pyNMMS 0.1.1
Non-Monotonic Multi-Succedent sequent calculus — propositional NMMS from Hlobil & Brandom 2025
Requires Python: >=3.10
Keywords: inferentialism, logic, nonmonotonic, reasoning, sequent-calculus

# pyNMMS

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Non-Monotonic Multi-Succedent sequent calculus — propositional NMMS from Hlobil & Brandom 2025, Ch. 3.

**[Documentation](https://bradleypallen.github.io/nmms-reasoner/)** | **[PyPI](https://pypi.org/project/pyNMMS/)** | **[GitHub](https://github.com/bradleypallen/nmms-reasoner)**

## Installation

```bash
pip install pyNMMS
```

For development:

```bash
git clone https://github.com/bradleypallen/nmms-reasoner.git
cd nmms-reasoner
pip install -e ".[dev]"
```

## Quick Start

```python
from pynmms import MaterialBase, NMMSReasoner

# Create a material base with defeasible inferences
base = MaterialBase(
    language={"A", "B", "C"},
    consequences={
        (frozenset({"A"}), frozenset({"B"})),  # A |~ B
        (frozenset({"B"}), frozenset({"C"})),  # B |~ C
    },
)

reasoner = NMMSReasoner(base)

# A derives B (base consequence)
result = reasoner.derives(frozenset({"A"}), frozenset({"B"}))
assert result.derivable  # True

# A does NOT derive C (nontransitivity — no [Mixed-Cut])
result = reasoner.derives(frozenset({"A"}), frozenset({"C"}))
assert not result.derivable  # False

# A, C does NOT derive B (nonmonotonicity — no [Weakening])
result = reasoner.derives(frozenset({"A", "C"}), frozenset({"B"}))
assert not result.derivable  # False

# Classical tautologies still hold (supraclassicality)
result = reasoner.derives(frozenset(), frozenset({"A | ~A"}))
assert result.derivable  # True
```

## CLI

```bash
# Create a base and add consequences
pynmms tell -b base.json --create "A |~ B"
pynmms tell -b base.json "B |~ C"

# Query derivability
pynmms ask -b base.json "A => B"        # DERIVABLE
pynmms ask -b base.json "A => C"        # NOT DERIVABLE
pynmms ask -b base.json "A, C => B"     # NOT DERIVABLE

# Interactive REPL
pynmms repl -b base.json
```

## Key Properties

- **Nonmonotonicity**: Adding premises can defeat inferences (no Weakening)
- **Nontransitivity**: Chaining good inferences can yield bad ones (no Mixed-Cut)
- **Supraclassicality**: All classically valid sequents are derivable
- **Conservative Extension**: Logical vocabulary doesn't change base-level relations
- **Explicitation Conditions**: DD, II, AA, SS biconditionals hold

## Theoretical Background

This implements the NMMS sequent calculus from:

- Hlobil, U. & Brandom, R. B. (2025). *Reasons for Logic, Logic for Reasons*. Ch. 3: "Introducing Logical Vocabulary."

NMMS codifies *open reason relations* — consequence relations where Monotonicity and Transitivity can fail. The material base encodes defeasible material inferences among atomic sentences, and the Ketonen-style logical rules extend this to compound sentences while preserving nonmonotonicity.

## License

MIT