Abstract
Semantic Networks have long been recognised as an important tool for modelling human type reasoning. This paper describes an attempt to give a formal semantics of a semantic network in constructive type theory.
The particular net studied is SemNet, the internal knowledge representation for LOLITA: a large scale natural language engineering system. SemNet has been designed with large scale, efficiency, integration and expressiveness in mind. It supports many different forms of plausible and valid reasoning, including: analogy, epistemic reasoning and inheritance. Type theory is used to define the syntactic and semantic models of SemNet. Because of the notion of an internal logic, which follows from the ‘propositions as types’ principle, both of these models can be reasoned about in the same framework. Once formal semantics have been defined they can then be used to analyse the different reasoning mechanisms.
A further advantage is that (because of applications to formal methods for software engineering) type checkers/proof assistants have been built. These tools are ideal for organising and managing the analysis of formal models.
The models are shown to be useful in analysing correctness of implementation of the algorithms, proving consistency and highlighting the assumptions and meaning of the valid and plausible reasoning.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
S. S. Ali and S. C. Shapiro. Natural language processing using a propositional semantic network with structured variables. Minds and Machines, 3, No 4, 1993.
Ronnie Cann. Formal Semantics, An Introduction. Cambridge University Press, 1993.
H. B. Curry and R. Feys. Cominatory Logic, volume 1. North Holland Publishing Company, 1958.
Th. Coquand and G. Huet. The Calculus of Constructions. Information and Computation, 76(2/3), 1988.
R. L. Constable. Implementing Mathematics with the NuPRL Proof Development System. Prentice Hall, 1986.
G. Dowek. The coq proof assistant: User's guide (version 5.6). Technical report, INRIA-Rocquencourt and CNRS-ENS Lyon, 1990.
C. Froidevaux and D. Kayser. Inheritance in semantic networks and default logic. In P.Smets, E. H. Mamdani, D. Dubois, and H. Prade, editors, Non-Standard Logics for Automated Reasoning. Academic Press, Harcourt Brace Jovanovich Publishers, 1988.
J. Y. Girard. Interprétation fonctionelle et élimination des coupures de l'arithmetique. PhD thesis, 1972.
W. A. Howard. The formulae-as-types notion of construction. In J. Hindley and J. Seldin, editors, To H. B. Curry: Essays on Combinatory Logic. Academic Press, 1980.
D. Kumar and H. Chalupsky. Guest Editorial for Special Issue on Propositional Knowledge Representation. Journal of Experimental and Theoretical Artificial Intelligence, 5, No 2 and 3, 1993.
D. Long and R. Garigliano. Reasoning By Analogy And Causality: A model and application. Artificial Intelligence. Ellis Horwood, 1994.
Z. Luo and R. Pollack. LEGO Proof Development System: User's Manual. Technical report, University of Edinburgh LFCS report series, 1992.
Z. Luo. Computation and Reasoning: A Type Theory for Computer Science. Oxford Science Publications, 1994.
R. Morgan et al. Description of the lolita system as used in muc-6. In to appear in — Proceedings Sixth Message Understanding Conference (MUC-6), 1995.
P. Martin-Lof. Intuitionistic Type Theory. Bibliopolis, 1984.
L. Magnusson and B. Nordström. The ALF proof editor and its proof engine. In Types for proof and programs, LNCS, 1994.
B. Nordstrom, K. Petersson, and J. Smith. Programming in Martin-Lofs Type Theory: An Introduction. Oxford University Press, 1990.
A. Rante. Type-Theoretical Grammar. Oxford Science Publications, 1994.
S. Short. Knowledge Representation of Lolita. PhD thesis, (to be submitted) Department of Computer Science, University of Durham, 1996.
J. F. Sowa. Conceptual Structures: Information Processing in Mind and Machine. The Systems Programming Series. Addison Wesley, 1984.
W. A. Woods. Understanding subsumption and taxonomy: A framework for progress. In J. F. Sowa, editor, Principles of Semantic Networks: Explorations in the Representation of Knowledge, chapter 1. Morgan Kauffman, 1991.
W. A. Woods and J. G. Schmolze. The KL-One family. Computers Mathematics and Applications, 23, No 2 and 3:133–177, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shiu, S., Luo, Z., Garigliano, R. (1996). Type theoretic semantics for SemNet. In: Gabbay, D.M., Ohlbach, H.J. (eds) Practical Reasoning. FAPR 1996. Lecture Notes in Computer Science, vol 1085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61313-7_102
Download citation
DOI: https://doi.org/10.1007/3-540-61313-7_102
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61313-8
Online ISBN: 978-3-540-68454-1
eBook Packages: Springer Book Archive