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LPAR

2005

Springer

2005

Springer

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...

Related Content

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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