### Abstract

In this paper we develop and study the Recursive Weighted Logic (RWL), a multi-modal logic that expresses qualitative and quantitative properties of labelled weighted transition systems (LWSs). LWSs are transition systems labelled with actions and real-valued quantities representing the costs of transitions with respect to various resources. RWL uses first-order variables to measure local costs. The main syntactic operators are similar to the ones of timed logics for real-time systems. In addition, our logic is endowed, with simultaneous recursive equations, which specify the weakest properties satisfied by the recursive variables. We prove that unlike in the case of the timed logics, the satisfiability problem for RWL is decidable. The proof uses a variant of the region construction technique used in literature with timed automata, which we adapt to the specific settings of RWL. This paper extends previous results that we have demonstrated for a similar but much more restrictive logic that can only use one variable for each type of resource to encode logical properties.

Original language | English |
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Title of host publication | Theoretical Aspects of Computing – ICTAC 2014 |

Subtitle of host publication | Proceedings of 11th International Colloquium Bucharest, Romania, September 17-19, 2014 |

Editors | Gabriel Ciobanu, Dominique Méry |

Place of Publication | Cham |

Publisher | Springer |

Pages | 460-476 |

Number of pages | 17 |

ISBN (Print) | 9783319108810, 9783319108827 |

DOIs | |

Publication status | Published - 23 Sep 2014 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer Verlag |

Volume | 8687 |

ISSN (Print) | 0302-9743 |

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### Keywords

- labelled weighted transition system
- maximal fixed point computation
- multi-modal logic

### Cite this

*Theoretical Aspects of Computing – ICTAC 2014: Proceedings of 11th International Colloquium Bucharest, Romania, September 17-19, 2014*(pp. 460-476). (Lecture Notes in Computer Science; Vol. 8687). Cham: Springer. https://doi.org/10.1007/978-3-319-10882-7_27