# FCube-4.1 for Intuitionistic Propositional Logic

2022-09-04, updated 2022-09-05 next - previous

Ferrari, Fiorentini and Fiorino made fCube i.e. $$F^{3}$$.

## 1. FCube-4.1 verbose version

• This is version 4.1 of FCube-verbose for Tau Prolog (see this discussion), a prover which provides proofs for intuitionistically valid formulas, and countermodels for those that are intuitionistically unprovable.
• I changed the code to use infix notation.
• For the description of FCube algorithm, see [1], [2], below.

Enjoy !

A - Prolog Code:

D - Examples of Queries:

1. Excluded Middle: a | ~ a
2. Dilemma : ((~ a => b) & (a => b)) => b
3. Double Negation: ~(~a) <=> a
4. Peirce’s Law: (((a => b) => a) => a)
5. Dummett Formula : (a => b)| (b => a)
6. Classical equivalence for negation : (~a => a) <=> a
7. Classical De Morgan's Law : ~((a & b)) => (~ a | ~b)
8. Pelletier Problem 17 : ( ( ( p & ( q => r ) ) => s ) <=> ( ( ~ p | q | s ) & ( ~ p | ~ r | s ) ) )
9. a
10. a => b
11. (a | b) => (a & b)

## 2. References

1.
Ferrari, M., Fiorentini, C., Fiorino, G. Towards the use of Simplification Rules in Intuitionistic Tableaux. In: Atti del convegno CILC09 - 24-esimo Convegno Italiano di Logica Computazionale, 2009, 148–159, [Online]. Available: https://www.vidal-rosset.net/pdf/ferrari2009.pdf.
2.
Ferrari, M., Fiorentini, C., Fiorino, G. FCube: An Efficient Prover for Intuitionistic Propositional Logic. In: Logic for Programming, Artificial Intelligence, and Reasoning, 2010, 294–301, [Online]. Available: https://www.vidal-rosset.net/pdf/ferrarietal2010.pdf.

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