boolean-algebra-engine 0.3.13

Deterministic logic layer for AI agents — catch logical contradictions in system prompts, rules, and agent reasoning

boolean-algebra-engine

Your AI agent's decision rules might contradict each other. LLMs can't reliably catch that. This engine can — provably, in under 10ms.

AI agents with decision logic — loan approval, compliance checks, access control, policy enforcement — run on boolean rules written by humans. Nobody verifies those rules don't conflict before the agent acts on them. This engine does.

The benchmark shows why you need it: even a 70B model gets ~20% of boolean logic questions wrong. You can't ask an LLM if your rules conflict and trust the answer. You need a deterministic layer that computes it.

90 tests passing · <10ms evaluation · zero dependencies · exhaustive enumeration, not sampling

pip install boolean-algebra-engine

---

The benchmark

Every model tested hallucinates on boolean logic — but in different ways depending on size and architecture.

Model	Size	Hallucination	Pattern
tinyllama	1.1B	50%	always says "yes" — never reasoning
llama3.2:3b	3B	50%	always says "no" — never reasoning
gemma3:4b	4B	35%	reasoning per case, but wrong 1 in 3
qwen3-32b	32B	17%	reasoning, consistent ~17% baseline
llama-3.3-70b	70B	20%	reasoning, but over-cautious — misses 40% of compatible pairs

The small models aren't reasoning at all — they picked a default and stuck to it. The larger models reason but still hallucinate. llama-3.3-70b scores 20% but makes only one type of error: it assumes rules conflict when they don't (0% missed conflicts, 40% missed compatibles).

---

Quick start

Zero dependencies. Works immediately after install.

from boolean_algebra_engine import evaluate, synthesize

# Does a contradiction exist?
table, _ = evaluate("A.!A")
print(table.satisfiable)   # False — always a contradiction

# Can two rules both be true simultaneously?
table, _ = evaluate("(A.B).(!A)")
print(table.satisfiable)   # False — A and !A can't both hold

# Full truth table
table, _ = evaluate("A.(B+C)")
print(table.variables)     # ['A', 'B', 'C']
print(table.minterms)      # [5, 6, 7]
print(table.satisfiable)   # True

# Simplify to minimal form
minimal, _ = synthesize(table)
print(minimal)             # A.C+A.B

---

Try it immediately

pip install boolean-algebra-engine
python -c "from boolean_algebra_engine import evaluate; t,_ = evaluate('A.!A'); print(t.satisfiable)"

False — contradiction detected

Optional extras

# With CLI
pip install "boolean-algebra-engine[cli]"

# With MCP server (for Claude Desktop)
pip install "boolean-algebra-engine[mcp]"

# With REST API
pip install "boolean-algebra-engine[api]"

# With NL layer (Anthropic)
pip install "boolean-algebra-engine[nl-anthropic]"

# With NL layer (OpenAI)
pip install "boolean-algebra-engine[nl-openai]"

---

The problem

Six rules. Three variables. Written by four people over six months.

A fintech AI agent auto-approves or rejects loan applications based on these rules — nobody ever verified them together. The engine checks all 8 input combinations for every rule, in every combination:

# pip install boolean-algebra-engine[mcp]
from mcp_server.server import check_prompt_logic

result = check_prompt_logic([
    "A.B",  # approve: good credit AND income verified
    "!A",   # reject:  bad credit
    "C",    # approve: collateral exists
    "!C",   # reject:  no collateral
])

print(result["summary"])
# {'total': 4, 'contradictions': 0, 'tautologies': 0,
#  'equivalent_pairs': 0, 'conflicting_pairs': 2}

print([(p["rule1"], p["rule2"]) for p in result["pairwise"] if p["always_conflict"]])
# [('A.B', '!A'), ('C', '!C')]

What it found:

• A.B and !A conflict — good credit approval and bad credit rejection fire simultaneously when A=1. The agent picks a winner arbitrarily.
• C and !C conflict — collateral approval and no-collateral rejection are mutually exclusive by definition. Both rules can never apply at the same time.

Nobody caught these by reading the rules. The engine caught them by checking every combination.

---

The benchmark (full results)

Variable curve — does complexity make it worse?

qwen3-32b was run across variable counts from 3 to 10 (8 to 1,024 truth table rows), 100 cases each. The hallucination rate stayed flat at 16–19% throughout. Complexity doesn't degrade it — the errors are a consistent baseline, not caused by harder logic.

variables (n)	truth table rows	hallucination rate
3	8	16%
5	32	19%
7	128	16%
10	1,024	19%

Full benchmark results

The engine is the oracle — ground truth is computed by exhaustive enumeration, not guessed. Every LLM disagreement is a provable hallucination.

