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Gödel logics and the fully boxed fragment of LTL

13 pagesPublished: May 4, 2017

Abstract

In this paper we show that a very basic fragment of FO-LTL, the monadic fully boxed fragment (all connectives and quantifiers are guarded by P) is not recursively enumerable wrt validity and 1-satisfiability if three predicates are present. This result is obtained by reduction of the fully boxed fragment of FO-LTL to the Gödel logic G↓, the infinitely valued Gödel logic with truth values in [0,1] such that all but 0 are isolated. The result on 1-satisfiability is in no way symmetric to the result on validity as in classical logic: this is demonstrated by the analysis of G↑, the related infinitely-valued Gödel logic with truth values in [0, 1] such that all but 1 are isolated. Validity of the monadic fragment with at least two predicates is not recursively enumerable, 1-satisfiability of the monadic fragment is decidable.

Keyphrases: Gödel logic, LTL, monadic fragment

In: Thomas Eiter and David Sands (editors). LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 46, pages 404--416

Links:
BibTeX entry
@inproceedings{LPAR-21:Godel_logics_and_fully,
  author    = {Matthias Baaz and Norbert Preining},
  title     = {G\textbackslash{}"odel logics and the fully boxed fragment of LTL},
  booktitle = {LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Thomas Eiter and David Sands},
  series    = {EPiC Series in Computing},
  volume    = {46},
  pages     = {404--416},
  year      = {2017},
  publisher = {EasyChair},
  bibsource = {EasyChair, http://www.easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/xfX},
  doi       = {10.29007/bdbm}}
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