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LPAR
2005
Springer

Comparative Similarity, Tree Automata, and Diophantine Equations

14 years 19 days ago
Comparative Similarity, Tree Automata, and Diophantine Equations
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 τ1 than to a set τ2’ 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 equation...
Mikhail Sheremet, Dmitry Tishkovsky, Frank Wolter,
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where LPAR
Authors Mikhail Sheremet, Dmitry Tishkovsky, Frank Wolter, Michael Zakharyaschev
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