### Abstract

The semantics of most logics of time and probability is given via a probability distribution over threads, where a thread is a structure specifying what will be true at different points in time (in the future). When assessing the probabilities of statements such as "Event a will occur within 5 units of time of event b," there are many different semantics possible, even when assessing the truth of this statement within a single thread. We introduce the syntax of annotated probabilistic temporal (APT) logic programs and axiomatically introduce the key notion of a frequency function (for the first time) to capture different types of intrathread reasoning, and then provide a semantics for intrathread and interthread reasoning in APT logic programs parameterized by such frequency functions. We develop a comprehensive set of complexity results for consistency checking and entailment in APT logic programs, together with sound and complete algorithms to check consistency and entailment. The basic algorithms use linear programming, but we then show how to substantially and correctly reduce the sizes of these linear programs to yield better computational properties. We describe a real world application we are developing using APT logic programs.

Original language | English (US) |
---|---|

Article number | 14 |

Journal | ACM Transactions on Computational Logic |

Volume | 12 |

Issue number | 2 |

DOIs | |

State | Published - Jan 2011 |

Externally published | Yes |

### Fingerprint

### Keywords

- Frequency functions
- Imprecise probabilities
- Probabilistic and temporal reasoning
- Threads

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science
- Computational Mathematics
- Logic

### Cite this

*ACM Transactions on Computational Logic*,

*12*(2), [14]. https://doi.org/10.1145/1877714.1877720

**Annotated probabilistic temporal logic.** / Shakarian, Paulo; Parker, Austin; Simari, Gerardo; Subrahmanian, Venkatramana.

Research output: Contribution to journal › Article

*ACM Transactions on Computational Logic*, vol. 12, no. 2, 14. https://doi.org/10.1145/1877714.1877720

}

TY - JOUR

T1 - Annotated probabilistic temporal logic

AU - Shakarian, Paulo

AU - Parker, Austin

AU - Simari, Gerardo

AU - Subrahmanian, Venkatramana

PY - 2011/1

Y1 - 2011/1

N2 - The semantics of most logics of time and probability is given via a probability distribution over threads, where a thread is a structure specifying what will be true at different points in time (in the future). When assessing the probabilities of statements such as "Event a will occur within 5 units of time of event b," there are many different semantics possible, even when assessing the truth of this statement within a single thread. We introduce the syntax of annotated probabilistic temporal (APT) logic programs and axiomatically introduce the key notion of a frequency function (for the first time) to capture different types of intrathread reasoning, and then provide a semantics for intrathread and interthread reasoning in APT logic programs parameterized by such frequency functions. We develop a comprehensive set of complexity results for consistency checking and entailment in APT logic programs, together with sound and complete algorithms to check consistency and entailment. The basic algorithms use linear programming, but we then show how to substantially and correctly reduce the sizes of these linear programs to yield better computational properties. We describe a real world application we are developing using APT logic programs.

AB - The semantics of most logics of time and probability is given via a probability distribution over threads, where a thread is a structure specifying what will be true at different points in time (in the future). When assessing the probabilities of statements such as "Event a will occur within 5 units of time of event b," there are many different semantics possible, even when assessing the truth of this statement within a single thread. We introduce the syntax of annotated probabilistic temporal (APT) logic programs and axiomatically introduce the key notion of a frequency function (for the first time) to capture different types of intrathread reasoning, and then provide a semantics for intrathread and interthread reasoning in APT logic programs parameterized by such frequency functions. We develop a comprehensive set of complexity results for consistency checking and entailment in APT logic programs, together with sound and complete algorithms to check consistency and entailment. The basic algorithms use linear programming, but we then show how to substantially and correctly reduce the sizes of these linear programs to yield better computational properties. We describe a real world application we are developing using APT logic programs.

KW - Frequency functions

KW - Imprecise probabilities

KW - Probabilistic and temporal reasoning

KW - Threads

UR - http://www.scopus.com/inward/record.url?scp=79551655427&partnerID=8YFLogxK

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U2 - 10.1145/1877714.1877720

DO - 10.1145/1877714.1877720

M3 - Article

AN - SCOPUS:79551655427

VL - 12

JO - ACM Transactions on Computational Logic

JF - ACM Transactions on Computational Logic

SN - 1529-3785

IS - 2

M1 - 14

ER -