Comparative similarity, tree automata, and diophantine equations

Sheremet, Mikhail and Tishkovsky, D. and Wolter, F. and Zakharyaschev, Michael (2005) Comparative similarity, tree automata, and diophantine equations. In: Sutcliffe, G. and Voronkov, A. (eds.) LPAR 2005: Logic for Programming, Artificial Intelligence, and Reasoning. Lecture Notes in Computer Science 3835. Springer, pp. 651-665. ISBN 9783540305538.

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Official URL: https://doi.org/10.1007/11591191_45

Abstract

The notion of comparative similarity ‘X is more similar or closer to Y than to Z’ has been investigated in both foundational and applied areas of knowledge representation and reasoning, e.g., in concept formation, similarity-based reasoning and areas of bioinformatics such as protein sequence alignment. In this paper we analyse the computational behaviour of the ‘propositional’ logic with the binary operator ‘closer to a set τ 1 than to a set τ 2’ and nominals interpreted over various classes of distance (or similarity) spaces. In particular, using a reduction to the emptiness problem for certain tree automata, we show that the satisfiability problem for this logic is ExpTime-complete for the classes of all finite symmetric and all finite (possibly non-symmetric) distance spaces. For finite subspaces of the real line (and higher dimensional Euclidean spaces) we prove the undecidability of satisfiability by a reduction of the solvability problem for Diophantine equations. As our ‘closer’ operator has the same expressive power as the standard operator > of conditional logic, these results may have interesting implications for conditional logic as well.

Metadata

Item Type:	Book Section
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Sarah Hall
Date Deposited:	01 Nov 2021 12:46
Last Modified:	09 Aug 2023 12:52
URI:	https://eprints.bbk.ac.uk/id/eprint/46550

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