python-tensorlogic 0.2.0

Neural-symbolic AI framework unifying logical reasoning and tensor computation

TensorLogic

Neural-symbolic AI framework unifying logical reasoning and tensor computation. Bridge neural networks and symbolic reasoning through tensor operations based on Pedro Domingos' Tensor Logic paper (arXiv:2510.12269).

Core Insight: Logical operations map directly to tensor operations:

• Logical AND → Hadamard product
• Logical OR → Maximum operation
• Implications → max(1-a, b)
• Quantifiers → Einsum summation with Heaviside step

Beyond Deduction: Enabling Generalization with Analogical Reasoning

TensorLogic's breakthrough capability: temperature-controlled reasoning that bridges pure logic and neural approximation.

Temperature	Behavior	Use Case
T=0	Pure deductive inference	Verification, provable correctness, zero hallucinations
T=0.1-0.5	Cautious generalization	Robust inference with uncertainty
T=1.0	Analogical reasoning	Pattern completion, missing link prediction
T>1.0	Exploratory	Creative hypotheses, knowledge graph expansion

Why this matters: Standard logical solvers give you T=0 only. Standard neural networks give you T>0 only with no guarantees. TensorLogic gives you the entire spectrum—from mathematically provable deduction to neural-style generalization—in a unified framework.

from tensorlogic.api import reason

# Pure deduction: mathematically provable, zero hallucinations
result = reason('Grandparent(x, z)', temperature=0.0, ...)

# Analogical: can infer "likely grandparent" even with incomplete data
result = reason('Grandparent(x, z)', temperature=0.5, ...)

This capability is theoretically grounded in Pedro Domingos' Tensor Logic paper (arXiv:2510.12269). For a deep dive on temperature semantics, see the Temperature-Controlled Inference Guide.

Quick Start

Installation

# Basic Installation (NumPy backend)
uv add tensorlogic

# Recommended (MLX backend for Apple Silicon)
uv add tensorlogic mlx>=0.30.0

Performance Architecture

TensorLogic is built for scale. The MLX backend enables 1M+ entity knowledge graphs on Apple Silicon:

from tensorlogic.backends import create_backend

# Auto-selects MLX (GPU) on Apple Silicon, NumPy fallback elsewhere
backend = create_backend()  # ← This step selects your hardware backend

Backend	Hardware	Key Advantage
MLX	Apple Silicon (M1/M2/M3)	Unified memory + Metal GPU, lazy evaluation
NumPy	Universal CPU	Compatibility fallback

The MLX backend's lazy evaluation enables 10-100x speedups for complex knowledge graph queries. See Performance Benchmarks for detailed metrics.

Logical Reasoning in Tensors

from tensorlogic.core import logical_and, logical_or, logical_not, logical_implies
from tensorlogic.core.quantifiers import exists, forall
from tensorlogic.backends import create_backend

backend = create_backend()

# Define relations as tensors (family knowledge graph)
# Rows = subject, Columns = object
parent = backend.asarray([
    [0., 1., 1., 0.],  # Alice is parent of Bob, Carol
    [0., 0., 0., 1.],  # Bob is parent of David
    [0., 0., 0., 0.],  # Carol has no children
    [0., 0., 0., 0.],  # David has no children
])

# Infer grandparent: exists y: Parent(x,y) AND Parent(y,z)
# Using einsum: sum over intermediate variable y
composition = backend.einsum('xy,yz->xz', parent, parent)
grandparent = backend.step(composition)  # Alice is grandparent of David

# Quantified query: "Does Alice have any children?"
has_children = exists(parent[0, :], backend=backend)  # True

# Logical implication: Parent(x,y) -> Ancestor(x,y)
ancestor = logical_implies(parent, parent, backend=backend)

Knowledge Graph Reasoning

TensorLogic's flagship capability: neural-symbolic reasoning over knowledge graphs with temperature-controlled inference.

from tensorlogic.api import quantify, reason

# Pattern-based quantified queries
result = quantify(
    'exists y: Parent(x, y) and Parent(y, z)',
    predicates={'Parent': parent_tensor},
    backend=backend
)

# Temperature-controlled reasoning
# T=0: Pure deductive (no hallucinations)
# T>0: Analogical reasoning (generalization)
inference = reason(
    'Grandparent(x, z)',
    bindings={'x': alice_idx, 'z': david_idx},
    temperature=0.0,  # Strict deductive mode
    backend=backend
)

Comprehensive Example

Run the full knowledge graph reasoning example:

uv run python examples/knowledge_graph_reasoning.py

Demonstrates:

• Family knowledge graph with 8 entities and 4 relation types
• Logical operations: AND, OR, NOT, IMPLIES
• Relation inference: Grandparent, Aunt/Uncle rules via implication
• Quantified queries: EXISTS ("has children?"), FORALL ("loves all?")
• Temperature control: T=0 deductive vs T>0 analogical reasoning
• Compilation strategy comparison across 5 semantic modes
• Uncertain knowledge handling with fuzzy relations

See examples/README.md for detailed documentation.

