A naive model generator, model checker and theorem prover
for some combinations of classical and intuitionistic, non-modal and modal, propositional and first-order logic, analytic tableau and sequent calculus.

This software can compute

• the denotation (truth value) of a given logical expression in a given structure,
• a tableau or sequent deduction tree with associated minimal (counter) models for a given inference or set of sentences.

© Natalie Clarius [email protected]
License: CC BY-NC-SA 4.0 (https://creativecommons.org/licenses/by-nc-sa/4.0/).

You can try the model checking feature out here.
If you want to dive in deeper, I recommend downloading pyPL to your own computer.

To run this software locally on your machine:

1. Install dependencies:
   • core functionality: Python (version >= 3.9) + Python packages: os, re
   • for graphical interface: Tk
   • for nicely formatted output: LaTeX with pdflatex + LaTeX packages: geometry, array, forest, amssymb, amsmath, amstext, wasysym, mathtools
2. Download this repository.
3. Execute pyPL/main.py.

Documentation on how to enter formulas, structures and input files can be found in pyPL/doc/parser.md.
Some sample input files are available in pyPL/input.
Generated output files are stored in pyPL/output.

Information on the functionality of some of the buttons and options are shown as tooltips on mouse hover.
For troubleshooting information, see pyPL/doc/troubleshooting.md.
If that doesn't help, please open a GitHub issue or e-mail me.

Some background on the theory underlying the implementation can be found in pyPL/doc/paper.pdf.

• theorem proving: generate an analytic tableau or sequent tree to show that a formula or inference is valid/invalid
• (counter) model generation: generate a minimal structure in which a given (set of) formulas is true/false
• model checking: evaluation of expressions relative to structures, variable assignments and possible worlds
• truth table generation

• propositional logic
• first-order logic with zero-place predicates, function symbols and term equality
• intensional logic with operators □, ◇, ^, ⱽ; propositional, constant and varying domains; frame K
• intuitionistic logic with Kripke semantics (only model checking)
• three-valued logic (not yet implemented)

• analytic tableaux
• sequent calculus (classical logic only)

• input of formulas and structures with ordinary keyboard characters, directly or from a file
• output in plain text or LaTeX-generated PDF

• model checking works only on structures with finite domains
• model generation and theorem proving works only on formulas of relatively small size due to performance limitations

• tableau algorithm relatively inefficient
• GUI and parser can be glitchy (window not scrollable, buttons sometimes not behaving as expected, parser not always recognizing bracketing correctly)
• global variables are bad

• useful feedback on incorrectly entered input rather than no parser response
• more efficient proof search and model generation
• in model checking, print out detailed derivation rather than just final result of evaluation
• broader coverage:
  • lambda calculus and e-t type theory
  • more frames for modal logic; temporal logic; model generation and modal logic for intuitionistic logic
  • tableaus with free variables
  • other frameworks and calculi, e.g. DRT, ND

• This implementation is an experimental proof-of-concept. It is not efficient or designed for real-life applications.
• Although the software has been extensively tested, I do not guarantee soundness. Use at your own risk.

© 2021-2024 Natalie Clarius <[email protected]> nclarius.github.io

This work is licensed under the GNU General Public License v3.0.
This program comes with absolutely no warranty.
This is free software, and you are welcome to redistribute and/or modify it under certain conditions.

I am glad to receive comments, bug reports and improvement suggestions via GitHub issues or e-mail to [email protected].