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Implicit Quantification Made Explicit: How to Interpret Blank Nodes and Universal Variables in Notation3 Logic

34 Pages Posted: 2 May 2019 First Look: Accepted

See all articles by Dörthe Arndt

Dörthe Arndt

Ghent University-Universiteit Gent - IDLab

Tom Schrijvers

KU Leuven - Department of Computer Science

Jos De Roo

Agfa Healthcare

Ruben Verborgh

Ghent University-Universiteit Gent - IDLab

Abstract

Since the invention of Notation3 Logic, several years have passed in which the theory has been refined and applied in different reasoning engines like Cwm, EYE, and FuXi. But despite these developments, a clear formal definition of Notation3’s semantics is still missing. This does not only form an obstacle for the formal investigation of that logic and its relations to other formalisms, it has also practical consequences: in many cases the interpretations of the same formula di er between reasoning engines. In this paper we tackle one of the main sources of that problem, namely the uncertainty about implicit quantification. This refers to Notation3’s ability to use bound variables for which the universal or existential quantifiers are not explicitly stated, but implicitly assumed. We provide a tool for clarification through the definition of a core logic for Notation3 that only supports explicit quantification. We specify an attribute grammar which maps Notation3 formulas to that logic according to the different interpretations and thereby define the semantics of Notation3. This grammar is then implemented and used to test the impact of the differences between interpretations on practical cases. Our dataset includes Notation3 implementations from former research projects and test cases developed for the reasoner EYE. We find that 31% of these files are understood differently by different reasoners. We further analyse these cases and categorize them in different classes of which we consider one most harmful: if a file is manually written by a user and no specific built-in predicates are used (13% of our critical files), it is unlikely that this user is aware of possible differences. We therefore argue the need to come to an agreement on implicit quantification, and discuss the different possibilities.

Keywords: N3, Scoping, RDF, Attribute Grammar, Formal Semantics

Suggested Citation

Arndt, Dörthe and Schrijvers, Tom and Roo, Jos De and Verborgh, Ruben, Implicit Quantification Made Explicit: How to Interpret Blank Nodes and Universal Variables in Notation3 Logic (April 30, 2019). Available at SSRN: https://ssrn.com/abstract=3380233 or http://dx.doi.org/10.2139/ssrn.3380233

Dörthe Arndt (Contact Author)

Ghent University-Universiteit Gent - IDLab

Gent
Belgium

Tom Schrijvers

KU Leuven - Department of Computer Science

Belgium

Jos De Roo

Agfa Healthcare

Belgium

Ruben Verborgh

Ghent University-Universiteit Gent - IDLab ( email )

Gent
Belgium

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