Methodology: generate pairs of boolean expressions where the correct answer (satisfiable or not) is known exactly. Ask the LLM. Compare. No ambiguity, no human labeling, no interpretation.

python3 benchmark.py --provider ollama --model tinyllama --cases 20
python3 benchmark.py --provider ollama --model llama3.2:3b --cases 20
python3 benchmark.py --provider ollama --model gemma3:4b --cases 20

tinyllama — 1.1B parameters

⬡ z3  verifying 20 ground truth labels... ✓  all 20 cases agree

╭───────────── benchmark config ──────────────╮
│ model        ollama/tinyllama               │
│ cases        20  (10 conflict · 10 compat)  │
│ variables    3  (A, B, C)                   │
│ temperature  0  (deterministic)             │
│ max tokens   5  (yes / no)                  │
│ workers      8  parallel                    │
╰─────────────────────────────────────────────╯

  ollama/tinyllama — 20/20 cases | 50.0% hallucination rate

  #      Rule 1          Rule 2          vars    engine  llm
 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
  1  ✗   B               !B              B         no    yes
  2  ✗   A.B+C           !A.!B.!C        A B C     no    yes
  3  ✗   A.B             A.!B            A B       no    yes
  4  ✓   A+!B            A.(B+C)         A B C    yes    yes
  5  ✗   A.B             A^B             A B       no    yes
  6  ✓   !A+B.C          B               A B C    yes    yes
  7  ✓   A.B+C           A+B             A B C    yes    yes
  8  ✓   A+B.C.D         C               A B C D  yes    yes
  9  ✓   A.B             B               A B      yes    yes
 10  ✓   !C              !B              B C      yes    yes
 ...

╭─────────── results — ollama/tinyllama ─────────────╮
│ model               ollama/tinyllama               │
│ total cases         20  (10 conflict · 10 compat)  │
│ variables           3  (A, B, C)                   │
│ temperature         0  (deterministic)             │
│ max tokens          5                              │
│ correct             10                             │
│ hallucinated        10                             │
│ hallucination rate  50.0%                          │
│ missed conflicts    10/10  (100.0%)                │
│ missed compatibles  0/10   (0.0%)                  │
╰────────────────────────────────────────────────────╯

llama3.2:3b — 3B parameters

⬡ z3  verifying 20 ground truth labels... ✓  all 20 cases agree

╭───────────── benchmark config ──────────────╮
│ model        ollama/llama3.2:3b             │
│ cases        20  (10 conflict · 10 compat)  │
│ variables    4  (A, B, C, D)                │
│ temperature  0  (deterministic)             │
│ max tokens   5  (yes / no)                  │
│ workers      8  parallel                    │
╰─────────────────────────────────────────────╯

  ollama/llama3.2:3b — 20/20 cases | 50.0% hallucination rate

  #      Rule 1          Rule 2          vars    engine  llm
 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
  1  ✓   B               !B              B         no     no
  2  ✓   A.B+C           !A.!B.!C        A B C     no     no
  3  ✓   A.B             A.!B            A B       no     no
  4  ✗   A+!B            A.(B+C)         A B C    yes     no
  5  ✓   A.B             A^B             A B       no     no
  6  ✗   !A+B.C          B               A B C    yes     no
  7  ✗   A.B+C           A+B             A B C    yes     no
  8  ✗   A+B.C.D         C               A B C D  yes     no
  9  ✗   A.B             B               A B      yes     no
 10  ✗   !C              !B              B C      yes     no
 ...

╭─────────── results — ollama/llama3.2:3b ───────────╮
│ model               ollama/llama3.2:3b             │
│ total cases         20  (10 conflict · 10 compat)  │
│ variables           4  (A, B, C, D)                │
│ temperature         0  (deterministic)             │
│ max tokens          5                              │
│ correct             10                             │
│ hallucinated        10                             │
│ hallucination rate  50.0%                          │
│ missed conflicts    0/10   (0.0%)                  │
│ missed compatibles  10/10  (100.0%)                │
╰────────────────────────────────────────────────────╯

gemma3:4b — 4B parameters

╭───────────── benchmark config ──────────────╮
│ model        ollama/gemma3:4b               │
│ cases        20  (10 conflict · 10 compat)  │
│ variables    4  (A, B, C, D)                │
│ temperature  0  (deterministic)             │
│ max tokens   5  (yes / no)                  │
╰─────────────────────────────────────────────╯

