asynchronous Reasoning (also available via Cite this repository on GitHub):

@article{kohaut2026reactive,
  title={Reactive Knowledge Representation and Asynchronous Reasoning},
  author={Kohaut, Simon and Flade, Benedict and Eggert, Julian and Kersting, Kristian and Dhami, Devendra Singh},
  journal={arXiv preprint arXiv:2602.05625},
  year={2026},
  doi={10.48550/arXiv.2602.05625},
  url={https://arxiv.org/abs/2602.05625}
}