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SOME MODEL THEORY OF GUARDED NEGATION

Published online by Cambridge University Press:  21 December 2018

VINCE BÁRÁNY ,
MICHAEL BENEDIKT  and
BALDER TEN CATE
VINCE BÁRÁNY
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF OXFORD 15 PARKS ROAD OXFORD, OX1 3QD, UKE-mail:vbarany@googlemail.com
MICHAEL BENEDIKT
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF OXFORD 15 PARKS ROAD OXFORD, OX1 3QD, UKE-mail:michael.benedikt@gmail.com
BALDER TEN CATE
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE UC SANTA CRUZ 1156 HIGH STREET SANTA CRUZ, CA95064, USAE-mail:balder.tencate@gmail.com
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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.

Keywords

03B70guarded negationinterpolationrewriting
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 4 , December 2018 , pp. 1307 - 1344
Copyright
Copyright © The Association for Symbolic Logic 2018 

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