  ollama/gemma3:4b — 20/20 cases | 35.0% hallucination rate

  #      Rule 1          Rule 2          vars      engine  llm
 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
  1  ✗   B               !B              B           no    yes
  2  ✓   A.B+C           !A.!B.!C        A B C       no     no
  3  ✓   A.B             A.!B            A B         no     no
  4  ✓   A+!B            A.(B+C)         A B C      yes    yes
  5  ✗   A.B             A^B             A B         no    yes
  6  ✗   !A+B.C          B               A B C      yes     no
  7  ✓   A.B+C           A+B             A B C      yes    yes
  8  ✓   A+B.C.D         C               A B C D    yes    yes
  9  ✓   A.B             B               A B        yes    yes
 10  ✗   !C              !B              B C        yes     no
 11  ✓   A.B+!A.!B       !A.B            A B         no     no
 12  ✓   !A+B.C          A.B.!C          A B C       no     no
 13  ✓   A.B.!C          !A              A B C       no     no
 14  ✗   A.B.C           A.!B            A B C       no    yes
 15  ✗   !A.B            A+B.C.D         A B C D    yes     no
 16  ✓   A.!B            !A+B            A B         no     no
 17  ✓   A+B+C           A.B+C           A B C      yes    yes
 18  ✓   A+!B            A               A B        yes    yes
 19  ✗   A.(B+C)         !A.B            A B C       no    yes
 20  ✓   A.B.C           A.B+C.D         A B C D    yes    yes

╭─────────── results — ollama/gemma3:4b ─────────────╮
│ model               ollama/gemma3:4b               │
│ total cases         20  (10 conflict · 10 compat)  │
│ variables           4  (A, B, C, D)                │
│ temperature         0  (deterministic)             │
│ max tokens          5                              │
│ correct             13                             │
│ hallucinated        7                              │
│ hallucination rate  35.0%                          │
│ missed conflicts    4/10  (40.0%)                  │
│ missed compatibles  3/10  (30.0%)                  │
╰────────────────────────────────────────────────────╯

The vars column shows how many variables each case involves. The engine column is ground truth. Every mismatch with llm is a provable hallucination — not an opinion.

Per-case strips (bottom row of the chart): tinyllama and llama3.2:3b show uniform colour across all cells of each type — a constant output, no case-by-case variation. gemma3:4b shows mixed cells, indicating it engages with each case individually rather than defaulting to one answer.

---

Core API

from boolean_algebra_engine import evaluate, synthesize

# Forward: expression → truth table
table, _ = evaluate("A.(B+C)")
print(table.variables)    # ['A', 'B', 'C']
print(table.minterms)     # [5, 6, 7]
print(table.satisfiable)  # True

# Inverse: truth table → minimal expression
minimal, _ = synthesize(table)
print(minimal)            # A.C+A.B

# Equivalence and satisfiability (via MCP server functions — no HTTP, direct call)
# pip install boolean-algebra-engine[mcp]
from boolean_algebra_engine.mcp.server import equivalent, satisfiable

print(equivalent("A.(B+C)", "A.B+A.C")["equivalent"])  # True — distributive law
print(satisfiable("A.!A")["satisfiable"])               # False — contradiction

core/ has zero external dependencies. Import it into any Python project.

---

MCP — Claude calls the engine

Wire the engine into Claude Desktop and Claude stops predicting boolean logic. It computes it.

{
  "mcpServers": {
    "boolean-algebra-engine": {
      "command": "python",
      "args": ["-m", "boolean_algebra_engine.mcp.server"]
    }
  }
}

Five tools Claude can call mid-conversation:

• evaluate — expression → truth table
• simplify — expression → minimal form
• equivalent — are two expressions identical?
• satisfiable — does any input make this true?
• check_prompt_logic — audit a full rule set for contradictions, tautologies, conflicts, duplicates

---

NL Layer

The LLM translates. The engine decides. The logic is always exact.

Most tools that accept plain English rules pass them to an LLM and trust whatever comes back. That works for summarisation. It doesn't work for logic — the benchmark in this repo proves it, with hallucination rates from 17% to 50% across every model tested.

The NL layer takes a different approach. It uses the LLM for the one thing it's actually good at: mapping human language to symbols. Once the sentence becomes an expression, the LLM is done. The engine takes over, evaluates every possible input combination, and returns a result that is provably correct. The LLM can misname a variable. It cannot miscalculate the truth table — because it never touches it.

