# Certification of Prefixed Tableau Proofs for Modal Logic

@inproceedings{Libal2016CertificationOP, title={Certification of Prefixed Tableau Proofs for Modal Logic}, author={Tomer Libal and Marco Volpe}, booktitle={International Symposium on Games, Automata, Logics and Formal Verification}, year={2016} }

Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the general project of establishing a common specification language in order to certify proofs given in a wide range of deductive formalisms. In particular, by using a translation from the modal language into a first-order polarized language and a checker whose…

## 6 Citations

### A general proof certification framework for modal logic

- 2019

Computer Science

Mathematical Structures in Computer Science

This work proposes here a general framework for checking modal proofs using a classical focused sequent calculus as a kernel and presents the implementation of the framework in a Prolog-like language and shows how it is possible to specialize it in a simple and modular way in order to cover different proof formalisms.

### Certification of labeled proofs for modal logics with geometric frame conditions

- 2017

Computer Science, Mathematics

The general method for modal logics characterized by geometric frame conditions is described, its implementation in a Prolog-like language is presented, and several examples of proof certification in the case of well-known normal modallogics, like K, S4 and S5 are provided.

### An interactive assistant for the definition of proof certificates

- 2016

Computer Science

To facilitate broader adoption, techniques that abstract away part of this complexity and bring the FPC framework closer to a user-friendly, programmable platform in which a wide range of high-level certificate definitions can be easily encoded are explored.

### Translating Between Implicit and Explicit Versions of Proof

- 2017

Computer Science

CADE

This paper illustrates how it is possible to automate moving from implicit to explicit (elaboration) and from explicit to implicit (distillation) proof evidence via the proof checking of a pair of proof certificates.

### Applications of Foundational Proof Certificates in theorem proving. (Applications des Certificats de Preuve Fondamentaux à la démonstration automatique de théorèmes)

- 2017

Computer Science, Mathematics

This thesis extends initial results in certification of first-order proofs in several directions and applies developments to fully certify results produced by two families of standard automated theorem provers: resolution- and satisfiability-based.

### Modal proof theory through a focused telescope

- 2018

Computer Science

In this thesis, we use in two ways the concept of synthetic inference rules that can be obtained from a focused proof system; from one side of the “telescope”, focusing allows us to analyse the…

## 24 References

### A focused framework for emulating modal proof systems

- 2016

Computer Science

Advances in Modal Logic

A general framework is proposed, based on a focused version of the labeled sequent calculus by Negri, augmented with some parametric devices allowing to restrict the set of proofs, to emulate in this framework the behavior of a range of existing formalisms and proof systems for modal logic.

### A Resolution Calculus for Modal Logics

- 1988

Philosophy

CADE

A syntax transformation is presented that eliminates themodal logic operators from modal logic formulae by shifting the modal context information to the term level and can be brought into conjunctive normal form such that a clause based resolution calculus without any additional inference rule, but with special modal unification algorithms, can be defined.

### Tableau methods of proof for modal logics

- 1972

Philosophy

Notre Dame J. Formal Log.

This paper incorporates the device into a tableau proof system and it is seen that the resulting (propositional) proof system is highly analogous to a classical first order tableau system, with the modal operators behaving like quantifiers.

### The Proof Certifier Checkers

- 2015

Computer Science

TABLEAUX

The architecture of Checkers is described and it is demonstrated how it can be used to check proof objects by supplying the fpc specification for a subset of the inferences used by eprover and checking proofs using these inferences.

### The λΠ-calculus Modulo as a Universal Proof Language

- 2012

Computer Science, Mathematics

PxTP

This paper motivates the resulting language, the -calculus modulo, as a universal proof language, capable of expressing proofs from many other systems without losing their computational properties, and shows how to very simply and eciently check proofs from this language.

### Proof Analysis in Modal Logic

- 2005

Philosophy

J. Philos. Log.

A general method for generating contraction- and cut-free sequent calculi for a large family of normal modal logics and it can be extended to treat also Gödel–Löb provability logic.

### A Benchmark Method for the Propositional Modal Logics K, KT, S4

- 2004

Computer Science

Journal of Automated Reasoning

A set of benchmark formulas for proof search in propositional modal logics K, KT, and S4 are presented and the discussion of postulates concerning ATP benchmark helps to obtain improved benchmark methods for other logics, too.

### Checking Zenon Modulo Proofs in Dedukti

- 2015

Computer Science, Mathematics

PxTP@CADE

A shallow embedding is presented into Dedukti of proofs produced by Zenon Modulo, an extension of the tableau-based first-order theorem prover Zenon to deduction modulo and typing that is applied to the verification of programs in both academic and industrial projects.