## Of starships and Klingons: Bayesian logic for 23rd century (2005)

Venue: | Proc. UAI-05 |

Citations: | 8 - 1 self |

### BibTeX

@INPROCEEDINGS{Laskey05ofstarships,

author = {Kathryn B. Laskey and Paulo C. G. Da Costa},

title = {Of starships and Klingons: Bayesian logic for 23rd century},

booktitle = {Proc. UAI-05},

year = {2005},

pages = {346--353}

}

### OpenURL

### Abstract

Intelligent systems in an open world must reason about many interacting entities related to each other in diverse ways and having uncertain features and relationships. Traditional probabilistic languages lack the expressive power to handle relational domains. Classical first-order logic is sufficiently expressive, but lacks a coherent plausible reasoning capability. Recent years have seen the emergence of a variety of approaches to integrating first-order logic, probability, and machine learning. This paper presents Multi-entity Bayesian networks (MEBN), a formal system that integrates First Order Logic (FOL) with Bayesian probability theory. MEBN extends ordinary

### Citations

3576 |
Convergence of Probability Measures
- Billingsley
- 1968
(Show Context)
Citation Context ...as an induction hypothesis that mutually consistent joint distributions exist for all finite sets of RV instances containing only instances of depth no greater than d, Kolmogorov’s existence theorem (=-=Billingsley 1995-=-) implies the existence of a joint distribution on the set of all RV instances of depth no greater than d. From this, the induction hypothesis follows for depth d+1. A second application of Kolmogorov... |

607 | Dynamic Bayesian networks: Representation, inference and learning
- Murphy
- 2002
(Show Context)
Citation Context ...bance caused by a starship in cloak mode would show a characteristic temporal pattern. Standard BNs do not provide a natural way to represent such repeated patterns. Dynamic Bayesian networks (DBNs) (=-=Murphy 1998-=-) and partially dynamic Bayesian networks (e.g. Takikawa et al. 2001) extend BNs to model temporal patterns. However, there is no standard means to represent general recursive probabilistic relationsh... |

397 |
Statistical inference for probabilistic functions of finite state Markov chains
- Baum, Petrie
- 1966
(Show Context)
Citation Context ...ow to represent any FOL sentence as an MFrag, as well as an overview of Bayesian learning, which is treated in MEBN logic as a sequence of MTheories. 5 RELATED RESEARCH Hidden Markov models, or HMMs (=-=Baum & Petrie 1966-=-), have been applied extensively in pattern recognition applications. HMMs can be viewed as a special case of dynamic Bayesian networks, or DBNs (Murphy 1998). A HMM is a DBN having hidden states with... |

194 | Object-oriented Bayesian networks
- Koller, Pfeffer
- 1997
(Show Context)
Citation Context ...ty to handle continuous distributions without resorting to discretization, and support for parameter learning in a wide variety of parameterized statistical models. Object-oriented Bayesian Networks (=-=Koller & Pfeffer 1997-=-) represent entities as instances of object classes with class-specific attributes and probability distributions. Probabilistic Relational Models (PRMs) (Getoor et al. 2000) integrate the relational d... |

160 |
Causality
- Pearl
- 2000
(Show Context)
Citation Context ...Exists(!S4) is updated by Bayesian conditioning as relevant evidence accrues. Representing existence uncertainty is especially useful for counterfactual reasoning and reasoning about causality (e.g., =-=Pearl 2000-=-). MEBN logic can also represent association uncertainty, a major problem for multi-source fusion systems. Association uncertainty means we are not sure about the source of a given report. For example... |

131 |
D.J.: A language and program for complex Bayesian modelling. The Statistician 43
- Gilks, Thomas, et al.
- 1994
(Show Context)
Citation Context ...nt complementary approaches to specifying firstorder probabilistic theories. BLPs represent fragments ofsBayesian networks in first-order logic; MEBN theories represent FOL sentences as MFrags. BUGS (=-=Gilks et al. 1994-=-) is a software package based on plates. Plates represent repeated fragments of directed or undirected graphical models. Visually, a plate is represented as a rectangle enclosing a set of repeated nod... |