How it works

Take this sentence:

"access granted if the user is an admin, or if they're verified and not suspended"

"access granted if admin, or verified and not suspended"
        │
        ▼  LLM — maps words to variables, returns an expression
   A+(V.!S)
        │
        ▼  core engine — evaluates every input combination
   truth table: 8 rows · 6 rows where output = 1
   minimal form: A+V.!S
   satisfiable: yes  ·  tautology: no  ·  contradiction: no
        │
        ▼  LLM — turns the result back into plain English
   "Access is granted in 6 of 8 cases. A suspended verified
    user is always denied, regardless of admin status."

The LLM is involved twice — both times doing something fuzzy (language), never something exact (logic). If it mis-maps a variable, you fix the label. It cannot mis-compute the outcome.

---

Try it in 5 minutes

The fastest path is Ollama — runs locally, no API key, free.

Step 1 — Install Ollama

Download from ollama.com or on Linux:

curl -fsSL https://ollama.com/install.sh | sh

Step 2 — Pull a model

ollama pull deepseek-r1:latest   # 5.2 GB, best quality
# or, on low-memory machines:
ollama pull deepseek-r1:1.5b     # 1.1 GB, faster

Step 3 — Install the package

pip install boolean-algebra-engine

No extra dependencies for Ollama — the layer uses Python's standard library only.

Step 4 — Run your first query

from boolean_algebra_engine.nl.nl import ask

result = ask("alarm on if door open or window open, but not if system disabled")

print(result.expression)   # (D+W).!S
print(result.minimal)      # D.!S+W.!S
print(result.satisfiable)  # True
print(result.variables)    # {'D': 'door is open', 'W': 'window is open', 'S': 'system is disabled'}
print(result.explanation)  # plain English summary

The provider is auto-detected: if Ollama is running, it's used automatically. No configuration needed.

Or via the CLI:

boolcalc ask "alarm on if door open or window open, but not if system disabled"
boolcalc check-rules "access if admin" "access if verified" "no access if suspended"

---

Choosing a provider

Provider	Cost	Setup
Ollama	Free	Install Ollama, pull a model
Anthropic	API usage	export ANTHROPIC_API_KEY=...
OpenAI	API usage	export OPENAI_API_KEY=...
OpenAI-compatible	Varies	Groq, Together, LM Studio, vLLM

Anthropic (Claude)

pip install "boolean-algebra-engine[nl-anthropic]"
export ANTHROPIC_API_KEY=sk-ant-...

from boolean_algebra_engine.nl.nl import ask, AnthropicProvider

result = ask("...", provider=AnthropicProvider())                           # picks up env var
result = ask("...", provider=AnthropicProvider(model="claude-opus-4-7"))   # specific model

OpenAI

pip install "boolean-algebra-engine[nl-openai]"
export OPENAI_API_KEY=sk-...

from boolean_algebra_engine.nl.nl import ask, OpenAIProvider

result = ask("...", provider=OpenAIProvider())                       # defaults to gpt-4o
result = ask("...", provider=OpenAIProvider(model="gpt-4-turbo"))

OpenAI-compatible endpoint — Groq, Together, LM Studio, vLLM

from boolean_algebra_engine.nl.nl import ask, OpenAICompatProvider

result = ask("...", provider=OpenAICompatProvider(
    api_key="your-key",
    base_url="https://api.groq.com/openai/v1",
    model="llama3-8b-8192",
))

Ollama with specific model or remote host

from boolean_algebra_engine.nl.nl import ask, OllamaProvider

result = ask("...", provider=OllamaProvider(model="deepseek-r1:1.5b"))
result = ask("...", provider=OllamaProvider(base_url="http://192.168.1.10:11434"))

---

Bring your own model

The layer is built around a single-method protocol. Any model that can receive a system prompt and a user message can be plugged in:

from boolean_algebra_engine.nl.nl import ask, Provider

class MyProvider(Provider):
    def complete(self, system: str, user: str, max_tokens: int = 512) -> str:
        response = my_llm.generate(system_prompt=system, user_message=user, max_tokens=max_tokens)
        return response.text

result = ask("access granted if admin or verified user", provider=MyProvider())

complete() is called twice per ask() — once to parse the sentence (expects JSON back), once to explain the result (expects plain text). That's the entire contract.

