# Facets of the PIE Environment for Proving, Interpolating and Eliminating on the Basis of First-Order Logic

@inproceedings{Wernhard2019FacetsOT, title={Facets of the PIE Environment for Proving, Interpolating and Eliminating on the Basis of First-Order Logic}, author={Christoph Wernhard}, booktitle={DECLARE}, year={2019} }

PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. Its main focus is on formulas, as constituents of complex formalizations that are structured through formula macros, and as outputs of reasoning tasks such as second-order quantifier elimination and Craig interpolation. It supports a workflow based on documents that intersperse macro definitions, invocations of reasoners, and LaTeX-formatted natural language text. Starting from various examples, the…

## 6 Citations

Applying Second-Order Quantifier Elimination in Inspecting Gödel's Ontological Proof

- Computer ScienceSOQE@KR
- 2021

Previously unnoticed or obscured aspects and details of Gödel’s proof become apparent and practical application possibilities of second-order quantifier elimination are shown.

Learning from Łukasiewicz and Meredith: Investigations into Proof Structures (Extended Version)

- MathematicsCADE
- 2021

First experiments resulting from the study indicate novel ways of lemma generation to supplement automated first-order provers of various families, strengthening in particular their ability to find short proofs.

CD Tools - Condensed Detachment and Structure Generating Theorem Proving (System Description)

- Computer ScienceArXiv
- 2022

SGCD is a Prolog library for experimenting with condensed detachment in first-order ATP, which puts a recent formal view centered around proof structures into practice and permits to blend goal- and axiom-driven proof search in particularly flexible ways.

KBSET - Knowledge-Based Support for Scholarly Editing and Text Processing

- Computer ScienceDECLARE
- 2019

KBSET supports a practical workflow for scholarly editing, based on using LaTeX with dedicated commands for semantics-oriented markup and a Prolog-implemented core system, which includes a LaTeX parser and a facility for the identification of named entities.

Declarative Programming and Knowledge Management: Conference on Declarative Programming, DECLARE 2019, Unifying INAP, WLP, and WFLP, Cottbus, Germany, September 9–12, 2019, Revised Selected Papers

- Computer ScienceDECLARE
- 2020

This paper describes a new approach for solving Answer Set Programming that exploits the parallelism provided by GPUs.

Craig Interpolation with Clausal First-Order Tableaux

- Computer ScienceJ. Autom. Reason.
- 2021

We develop foundations for computing Craig-Lyndon interpolants of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way…

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