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

Wernhard, Christoph

doi:10.1007/978-3-030-46714-2_11

Cited by 11 publications

(14 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Unfortunately, in current practice such schema specifications and documentations for digital editions are only rarely made easily accessible. 16 The suggested way to associate a TEI/XML document instance with a schema by the xml-model processing instruction [14,Sect. v.7.2] seems not used at all.…”

Section: Discussionmentioning

confidence: 99%

“…KBSET is free software. It depends only on a T E X distribution (it has been tested with TeX Live) and on SWI-Prolog, both of which are also free software, 16 Actually, the authors were (in November 2019) not able to find any correspondence edition where a formal specification of the used customized schema is referenced from the TEI/XML documents or specified on the Web site. Informal edition guidelines can be found, for example, on the Web sites of Alfred-Escher Briefedition, Briefe und Texte aus dem intellektuellen Berlin um 1800 and hallerNet.…”

Section: Discussionmentioning

confidence: 99%

“…Recent approaches to interpolation-based query reformulation [15,1] investigate a declarative approach for this. The optimized version of a query is there extracted as a Craig interpolant [2,16] from a proof obtained from a first-order prover. It seems also possible to apply this approach to determine from a given set of queries the caches that need to be constructed for efficient evaluation of the queries.…”

Section: Some Issues For Logic-based Knowledge Processingmentioning

confidence: 99%

See 2 more Smart Citations

KBSET -- Knowledge-Based Support for Scholarly Editing and Text Processing with Declarative LaTeX Markup and a Core Written in SWI-Prolog

Kittelmann,

Wernhard

2020

Preprint

Self Cite

View full text Add to dashboard Cite

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. Second, as a prototypical tool KBSET/NER for experimentally investigating novel forms of working on editions that are centered around automated named entity recognition. KBSET can process declarative application-specific markup that is expressed in L A T E X notation and incorporate large external fact bases that are typically provided in RDF. KBSET includes specially developed L A T E X styles and a core system that is written in SWI-Prolog, which is used there in many roles, utilizing that it realizes the potential of Prolog as a unifying language.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Some Issues For Logic-based Knowledge Processingmentioning

confidence: 99%

See 1 more Smart Citation

KBSET -- Knowledge-Based Support for Scholarly Editing and Text Processing with Declarative LaTeX Markup and a Core Written in SWI-Prolog

Kittelmann,

Wernhard

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…As embedded reasoners we used the first-order theorem provers Prover9 [20] and CMProver [9,29], the first-order model generator Mace4 [20], and an implementation [29,30] of the DLS algorithm [10] for second-order quantifier elimination, which is based on Ackermann's Lemma [1]. Reasoner outputs computed during processing of the PIE document are presented with the introductory phrases This formula is valid:, This formula is not valid: and Result of elimination:.…”

Section: Preliminariesmentioning

confidence: 99%

“…The expectation is that further, previously unnoticed or obscured aspects and details of the proof become apparent. The used framework, PIE ("Proving, Interpolating, Eliminating") [29,30] embeds automated reasoners, in particular for first-order theorem proving and second-order quantifier elimination, in a system for defining formula macros and rendering L A T E X-formatted presentations of formula macro definitions and reasoner outputs. In fact, the present paper is the generated output of such a PIE document.…”

Section: Introductionmentioning

confidence: 99%

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

Wernhard¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

In recent years, Gödel's ontological proof and variations of it were formalized and analyzed with automated tools in various ways. We supplement these analyses with a modeling in an automated environment based on first-order logic extended by predicate quantification. Formula macros are used to structure complex formulas and tasks. The analysis is presented as a generated type-set document where informal explanations are interspersed with pretty-printed formulas and outputs of reasoners for first-order theorem proving and second-order quantifier elimination. Previously unnoticed or obscured aspects and details of Gödel's proof become apparent. Practical application possibilities of second-order quantifier elimination are shown and the encountered elimination tasks may serve as benchmarks.

show abstract

KBSET – Knowledge-Based Support for Scholarly Editing and Text Processing with Declarative Markup and a Core Written in SWI-Prolog

Kittelmann¹,

Wernhard²

2020

Declarative Programming and Knowledge Management

Self Cite

View full text Add to dashboard Cite

KBSET supports a practical workflow for scholarly editing, based on using L A T E X with dedicated commands for semantics-oriented markup and a Prolog-implemented core system. Prolog plays there various roles: as query language and access mechanism for large Semantic Web fact bases, as data representation of structured documents and as a workflow model for advanced application tasks. The core system includes a L A T E X parser and a facility for the identification of named entities. We also sketch future perspectives of this approach to scholarly editing based on techniques of computational logic.

show abstract

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

Cited by 11 publications

References 41 publications

KBSET -- Knowledge-Based Support for Scholarly Editing and Text Processing with Declarative LaTeX Markup and a Core Written in SWI-Prolog

KBSET -- Knowledge-Based Support for Scholarly Editing and Text Processing with Declarative LaTeX Markup and a Core Written in SWI-Prolog

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

KBSET – Knowledge-Based Support for Scholarly Editing and Text Processing with Declarative Markup and a Core Written in SWI-Prolog

Contact Info

Product

Resources

About