### Abstract

We develop a fusion of logical and metrical principles for reasoning about Markov processes. More precisely, we lift metrics from processes to sets of processes satisfying a formula and explore how the satisfaction relation behaves as sequences of processes and sequences of formulas approach limits. A key new concept is dynamically-continuous metric bisimulation which is a property of (pseudo)metrics. We prove theorems about satisfaction in the limit, robustness theorems as well as giving a topological characterization of various classes of formulas. This work is aimed at providing approximate reasoning principles for Markov processes.

Original language | English |
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Title of host publication | Mathematical Foundations of Computer Science 2012. MFCS 2012. |

Editors | B. Rovan, V. Sassone, P. Widmayer |

Place of Publication | Berlin |

Publisher | Springer-Verlag |

Pages | 681-692 |

Number of pages | 12 |

ISBN (Print) | 9783642325885 |

DOIs | |

Publication status | Published - 20 Aug 2012 |

Event | 37th International Symposium on Mathematical Foundations of Computer Science 2012, MFCS 2012 - Bratislava, Slovakia Duration: 27 Aug 2012 → 31 Aug 2012 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7464 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 37th International Symposium on Mathematical Foundations of Computer Science 2012, MFCS 2012 |
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Country | Slovakia |

City | Bratislava |

Period | 27/08/12 → 31/08/12 |

### Keywords

- Markov process
- convergent sequence
- logical formula
- approximate reasoning
- Markov kernel

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## Cite this

*Mathematical Foundations of Computer Science 2012. MFCS 2012.*(pp. 681-692). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7464 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-642-32589-2_59