pyNMMS 0.1.0

Non-Monotonic Multi-Succedent sequent calculus — propositional NMMS from Hlobil & Brandom 2025

pyNMMS

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

Installation

pip install pyNMMS

For development:

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

Quick Start

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

# 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