111 | Raedt. Bayesian logic programs - Kersting, De - 2001 |

61 | Realworld applications of Bayesian networks
- Heckerman, Mamdani, et al.
- 1995
(Show Context)
Citation Context ...n phenomena. Bayesian networks (BNs) enable parsimonious specification and tractable inference for realistically complex probability distributions, and have been applied to a wide variety of domains (=-=Heckerman et al. 1995-=-). However, the simple attribute-value representation of BNs is insufficiently expressive for relational domains – that is, domains in which many entities of different types interact with each other i... |

46 | Probabilistic models for relational data
- Heckerman, Meek, et al.
- 2004
(Show Context)
Citation Context ...e statistical theory to define an infinite sequence of findings to falsify the theory, no logic can express a coherent distribution over models of arbitrary infinite axiom sets (Laskey, 2005). DAPER (=-=Heckerman et al. 2004-=-) combines the entityrelational model with DAG models to express probabilistic knowledge about structured entities and their relationships. Plate and PRM models can be represented in DAPER. Thus, DAPE... |

45 |
Bayesian Multiple Target Tracking
- Stone, Barlow, et al.
- 1999
(Show Context)
Citation Context ... any value other than !ST4. Many weakly discriminatory reports coming from possibly many starships produces an exponential set of combinations that require special hypothesis management methods (c.f. =-=Stone et al. 1999-=-). For example, we might not nominate !ST3 as a possible value for Subject(!SR4) if its distance from the reported location exceeded our gating threshold, even though if is logically possible for the ... |

37 |
Bayesian Semantics for the Semantic Web
- Costa
- 2005
(Show Context)
Citation Context ...through Bayesian learning, inherit distributions from parent types, and incorporate other features related to representing and reasoning with incomplete and/or uncertain information in typed systems (=-=Costa, 2005-=-). As an example, we might consider two subtypes of starships, fighters and cargo ships. When we are unsure about a starship’s type, the result of a query that depends on type will be a weighted avera... |

20 | Learning probabilistic relational models with structural uncertainty
- Getoor, Koller, et al.
(Show Context)
Citation Context ...ented Bayesian Networks (Koller & Pfeffer 1997) represent entities as instances of object classes with class-specific attributes and probability distributions. Probabilistic Relational Models (PRMs) (=-=Getoor et al. 2000-=-) integrate the relational data model and BNs. Results similar to Theorem 1 exist for both Bayesian logic programs and probabilistic relational models (e.g., Kersting & De Raedt 2001; Jaeger 1998). In... |

12 | Reasoning about infinite random structures with relational Bayesian networks
- Jaeger
- 1998
(Show Context)
Citation Context ...toor et al. 2000) integrate the relational data model and BNs. Results similar to Theorem 1 exist for both Bayesian logic programs and probabilistic relational models (e.g., Kersting & De Raedt 2001; =-=Jaeger 1998-=-). In particular, joint distributions can be specified over infinitely many random variables. Results for probabilistic relational models assume all random variables are binary, and in infinite domain... |

12 | Constructing situation specific networks - Mahoney, Laskey - 1998 |

8 | First-order Bayesian logic
- Laskey
- 2005
(Show Context)
Citation Context ... logic and probability. Our vehicle for presenting these ideas is Multi-entity Bayesian networks (MEBN), a knowledge representation formalism that combines firstorder logic with Bayesian probability (=-=Laskey 2005-=-). MEBN syntax is designed to highlight the relationship between a MEBN theory and its FOL counterpart. Although our examples are presented using MEBN, our main focus is on logical concepts that are t... |

4 | MEBN Logic: A Key Enabler for Network-Centric Warfare - Costa, Laskey, et al. - 2005 |