Abstract
Type hierarchies which arise in applications are often described incompletely; this missing information may be handled in a variety of ways. In this work, such incomplete hierarchies are viewed as open specifications; that is, descriptions which are sets of constraints. The actual hierarchy is then any structure satisfying these constraints. For such specifications, two forms of characterization are provided. The first is algebraic and utilizes a generalization of weak partial lattices; it provides a structure-based characterization in which optimality is characterized via an initial construction. The second is logical, an inference-based representation, in which models are characterized as products of models of propositional-based specifications.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J. Adámek, H. Herrlich, and G. Strecker. Abstract and Concrete Categories. Wiley-Interscience, 1990.
C. Beeri. A formal approach to object-oriented databases. Data and Knowledge Engineering, 5:353–382, 1990.
A. Borgida. Description logics in data management. IEEE Trans. Knowledge Data Engrg., 7:671–682, 1995.
T. Briscoe, V. de Paiva, and A. Copestake, editors. Inheritance, Defaults, and the Lexicon. Cambridge University Press, 1993.
B. Carpenter and G. Penn. ALE: The Attribute Logic Engine user’s guide, Version 3.1 Beta. Technical report, Bell Laboratories and Universität Tübingen, 1998.
B. A. Davey and H. A. Priestly. Introduction to Lattices and Order. Cambridge University Press, 1990.
J. Döerre and M. Dorna. CUF-a formalism for linguistic knowledge representation. In J. Dörre, editor, Computational Aspects of Constraint-Based Linguistic Description, DYANA-2 Deliverable R.1.2.A, pages 3–22. ESPRIT, 1993.
J. Dörre and A. Eisele. Feature logic with disjunctive unification. In Proceedings of the COLING 90, Volume 2, pages 100–105, 1990.
W. F. Dowling and J. H. Gallier. Linear-time algorithms for testing the satisfiability of propositional Horn clauses. J. Logic Programming, 3:267–284, 1984.
B. Ganter and R. Wille. Formal Concept Analysis. Springer-Verlag, 1999.
M. R. Garey and D. S. Johnson. Computers and Intractability. W. H. Freeman, 1979.
G. Grätzer. General Lattice Theory. Birkhäuser Verlag, second edition, 1998.
S. J. Hegner. Distributivity in incompletely specified type hierarchies: Theory and computational complexity. In J. Dörre, editor, Computational Aspects of Constraint-Based Linguistic Description II, DYANA-2, ESPRIT Basic Research Project 6852, Deliverable R1.2B, pages 29–120. DYANA, 1994.
S. J. Hegner. Properties of Horn clauses in feature-structure logic. In C. J. Rupp, M. A. Rosner, and R. L. Johnson, editors, Constraints, Languages and Computation, pages 111–147. Academic Press, 1994.
S. J. Hegner. Efficient inference algorithms for databases of type hierarchies with open specification. Submitted for publication, 2001.
S. J. Hegner. Computational and structural aspects of openly specified type hierarchies. In M. Moortgat, editor, Logical Aspects of Computational Linguistics, Third International Conference, LACL’ 98 Grenoble, France, December 1998, Selected Papers, in press, 2001.
C. Pollard and I. A. Sag. Head-Driven Phrase Structure Grammar. University of Chicago Press, 1994.
K.-D. Schewe and B. Thalheim. Fundamental concepts of object oriented databases. Acta Cybernetica, 11:49–84, 1993.
J. Van den Bussche. Formal Aspects of Object Identity in Database Manipulation. PhD thesis, University of Antwerp, 1993.
R. Zajac. Notes on the Typed Feature System, Version 4, January 1991. Technical report, Universität Stuttgart, Institut für Informatik, Project Polygloss, 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hegner, S.J. (2003). Characterization of Type Hierarchies with Open Specification. In: Bertossi, L., Katona, G.O.H., Schewe, KD., Thalheim, B. (eds) Semantics in Databases. SiD 2001. Lecture Notes in Computer Science, vol 2582. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36596-6_6
Download citation
DOI: https://doi.org/10.1007/3-540-36596-6_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00957-3
Online ISBN: 978-3-540-36596-9
eBook Packages: Springer Book Archive