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Found 13 papers, 1 papers with code
Range-Restricted Interpolation through Clausal Tableaux
We show how variations of range-restriction and also the Horn property can be passed from inputs to outputs of Craig interpolation in first-order logic.
Lemmas: Generation, Selection, Application
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving.
Investigations into Proof Structures
We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner.
Generating Compressed Combinatory Proof Structures -- An Approach to Automated First-Order Theorem Proving
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term.
CD Tools -- Condensed Detachment and Structure Generating Theorem Proving (System Description)
CD Tools 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.
Applying Second-Order Quantifier Elimination in Inspecting Gödel's Ontological Proof
In recent years, G\"odel's ontological proof and variations of it were formalized and analyzed with automated tools in various ways.
Learning from Łukasiewicz and Meredith: Investigations into Proof Structures (Extended Version)
The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction.
Facets of the PIE Environment for Proving, Interpolating and Eliminating on the Basis of First-Order Logic
PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic.
KBSET -- Knowledge-Based Support for Scholarly Editing and Text Processing with Declarative LaTeX Markup and a Core Written in SWI-Prolog
KBSET is an environment that provides support for scholarly editing in two flavors: First, as a practical tool KBSET/Letters that accompanies the development of editions of correspondences (in particular from the 18th and 19th century), completely from source documents to PDF and HTML presentations.
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.
PIE -- Proving, Interpolating and Eliminating on the Basis of First-Order Logic
PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic.
Heinrich Behmann's Contributions to Second-Order Quantifier Elimination from the View of Computational Logic
For relational monadic formulas (the L\"owenheim class) second-order quantifier elimination, which is closely related to computation of uniform interpolants, projection and forgetting - operations that currently receive much attention in knowledge processing - always succeeds.
The Boolean Solution Problem from the Perspective of Predicate Logic - Extended Version
We identify some cases that allow constructions, most of them based on Craig interpolation, and show a method to take vocabulary restrictions on solution components into account.
