# Reconstruction Proofs at the Assertion Level

@inproceedings{Huang1994ReconstructionPA, title={Reconstruction Proofs at the Assertion Level}, author={Xiaorong Huang}, booktitle={CADE}, year={1994} }

Most automated theorem provers suffer from the problem that they can produce proofs only in formalisms difficult to understand even for experienced mathematicians. Effort has been made to reconstruct natural deduction (ND) proofs from such machine generated proofs. Although the single steps in ND proofs are easy to understand, the entire proof is usually at a low level of abstraction, containing too many tedious steps. To obtain proofs similar to those found in mathematical textbooks, we…

## 109 Citations

Translating Machine-Generated Resolution Proofs into ND-Proofs at the Assertion Level

- MathematicsPRICAI
- 1996

This paper first study resolution proofs in terms of meaningful operations employed by human mathematicians, and thereby establishes a correspondence between resolution proofs and ND proofs at a more abstract level, and shows that if its unit initial clauses are CNFs of literal premises of a problem, a unit resolution corresponds directly to a well-structured ND proof segment that mathematicians intuitively understand as the application of a definition or a theorem.

PROVERB– A System Explaining Machine-Found Proofs

- Computer ScienceProceedings of the Sixteenth Annual Conference of the Cognitive Science Society
- 2019

An implemented system called PROVERB is outlined that explains machine -found natural deduction proofs in natural language using the concept of so-called assertion level inference rules and combines standard hierarchical text planning and techniques that locally organize argumentative texts based on the derivation relation under the guidance of a focus mechanism.

Finding Small Proofs for Description Logic Entailments: Theory and Practice (Extended Technical Report)

- Computer Science, MathematicsLPAR
- 2020

An approach for generating proofs for expressive DLs based on a non-standard reasoning task called forgetting is developed and implemented and compared the obtained proofs with proofs generated by the DL reasoner ELK, finding that forgetting-based proofs are often better w.r.t. different measures of proof complexity.

Finding Good Proofs for Description Logic Entailments Using Recursive Quality Measures (Extended Technical Report)

- Computer Science, MathematicsCADE
- 2021

Results are provided for a class of measures called recursive, which yields lower complexities and also encompasses proof depth and closes some gaps left open in the previous work, providing a comprehensive picture of the complexity landscape.

Finding Good Proofs for Description Logic Entailments Using Recursive Quality Measures (Extended Abstract)

- Computer Science, PhilosophyDescription Logics
- 2021

The complexity of finding proofs of a given quality among all possible alternative proofs is investigated, based on the notion of a deriver, which generates a so-called derivation structure consisting of possible proof steps, from which all proofs of the given consequence can be constructed.

Faithfully Reflecting the Structure of Informal Mathematical Proofs into Formal Type Theories

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2004

Presenting Proofs in a Human-Oriented Way

- PhilosophyCADE
- 1999

An approach is described that successively enhances a logically self-contained proof at the assertion level through communicatively justified modifications of the original line of reasoning, which includes expansion of involved theorem applications, omission of trivial justifications, compactification of intermediate inference steps, and broadening the scope of justifications to support focused argumentation.

Harpoon: Mechanizing Metatheory Interactively - (System Description)

- Computer ScienceCADE
- 2021

Harpoon is an interactive proof engine built on top of Beluga that allows users to develop proofs interactively using a small, fixed set of high-level actions that safely transform a subgoal.

Principles of Superdeduction

- Computer Science22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
- 2007

This paper presents and studies the dual concept where the theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way, and introduces a proof-term language and a cut-elimination procedure both based on Christian Urban's work on classical sequent calculus.

Interactive Proof Construction at the Task Level

- Computer Science
- 2003

A human oriented interaction layer is obtained that improves and combines ideas underlying the window inference technique [RS93], the proof by pointing approach [BKT94], and the focus windows of [PB02].

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