## Probabilistic reasoning with answer sets (2004)

Venue: | In Proceedings of LPNMR-7 |

Citations: | 63 - 9 self |

### BibTeX

@INPROCEEDINGS{Baral04probabilisticreasoning,

author = {Chitta Baral and Michael Gelfond and Nelson Rushton},

title = {Probabilistic reasoning with answer sets},

booktitle = {In Proceedings of LPNMR-7},

year = {2004},

pages = {21--33},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. We give a logic programming based account of probability and describe a declarative language P-log capable of reasoning which combines both logical and probabilistic arguments. Several non-trivial examples illustrate the use of P-log for knowledge representation. 1

### Citations

7314 |
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
- Pearl
- 1988
(Show Context)
Citation Context ... T0 ∪ {obs(roll(d1, 4))}. By definition, PT0 (even|roll(d1, 4)) = PT1 (even) = 1/2. The same result can be obtained by using classical definition of conditional probability, P (A|B) = P (A ∧ B)/P (B) =-=(15)-=- The following proposition shows that this is not a coincidence. Proposition 2. let Π be a consistent P-log program over the A-Prolog. Then for every formula A and every collection, B, of Σ-literals s... |

1077 | Bayesian Inductive Logic Programming
- Muggleton
- 1994
(Show Context)
Citation Context ...how that, in addition, P-log allows natural combination of logical and probabilistic information. We were influenced to a lesser degree, by various work incorporating probability in logic programming =-=[12, 10, 7, 11, 9]-=-. In part this is due to our use of answer set semantics, which introduces unique challenges (as well as benefits, in our opinion) for the integration of probabilities. The closest to our approach is ... |

868 | Classical negation in logic programs and disjunctive databases
- Gelfond, Lifschitz
- 1991
(Show Context)
Citation Context ...last two authors were partially supported by NASA under grants NCC9-157, NAG2-1560. 3 The language of logic programs with classical and default negation and disjunction under the answer set semantics =-=[4]-=-.scausal probabilities differ from ordinary conditional probabilities in two respects. First, a causal probability statement implicitly represents a set of conditional independence assumptions: given ... |

527 | Learning probabilistic relational models
- Friedman, Getoor, et al.
- 1999
(Show Context)
Citation Context ...vations, and the collection of rules: 1. Random Selection: – For each non-boolean attribute a with range {y1, . . . , ym}: – For each boolean attribute a: a(X, y1) or . . . or a(X, ym) ← random(a(X)) =-=(5)-=- a(X) or ¬a(X) ← random(a(X)) (6) (Note that in both cases X will not be present for attributes of arity 0). – For each attribute a: ¬a(X, Y1) ← a(X, Y2), Y1 �= Y2, (7) 2. Randomness and Deliberate Ac... |

315 | Extending and implementing the stable model semantics
- Simons, Niemelä, et al.
(Show Context)
Citation Context ...robabilities cannot do this in general (see Example 4). Both of these differences are captured in the semantics of P-log. 2 The P-log Language 2.1 Syntax of P-log Let L be a dialect of A-Prolog (e.g. =-=[13, 14, 3, 2]-=-). A probabilistic logic program (Plog program), Π, over L consists of sorted signature, declarations, regular rules of L, probabilistic information, observations, and actions. Signature: The sorted s... |

299 | Probabilistic Horn abduction and Bayesian networks
- Poole
- 1993
(Show Context)
Citation Context ... is due to our use of answer set semantics, which introduces unique challenges (as well as benefits, in our opinion) for the integration of probabilities. The closest to our approach is that of Poole =-=[20, 19]-=-. We note three major differences between our work and the work of Poole [20, 19]. First, A-Prolog provides a richer logical framework than does choice logic, including default and classical negation ... |

263 | Smodels – an implementation of the stable model and well-founded semantics for normal logic programs
- Niemelä, Simons
- 1997
(Show Context)
Citation Context ...robabilities cannot do this in general (see Example 4). Both of these differences are captured in the semantics of P-log. 2 The P-log Language 2.1 Syntax of P-log Let L be a dialect of A-Prolog (e.g. =-=[13, 14, 3, 2]-=-). A probabilistic logic program (Plog program), Π, over L consists of sorted signature, declarations, regular rules of L, probabilistic information, observations, and actions. Signature: The sorted s... |

