Proving Isomorphism of First-Order Logic Proof Systems in HOL

@inproceedings{Mikhajlova1998ProvingIO,
  title={Proving Isomorphism of First-Order Logic Proof Systems in HOL},
  author={Anna Mikhajlova and Joakim von Wright},
  booktitle={TPHOLs},
  year={1998}
}
We prove in HOL that three proof systems for classical first-order predicate logic, the Hilbertian axiomatization, the system of natural deduction, and a variant of sequent calculus, are isomorphic. The isomorphism is in the sense that provability of a conclusion from hypotheses in one of these proof systems is equivalent to provability of this conclusion from the same hypotheses in the others. Proving isomorphism of these three proof systems allows us to guarantee that meta-logical provability… 
A New Machine-checked Proof of Strong Normalisation for Display Logic
Embedding Display Calculi into Logical Frameworks: Comparing Twelf and Isabelle
Formalised Cut Admissibility for Display Logic
TLDR
This work uses a deep embedding of the display calculus for relation algebras δRA in the logical framework Isabelle/HOL to formalise a machine-checked proof of cut-admissibility for δ RA and believes this to be the first full formalisation of Cut-Admissibility in the presence of explicit structural rules.

References

SHOWING 1-10 OF 15 REFERENCES
Introduction to HOL: a theorem proving environment for higher order logic
TLDR
A tutorial on goal-directed proof: tactics and tacticals and theorem-Proving With HOL, a simple proof tool for goal-oriented proof of the binomial theorem.
Proofs and types
Sense, denotation and semantics natural deduction the Curry-Howard isomorphism the normalisation theorem Godel's system T coherence spaces denotational semantics of T sums in natural deduction system
A Structural Proof of Cut Elimination and Its Representation in a Logical Framework
TLDR
New proofs of cut elimination for intuitionistic and classical sequent calculi are presented, avoiding the explicit use of multi- sets and termination measures on sequent derivations and are amenable to elegant and concise representations in LF.
Formalized Mathematics
It is generally accepted that in principle it’s possible to formalize completely almost all of present-day mathematics. The practicability of actually doing so is widely doubted, as is the value of
Metamath A Computer Language for Pure Mathematics
Mathematics Revealed 3.1 Logic and Set Theory Set theory can be viewed as a form of exact theology.
Logic and structure
Contents: Introduction Propositional Logic Predicate Logic Completeness and Applications Second Order Logic Intuitionistic Logic Normalisation.
Introduction to HOL: A the- orem proving environment for higher order logic
  • 1993
...
...