- Set Description Languages and Reasoning about Numerical Features of Sets
- Modal Logics, Description Logics and Arithmetic Reasoning
- How to Augment a Formal System with a Boolean Algebra Component
- A Multi-Dimensional Terminological Knowledge Representation Language

**Set Description Languages and Reasoning about Numerical Features of Sets**

*Hans Jürgen Ohlbach*

**Abstract:**

Set description languages, for example description logics, can be
used to specify sets and set-theoretic relationships between
them. Mathematical programming, on the other hand, can be used to
find optimal solutions for arithmetical equation and in-equation
systems.
In this paper a combination methodology is
presented, which allows one to use numerical algorithms for
reasoning about numerical
features of sets specified with a set description language.
The method is applied to description logics as an examples for a set
description language. In this context new properties of
logical languages become interesting which have not been considered so
far.

uncompressed files | PostScript (386K) | PDF (228K) |

compressed files | PostScript (141K) | PDF (204K) |

**Modal Logics, Description Logics and Arithmetic Reasoning**

*Hans Jürgen Ohlbach and Jana Koehler*

uncompressed files | dvi (125K) | PostScript (386K) | PDF (228K) | bib |

compressed files | dvi ( 48K) | PostScript (141K) | PDF (204K) |

**How to Augment a Formal System with a Boolean Algebra Component**

*Hans Jürgen Ohlbach*

uncompressed files | PostScript (515K) | PDF (100K) | bib |

compressed files | PostScript (134K) | PDF ( 84K) |

uncompressed files | dvi (200K) | PostScript (378K) | PDF (275K) | bib |

compressed files | dvi ( 71K) | PostScript (128K) | PDF (248K) |