# nanoCoP: A Non-clausal Connection Prover

@inproceedings{Otten2016nanoCoPAN, title={nanoCoP: A Non-clausal Connection Prover}, author={Jens Otten}, booktitle={IJCAR}, year={2016} }

Most of the popular efficient proof search calculi work on formulae that are in clausal form, i.e. in disjunctive or conjunctive normal form. Hence, most state-of-the-art fully automated theorem provers require a translation of the input formula into clausal form in a preprocessing step. Translating a proof in clausal form back into a more readable non-clausal proof of the original formula is not straightforward. This paper presents a non-clausal theorem prover for classical first-order logic…

## 24 Citations

### nanoCoP: Natural Non-clausal Theorem Proving

- Computer ScienceIJCAI
- 2017

Working entirely on the original structure of the input formula yields not only a speed up of the proof search, but the resulting non-clausal proofs are also shorter.

### Non-clausal Connection-based Theorem Proving in Intuitionistic First-Order Logic

- Computer ScienceARQNL@IJCAR
- 2016

Details of the compact Prolog code are presented, which extends the non-clausal connection prover nanoCoP for classical logic by prefixes and an additional prefix unification, which encode the Kripke semantics of intuitionistic logic.

### Non-clausal Connection Calculi for Non-classical Logics

- Computer Science, PhilosophyTABLEAUX
- 2017

An experimental evaluation shows that non-clausal connection calculi are a solid basis for proof search in these logics, in terms of time complexity and proof size.

### Advances in Connection-Based Automated Theorem Proving

- Computer ScienceProvably Correct Systems
- 2017

Calculi to automate theorem proving in classical and some important non-classical logics, namely first- order intuitionistic and first-order modal logics are presented, which permits a goal-oriented and, hence, a more efficient proof search.

### Certification of Nonclausal Connection Tableaux Proofs

- Computer Science, MathematicsTABLEAUX
- 2019

A translation of nonclausal connection proofs to Gentzen’s sequent calculus LK is given and implemented in the interactive theorem prover HOL Light, enabling certification of nonclosure connection proofs as well as a new, complementary automation technique in HOL Light.

### Towards the Integration of an Intuitionistic First-Order Prover into Coq

- Computer ScienceHaTT@IJCAR
- 2016

This work proposes a two-phase approach: An intuitionistic prover generates a certificate based on the matrix characterization of intuitionistic first-order logic; the certificate is then translated into a sequent-style proof.

### Proof Search Optimizations for Non-Clausal Connection Calculi

- Computer SciencePAAR@FLoC
- 2018

The paper presents several proof search optimization techniques for non-clausal connection calculi that are the basis of the new version 1.1 of nanoCoP, and is evaluated on the problems in the TPTP library.

### Equality Preprocessing in Connection Calculi

- Computer SciencePAAR+SC²@IJCAI
- 2020

This work presents an extensible system for equality preprocessing in connection calculi (EPICC) that can be used as a tool in reducing the search space of problems that contain equality.

### A Vision for Automated Deduction Rooted in the Connection Method

- Computer ScienceTABLEAUX
- 2017

An informal overview of the Connection Method in Automated Deduction points out its unique advantage over competing methods which consists in its formula-orientedness and envisages a bright future for the field and point out promising directions for future research.

### Machine Learning Guidance and Proof Certification for Connection Tableaux

- Computer Science, MathematicsArXiv
- 2018

This work gives a translation of connection proofs to LK, enabling proof certification and automatic proof search in interactive theorem provers and shows two guidance methods based on machine learning, namely reordering of proof steps with Naive Bayesian probablities, and expansion of a proof search tree with Monte Carlo Tree Search.

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Calculi to automate theorem proving in classical and some important non-classical logics, namely first- order intuitionistic and first-order modal logics are presented, which permits a goal-oriented and, hence, a more efficient proof search.

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