152 | The independent choice logic for modelling multiple agents under uncertainty
- Poole
- 1997
(Show Context)
Citation Context ...should not take the drug. But what should the doctor do if he has forgotten to ask the patient’s sex? Following the same reasoning, the doctor might check whether P (recover|drug) > P (recover|¬drug) =-=(17)-=- This will lead to an unexpected result. P (recovery|drug) = 0.5 while P (recovery|¬drug) = 0.4. The drug seems to be beneficial to patients of unknown sex — though similar reasoning has shown that th... |

133 | Probabilistic logic programming
- Ng, Subrahmanian
- 1992
(Show Context)
Citation Context ...how that, in addition, P-log allows natural combination of logical and probabilistic information. We were influenced to a lesser degree, by various work incorporating probability in logic programming =-=[12, 10, 7, 11, 9]-=-. In part this is due to our use of answer set semantics, which introduces unique challenges (as well as benefits, in our opinion) for the integration of probabilities. The closest to our approach is ... |

113 | Nested expressions in logic programs
- Lifschitz, Tang, et al.
- 1999
(Show Context)
Citation Context ...tial. It is caused by the syntactic restriction of A-Prolog which prohibits arbitrary formulas in the heads of rules. The restriction can be lifted if instead of A-Prolog we consider its dialect from =-=[8]-=- which can be done with very minor changes in the proof. Example 3. Consider a program, P0 random a : boolean. pr(a) = 1. Recall that P0 will be (automatically) expanded to include a new probability a... |

94 | P.: Answering Queries from Context-Sensitive Probabilistic Knowledge Bases
- Ngo, Haddawy
- 1997
(Show Context)
Citation Context ...how that, in addition, P-log allows natural combination of logical and probabilistic information. We were influenced to a lesser degree, by various work incorporating probability in logic programming =-=[12, 10, 7, 11, 9]-=-. In part this is due to our use of answer set semantics, which introduces unique challenges (as well as benefits, in our opinion) for the integration of probabilities. The closest to our approach is ... |

65 | Logic Programs with ConsistencyRestoring Rules
- Balduccini, Gelfond
- 2003
(Show Context)
Citation Context ...robabilities cannot do this in general (see Example 4). Both of these differences are captured in the semantics of P-log. 2 The P-log Language 2.1 Syntax of P-log Let L be a dialect of A-Prolog (e.g. =-=[13, 14, 3, 2]-=-). A probabilistic logic program (Plog program), Π, over L consists of sorted signature, declarations, regular rules of L, probabilistic information, observations, and actions. Signature: The sorted s... |

45 | Probabilistic logic programming
- Lukasiewicz
- 1998
(Show Context)
Citation Context |

39 | Abducing through negation as failure: stable models within the independent choice logic
- Poole
- 2000
(Show Context)
Citation Context ... is due to our use of answer set semantics, which introduces unique challenges (as well as benefits, in our opinion) for the integration of probabilities. The closest to our approach is that of Poole =-=[20, 19]-=-. We note three major differences between our work and the work of Poole [20, 19]. First, A-Prolog provides a richer logical framework than does choice logic, including default and classical negation ... |

19 |
Representing and Reasoning with Uncertain Knowledge
- Bacchus
- 1990
(Show Context)
Citation Context ...roll(d1) = Y1, roll(d2) = Y2, (Y1 + Y2) mod 2 = 0. owns(d1, mike). owns(d2, john). Probabilistic information consist of statements of the form: random a(t) : B (3) pr(a(t) = y |c B) = v (4) where v ∈ =-=[0, 1]-=-, B is a collections of Σ-literals, and pr is a special symbol not belonging to Σ. By pr(a(t) = y |c B) we denote the probability of a(t) = y being caused by factors determined by B. If B in (3) (or (... |

19 |
Declarative problem-solving in dlv
- Eiter, Faber, et al.
- 2001
(Show Context)
Citation Context |

8 | What observations really tell us
- Iwan, Lakemeyer
- 2003
(Show Context)
Citation Context ...= Π ∪ {do(¬drug)}. ✷ Now we consider several reasoning problems associated with the behavior of a malfunctioning robot. The original version, not containing probabilistic reasoning, first appeared in =-=[6]-=- where the authors discuss the difficulties of solving the problem in Situation Calculus. Example 6. (A malfunctioning robot) There are rooms, r0, r1, and r2, reachable from the current position of a ... |