Improving legibility of natural deduction proofs is not trivial

Pąk, Karol

doi:10.2168/lmcs-10(3:23)2014

Cited by 11 publications

(9 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Additionally, as 3rd MIL is NP-complete even for E = E 1 (see [24]), we obtain by Theorem 3 that E 1 can be replaced by E in instances of Directed HCP.…”

Section: Directed Hamiltonian Path Completion (Directed Hpc)mentioning

confidence: 75%

See 1 more Smart Citation

Improving Legibility of Formal Proofs Based on the Close Reference Principle is NP-Hard

Pąk

2015

J Autom Reasoning

Self Cite

View full text Add to dashboard Cite

Proof development in proof assistants such as HOL, Coq, Mizar, etc. is an activity where authors usually produce proofs by typing out proof scripts or system tactics. Quite frequently, however, authors also have to read existing proof scripts, either to imitate smart proof pieces, or to refactor fragments of reasoning to make some theorem stronger, more easily applicable and so on. Therefore, it is important to develop techniques to improve legibility of proofs, since it directly affects productivity of script writers. To analyze the legibility of natural deduction proofs, we investigate proof graphs that represent the flow of information in given reasoning. Our analysis of the information flow leads to methods of improving proof readability based on Behaghel's First Law, which states that in legible text relevant pieces of information must occur close to each other. The presented method maximizes the number of close connections between premises and steps that use these steps as justification. In this paper we show that our optimization method is NP-hard.

show abstract

“…Additionally, as 3rd MIL is NP-complete even for E = E 1 (see [24]), we obtain by Theorem 3 that E 1 can be replaced by E in instances of Directed HCP.…”

Section: Directed Hamiltonian Path Completion (Directed Hpc)mentioning

confidence: 75%

“…The case E = E 1 is also NP-complete, and it was proved in [24], but the transformation there is not in LOGSPACE, and we do not know how to improve it to be in LOGSPACE.…”

Section: Theorem 2 the Problem 1st Mil N Is Np-complete For Each Nmentioning

confidence: 99%

Improving Legibility of Formal Proofs Based on the Close Reference Principle is NP-Hard

Pąk

2015

J Autom Reasoning

Self Cite

View full text Add to dashboard Cite

show abstract

“…MIZAR is also a common name for the components of the system: a formal language derived from the mathematical vernacular and dozens of computer programs responsible for formal verification, optimization of proofs [24,25]. An integrant part of the system is the Mizar Mathematical Library (MML), a collection of articles written in the MIZAR language.…”

Section: About Mizarmentioning

confidence: 99%

Definitional Expansions in Mizar

Korniłowicz

2015

J Autom Reasoning

View full text Add to dashboard Cite

The MIZAR VERIFIER uses definitional expansions for controlling proof structures. In this paper we propose another use of definitional expansions-enriching verified inferences by expansions of definitions of formulae included in the inferences and increasing the number of premises accessible by CHECKER. This introduces more knowledge to the reasoning, which helps to draw more conclusions. Some statistics about influence of such expansions on the MIZAR MATHEMATICAL LIBRARY are presented.

show abstract

“…As far as binary predicates are concerned, which is directly related to the topic of this paper, the current version of the Mizar system supports registering reflexivity, irreflexivity, symmetry, asymmetry and connectedness. The transitivity 1 The legibility of proofs is a subject of ongoing research [4], [5], [6].…”

Section: Introductionmentioning

confidence: 99%

“…4 Formally speaking, a binary relation R on a set X is Euclidean (sometimes called right Euclidean) if it satisfies the following condition:…”

Section: Introductionmentioning

confidence: 99%

Introducing Euclidean Relations to Mizar

Naumowicz

Korniłowicz

2017

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

View full text Add to dashboard Cite

Abstract-In this paper we present the methodology of implementing a new enhancement of the Mizar proof checker based on enabling special processing of Euclidean predicates, i.e. binary predicates which fulfill a specific variant of transitivity postulated by Euclid. Typically, every proof step in formal mathematical reasoning is associated with a formula to be proved and a list of references used to justify the formula. With the proposed enhancement, the Euclidean property of given relations can be registered during their definition, and so the verification of some proof steps related to these relations can be automated to avoid explicit referencing.

show abstract

Improving legibility of natural deduction proofs is not trivial

Cited by 11 publications

References 20 publications

Improving Legibility of Formal Proofs Based on the Close Reference Principle is NP-Hard

Improving Legibility of Formal Proofs Based on the Close Reference Principle is NP-Hard

Definitional Expansions in Mizar

Introducing Euclidean Relations to Mizar

Contact Info

Product

Resources

About