bhaaksema / superintuition

Automated Theorem Prover for Propositional Superintuitionistic Logics

Prover for Superintuitionistic Logics in Haskell

Installation

cabal install

Usage

super LOGIC FILE

#  LOGIC:
#    -cl        Classical Logic
#    -il        Intuitionistic Logic
#    -jn        Jankov Logic
#    -lc        Gödel-Dummett Logic
#    "FORMULA"  Axiomatisation over IL

#  FORMULA:
#    p | ~A | A&B | A|B | A=>B

#  FILE:
#    https://tptp.org/TPTP/SyntaxBNF.html

Examples

# Example (Jankov)
super -jn test/problems/LCL/LCL181+1.p

# Example (Jankov as extension over IPL)
super "~p | ~~p" test/problems/LCL/LCL181+1.p

# Example (Gödel-Dummett)
super -lc test/problems/LCL/LCL230+1.p

Features

• Based on a the rules of sequent calculi m-G4ip and intuitionistic tableau calculus.
• Once a variable $p$ or $\neg p$ is added to the antecedent, the sequent is substituted with $[\top/p]$ or $[\bot/p]$ respectively.
• Formulae are reduced with boolean simplification rules before proof attempt and during substitutions.
• Inference rules with propositional variables are omitted in favour of simplification and substitution rules.
• Formulae of the sequent are analyzed through naive focussing, some may be temporarily excluded to restrict backtracking.

References

1. Dyckhoff (1992). Contraction-free sequent calculi for intuitionistic logic. doi:10.2307/2275431
2. Ferrari (2012). Simplification Rules for Intuitionistic Propositional Tableaux. doi:10.1145/2159531.2159536
3. Dyckhoff (2016). Intuitionistic Decision Procedures Since Gentzen. doi:10.1007/978-3-319-29198-7_6