https://github.com/mohazamani/logic-project-spring00-01

https://github.com/mohazamani/logic-project-spring00-01

Last synced: 3 days ago
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• Host: GitHub
• URL: https://github.com/mohazamani/logic-project-spring00-01
• Owner: MohaZamani
• Created: 2022-07-28T03:51:08.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2022-07-28T04:16:48.000Z (over 2 years ago)
• Last Synced: 2024-10-17T23:23:17.435Z (28 days ago)
• Language: C++
• Size: 122 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Logic-Project-Spring00-01

## finding interpolant of a WFF formula in first order logic.

#### WFF formula defenition :

- True and False are wffs.

- Each atomic formula (i.e. a specific predicate with variables) is a wff.

- If A, B, and C are wffs, then so are  A, (A & B), (A | B), and (A > B).

- If C is wffs, then so are  (~C).

#### Craig interpolation :

In mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem says that if a formula φ implies a formula ψ, and the two have at least one atomic variable symbol in common, then there is a formula ρ, called an interpolant, such that every non-logical symbol in ρ occurs both in φ and ψ, φ implies ρ, and ρ implies ψ. The theorem was first proved for first-order logic by William Craig in 1957. Variants of the theorem hold for other logics, such as propositional logic. A stronger form of Craig's interpolation theorem for first-order logic was proved by Roger Lyndon in 1959; the overall result is sometimes called the Craig–Lyndon theorem.

How Run:

```

g++ main.cpp

./a.out

input : a WFF formula Like (A>B).

output : WFF formulas like C that is interpolation.

```