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

  title={Facets of the PIE Environment for Proving, Interpolating and Eliminating on the Basis of First-Order Logic},
  author={Christoph Wernhard},
  • C. Wernhard
  • Published in DECLARE 24 February 2020
  • Computer Science
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… 
Applying Second-Order Quantifier Elimination in Inspecting Gödel's Ontological Proof
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)
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)
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
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
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
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


Computing with Logic as Operator Elimination: The ToyElim System
A prototype system is described whose core functionality is the elimination of second-order operators, such as Boolean quantifiers and operators for projection, forgetting and circumscription, in a uniform operational system, backed by a uniform classical semantic framework.
Circumscription and Projection as Primitives of Logic Programming
This work utilizes the polarity sensitiveness of projection, in contrast to second-order quantification, and a variant of circumscription that allows to express predicate minimization in parallel with maximization.
An Implementation and Optimization of an Algorithm for Reducing Formulae in Second-Order Logic
The DLS algorithm for reducing secondorder logic to rst-order logic by Doherty, Lukaszewicz and Szalas can be implemented and a module for handling nested abnormality theories is included to show that the algoritm is general and can be useful in many areas.
Second-Order Quantifier Elimination - Foundations, Computational Aspects and Applications
This book provides the first comprehensive, systematic and uniform account of the state-of-the-art of second-order quantifier elimination in classical and non-classical logics.
System Description: E-KRHyper
It is the goal to extend the range of application possibilities of KRHyper by adding equality reasoning, which integrates a superposition-based handling of equality into the hyper tableau calculus.
The Boolean Solution Problem from the Perspective of Predicate Logic (Abstract)
It is shown that finding solution values for unknowns in Boolean equations can be modeled on the basis of first-order logic extended by second-order quantification, and a wealth of classical results transfers, foundations for algorithms unfold, and connections with second- order quantifier elimination and Craig interpolation show up.
Abduction in Logic Programming as Second-Order Quantifier Elimination
This work transfers application patterns and generalizations of second-order quantification in a unifying framework to abduction with three non-classical semantics of logic programming: stable model, partial stable model and well-founded semantics.
A prolog technology theorem prover: Implementation by an extended prolog compiler
  • M. Stickel
  • Computer Science
    Journal of Automated Reasoning
  • 2004
A Prolog technology theorem prover (PTTP) is an extension of Prolog that is complete for the full first-order predicate calculus. It differs from Prolog in its use of unification with the occurs
The Ackermann approach for modal logic, correspondence theory and second-order reduction
Computing Circumscription Revisited: A Reduction Algorithm
This article provides a general method that can be used in an algorithmic manner to reduce certain circumscription axioms to first-order formulas and demonstrates the generality of the algorithm using circumscriptive theories with mixed quantifiers, variable constants, nonseparated formulas, and formulas with n-ary predicate variables.