https://github.com/marcinbrojek/log-fo-prover

A tool for automatically verifying whether a given first-order logic formula is a tautology, based on Herbrand's theory and the Davis-Putnam SAT solver. Implemented in C++.
https://github.com/marcinbrojek/log-fo-prover

automated-theorem-proving cpp first-order-logic

Last synced: about 1 month ago
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A tool for automatically verifying whether a given first-order logic formula is a tautology, based on Herbrand's theory and the Davis-Putnam SAT solver. Implemented in C++.

• Host: GitHub
• URL: https://github.com/marcinbrojek/log-fo-prover
• Owner: MarcinBrojek
• Created: 2024-06-29T09:59:12.000Z (6 months ago)
• Default Branch: master
• Last Pushed: 2024-06-29T09:59:15.000Z (6 months ago)
• Last Synced: 2024-06-29T12:25:22.951Z (6 months ago)
• Topics: automated-theorem-proving, cpp, first-order-logic
• Language: C++
• Homepage:
• Size: 8.79 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# FO-prover

The objective of this assignment is to build a prover for tautologies of first-order

logic based on Herbrand’s theorem and the Davis-Putnam SAT solver. The solution program must read the standard input stdin. The input consists of a single line encoding a formula of first-order logic according to the following Backus-Naur grammar:

```haskell

formula ::= 

    | "T"

    | "F"

    | "Rel" string [t]*

    | "Not(" formula ")"

    | "And(" formula ")(" formula ")"

    | "Or(" formula ")(" formula ")"

    | "Implies(" formula ")(" formula ")"

    | "Iff(" formula ")(" formula ")"

    | "Exists" string "(" formula ")"

    | "Forall" string "(" formula ")"

t ::= "Var" string | "Fun" string [t]*

```

string is any sequence of alphanumeric characters.

---

FO-prover should output:

- timeout - when formula contains free variables and infinite Herbrand universe 

  (non-tautology)

otherwise:

- 1 - tautology,

- 0 - non-tautology.

---

## Example run

```bash

> make

> echo 'Or(Rel "r" [Var "a"])(Not(Rel "r" [Var "a"]))' | ./FO-prover

```

returns 1 (known tautology $p \vee \neg p$)

---

## File structure

- `README.md` (this)

- `parser.h`, `parser.cpp`

- `combination.h`, `combination.cpp`

- `skolem.h`, `skolem.cpp`

- `fdpll.h`, `fdpll.cpp`

- `main.cpp`

- `makefile`