Compilation Strategies

TensorLogic supports multiple semantic interpretations—choose based on your problem, not your logic background:

soft_differentiable — Train neural networks that respect logical rules

Problem: "I want to train a model where the loss includes logical constraints" Example: Learning embeddings where Parent(x,y) ∧ Parent(y,z) → Grandparent(x,z) is enforced during training

hard_boolean — Provable, exact inference

Problem: "I need mathematically guaranteed answers with no approximation" Example: Verifying that a knowledge graph satisfies business rules (integrates with Lean 4 verification)

godel — Score similarity on a continuous spectrum

Problem: "I need a grade (0.0-1.0), not just true/false" Example: Scoring product similarity in a recommendation engine

product — Probabilistic reasoning with independent events

Problem: "I'm combining probabilities and want P(A∧B) = P(A) × P(B)" Example: Computing joint probabilities in a Bayesian knowledge graph

lukasiewicz — Bounded arithmetic with saturation

Problem: "I need bounded confidence scores that don't explode" Example: Multi-hop reasoning where confidence degrades gracefully

Strategy	Differentiable	Best For
soft_differentiable	Yes	Neural network training with logic constraints
hard_boolean	No	Exact verification, theorem proving
godel	Yes	Similarity scoring, fuzzy matching
product	Yes	Probabilistic inference
lukasiewicz	Yes	Bounded multi-hop reasoning

from tensorlogic.compilation import create_strategy

# Choose based on your problem
strategy = create_strategy("soft_differentiable")  # Training with logic constraints
strategy = create_strategy("hard_boolean")         # Exact verification
strategy = create_strategy("godel")                # Continuous scoring

See Compilation Strategies Guide for detailed API reference and mathematical semantics.

API Reference

Core Operations

from tensorlogic.core import logical_and, logical_or, logical_not, logical_implies

# Element-wise logical operations on tensors
result = logical_and(a, b, backend=backend)      # a AND b
result = logical_or(a, b, backend=backend)       # a OR b
result = logical_not(a, backend=backend)         # NOT a
result = logical_implies(a, b, backend=backend)  # a -> b

Quantifiers

from tensorlogic.core.quantifiers import exists, forall

# Existential: "exists x such that P(x)"
result = exists(predicate, axis=0, backend=backend)

# Universal: "for all x, P(x)"
result = forall(predicate, axis=0, backend=backend)

High-Level Pattern API

from tensorlogic.api import quantify, reason

# Pattern-based quantified queries
result = quantify(
    'forall x: P(x) -> Q(x)',
    predicates={'P': predicate_p, 'Q': predicate_q},
    backend=backend
)

# Temperature-controlled reasoning
result = reason(
    'exists y: Related(x, y) and HasProperty(y)',
    bindings={'x': entity_batch},
    temperature=0.0,  # 0.0 = deductive, >0 = analogical
    backend=backend
)

Backend System

TensorLogic uses a minimal Protocol-based abstraction (~25-30 operations) supporting multiple tensor frameworks. See Performance Architecture for hardware selection.

from tensorlogic.backends import create_backend

# Explicit backend selection
numpy_backend = create_backend("numpy")
mlx_backend = create_backend("mlx")

MLX Lazy Evaluation: Operations are not computed until backend.eval(result) is called—critical for batching complex knowledge graph queries.

Protocol Operations:

• Creation: zeros, ones, arange, full, asarray
• Transformation: reshape, broadcast_to, transpose, squeeze, expand_dims
• Operations: einsum, maximum, add, subtract, multiply, divide, matmul
• Reductions: sum, max, min, mean, prod
• Utilities: eval, step, clip, abs, exp, log, sqrt, power, astype

See docs/backends/API.md for complete API reference.

Project Status

Current Phase: Production Ready

Completed:

• BACKEND-001: TensorBackend Protocol with MLX + NumPy (PR #6)
• CORE-001: Logical Operations & Quantifiers (PR #7)
• API-001: Pattern Language & Compilation (PR #8)
• VERIF-001: Lean 4 Verification Bridge (15 theorems proven)
• RAG-001: Integration module with LangChain adapter
• 1,257 tests, 99%+ pass rate, 100% type coverage

Features:

• Sparse tensor support for 1M+ entity knowledge graphs
• LangChain-compatible retriever with hybrid neural-symbolic scoring
• 4 Jupyter notebooks for interactive learning
• Benchmark suite for scale validation

See docs/tutorials/index.md for tutorials and docs/research/rag-goals.md for research roadmap.

Development

Running Tests

# All tests
uv run pytest

# With coverage
uv run pytest --cov=tensorlogic --cov-report=html

# Specific component
uv run pytest tests/test_core/
uv run pytest tests/test_backends/
uv run pytest tests/test_api/
uv run pytest tests/test_integrations/

Type Checking

uv run mypy --strict src/tensorlogic/
# Current status: 0 errors

Code Quality

uv run ruff check .   # Linting
uv run ruff format .  # Formatting

Documentation

• Conceptual Guide: docs/concepts/tensor-logic-mapping.md - How logic becomes tensors
• Examples: examples/README.md - Practical usage examples
• Backend API: docs/backends/API.md - Comprehensive API reference
• Research Goals: docs/research/rag-goals.md - RAG research roadmap
• Original Paper: arXiv:2510.12269 (Domingos, 2025)

License

MIT License