---

What you get back

Every ask() call returns an NLResult — the full picture of what the engine found:

• expression — the boolean expression the LLM parsed your sentence into
• variables — what each letter means ({'A': 'user is admin', ...})
• minimal — the Quine-McCluskey simplified form
• satisfiable — is there any input that makes this true?
• tautology / contradiction — always true or always false?
• minterms / maxterms — row indices where output is 1 or 0
• explanation — plain English summary from the LLM
• rows — the full truth table as a list of dicts

@dataclass
class NLResult:
    input_sentence: str
    expression:     str
    variables:      dict[str, str]
    minimal:        str
    satisfiable:    bool
    tautology:      bool
    contradiction:  bool
    minterms:       list[int]
    maxterms:       list[int]
    explanation:    str
    rows:           list[dict]

---

Why the engine layer matters

The NL layer is only useful because the engine underneath it is exact. Without it, you'd be asking an LLM to both parse and verify the logic — and the benchmark shows what happens:

Model	Hallucination rate
tinyllama 1.1B	50% — always outputs the same answer
llama3.2 3B	50% — always outputs the opposite answer
gemma3 4B	35%
qwen3 32B	17%
llama3.3 70B	20%

Even the 70B model gets 1 in 5 cases wrong — and its errors are systematic, not random. The NL layer sidesteps this entirely: the LLM never reasons about logic. It only names things.

Full benchmark methodology and per-case results are above.

---

What changed in this release

Branch: NL-Layer-Live

Change	Detail
Default model	deepseek-r1:7b → deepseek-r1:latest (8b)
Chain-of-thought off	think: false — stops the model spending its token budget on reasoning before producing JSON
CPU-friendly defaults	num_ctx: 2048, num_thread: 2 — avoids a 128K context window on memory-constrained hosts
Markdown fence stripping	Models wrap JSON in ```json ``` blocks despite instructions; stripped before parsing
Operator normalisation	|, &, AND, OR, XOR, ~ remapped to canonical +, ., ^, ! before validation

---

Contribute

The easiest way to contribute is adding a provider. Copy OllamaProvider, implement complete(), open a PR. Everything else — prompts, pipeline, result type — stays the same.

For bugs and feature requests: open an issue.

---

Operators

Symbol	Operation	Precedence
!	NOT	4 (highest)
.	AND	3
^	XOR	2
+	OR	1 (lowest)

Variables: uppercase A–Z. Parentheses override precedence. Up to 26 variables, arbitrary nesting.

---

Interfaces

Interface	How
Python library	from core.evaluator import evaluate — embed in any project
CLI / REPL	boolcalc "A.B+!A.C" — instant truth table in terminal
MCP server	Claude Desktop plugin — plug and play
REST API	POST /check-rules — callable from any language or stack
NL layer	Plain English → expression → verified result (Anthropic, OpenAI, Ollama, any OpenAI-compat)
Streamlit UI	Three modes: Expression, Rule Auditor, Plain English

---

vs SymPy and boolean.py

SymPy (sympy.logic) is more powerful for pure boolean mathematics — its DPLL-based satisfiable() scales better beyond 15 variables, and simplify_logic() covers similar minimization ground. If you're doing symbolic mathematics, use SymPy.

boolean.py handles expression parsing and symbolic simplification cleanly. If you need to manipulate boolean expressions as objects, it's the right tool.

This engine is different in three ways:

1. Zero-dependency core. SymPy pulls in numpy, mpmath, and the full symbolic stack. core/ is plain Python — no install side-effects, embeds anywhere.

2. Built for AI pipelines, not mathematics. check_prompt_logic audits a set of rules for pairwise conflicts — the kind of check you run on a system prompt or a business rule engine before an agent acts on it. Neither SymPy nor boolean.py has this concept.

3. The integration layer. MCP server for Claude Desktop, NL layer for plain English input, REST API, benchmark against LLMs — none of this exists in math-focused libraries because it's not a math problem. It's an AI reliability problem.

If you want to do boolean algebra, SymPy is the answer. If you want to verify that your AI agent's rules don't contradict each other, this is built for that.

---

Credibility

The engine does not sample, approximate, or predict. It evaluates every possible input combination:

• Satisfiable — an actual row where output = 1 was found
• Contradiction — every row was checked, all were 0
• Equivalent — output columns compared row-by-row across the full truth table
• Conflict — conjunction of both rules evaluated for every input, always returned 0

The core evaluator is 15 lines (core/evaluator.py). No black box, no model weights, no probability — just arithmetic. This is a stronger correctness claim than any probabilistic tool can make.

90 tests across unit, integration, edge cases, and round-trips. All passing.