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- Title
SOME MODEL THEORY OF GUARDED NEGATION.
- Authors
BÁRÁNY, VINCE; BENEDIKT, MICHAEL; CATE, BALDER TEN
- Abstract
The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences that arise in databases. It has been shown that the syntax of GNFO is restrictive enough so that computational problems such as validity and satisfiability are still decidable. This suggests that, in spite of its expressive power, GNFO formulas are amenable to novel optimizations. In this article we study the model theory of GNFO formulas. Our results include effective preservation theorems for GNFO, effective Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to a large class of GNFO sentences within very restricted logics.
- Subjects
MODEL theory; FIRST-order logic; NEGATION (Logic); DESCRIPTION logics; DEFINABILITY theory (Mathematical logic)
- Publication
Journal of Symbolic Logic, 2018, Vol 83, Issue 4, p1307
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2018.64