kg2: A Python Tool for Paraconsistent Gödel Modal Logic

This package implements model and evaluation for Paraconsistent Gödel Modal Logic. In this logic, the belief of an agent in a proposition is defined to be a pair of values in the interval $[0, 1]\times[0,1]$, representing the world's truth-value for and against the proposition.Paraconsistent Gödel Modal Logic is valuable for representing nuanced information about evidence, strength of belief, consistency and inconsistency, and certainty and uncertainty.

Installation

Use the package manager pip to install kg2.

pip install kg2

Usage

The full reference of the package can be found in DOCUMENTATION.md.

from kg2 import *

# Number of worlds in the model.
world_size = 4

# Accessibility relation.
relation = [[1, 1, 0.5, 0.5], [1, 1, 0.5, 0.5], [0.5, 0.5, 1, 1], [0.5, 0.5, 1, 1]]

# Valuation 1 for each variable and agent.
valuation1 = {"p": [1, 1, 0.4, 0.4]}

# Valuation 2 for each variable and agent.
valuation2 = {"p": [0, 0, 0.8, 0.8]}

# Model instantiation.
model = Model(4, relation, valuation1, valuation2)

# Define a formula.
formula = Diamond(Diamond(Variable("p")))

# Evaluate formula in the model for world 0.
formula.valuation1(model, 0)

Full example can be found in the Jupyter Notebook example.ipynb.

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

License

MIT

References

Bílková, M., Frittella, S., Kozhemiachenko, D. (2022). Paraconsistent Gödel Modal Logic. In: Blanchette, J., Kovács, L., Pattinson, D. (eds) Automated Reasoning. IJCAR 2022. Lecture Notes in Computer Science(), vol 13385. Springer, Cham. [https://doi.org/10.1007/978-3-031-10769-6_26]