### Abstract

Many real-world knowledge-based systems must deal with information coming from different sources that invariably leads to incompleteness, overspecification, or inherently uncertain content. The presence of these varying levels of uncertainty doesn’t mean that the information is worthless – rather, these are hurdles that the knowledge engineer must learn to work with. In this paper, we continue work on an argumentation-based framework that extends the well-known Defeasible Logic Programming (DeLP) language with probabilistic uncertainty, giving rise to the Defeasible Logic Programming with Presumptions and Probabilistic Environments (DeLP3E) model. Our prior work focused on the problem of belief revision in DeLP3E, where we proposed a non-prioritized class of revision operators called AFO (Annotation Function-based Operators) to solve this problem. In this paper, we further study this class and argue that in some cases it may be desirable to define revision operators that take quantitative aspects into account, such as how the probabilities of certain literals or formulas of interest change after the revision takes place. To the best of our knowledge, this problem has not been addressed in the argumentation literature to date. We propose the QAFO (Quantitative Annotation Function-based Operators) class of operators, a subclass of AFO, and then go on to study the complexity of several problems related to their specification and application in revising knowledge bases. Finally, we present an algorithm for computing the probability that a literal is warranted in a DeLP3E knowledge base, and discuss how it could be applied towards implementing QAFO-style operators that compute approximations rather than exact operations.

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

Journal | Annals of Mathematics and Artificial Intelligence |

DOIs | |

State | Accepted/In press - Sep 19 2015 |

### Fingerprint

### Keywords

- Belief revision
- Reasoning under probabilistic uncertainty
- Structured argumentation

### ASJC Scopus subject areas

- Artificial Intelligence
- Applied Mathematics

### Cite this

*Annals of Mathematics and Artificial Intelligence*. https://doi.org/10.1007/s10472-015-9476-4

**A quantitative approach to belief revision in structured probabilistic argumentation.** / Simari, Gerardo I.; Shakarian, Paulo; Falappa, Marcelo A.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - A quantitative approach to belief revision in structured probabilistic argumentation

AU - Simari, Gerardo I.

AU - Shakarian, Paulo

AU - Falappa, Marcelo A.

PY - 2015/9/19

Y1 - 2015/9/19

N2 - Many real-world knowledge-based systems must deal with information coming from different sources that invariably leads to incompleteness, overspecification, or inherently uncertain content. The presence of these varying levels of uncertainty doesn’t mean that the information is worthless – rather, these are hurdles that the knowledge engineer must learn to work with. In this paper, we continue work on an argumentation-based framework that extends the well-known Defeasible Logic Programming (DeLP) language with probabilistic uncertainty, giving rise to the Defeasible Logic Programming with Presumptions and Probabilistic Environments (DeLP3E) model. Our prior work focused on the problem of belief revision in DeLP3E, where we proposed a non-prioritized class of revision operators called AFO (Annotation Function-based Operators) to solve this problem. In this paper, we further study this class and argue that in some cases it may be desirable to define revision operators that take quantitative aspects into account, such as how the probabilities of certain literals or formulas of interest change after the revision takes place. To the best of our knowledge, this problem has not been addressed in the argumentation literature to date. We propose the QAFO (Quantitative Annotation Function-based Operators) class of operators, a subclass of AFO, and then go on to study the complexity of several problems related to their specification and application in revising knowledge bases. Finally, we present an algorithm for computing the probability that a literal is warranted in a DeLP3E knowledge base, and discuss how it could be applied towards implementing QAFO-style operators that compute approximations rather than exact operations.

AB - Many real-world knowledge-based systems must deal with information coming from different sources that invariably leads to incompleteness, overspecification, or inherently uncertain content. The presence of these varying levels of uncertainty doesn’t mean that the information is worthless – rather, these are hurdles that the knowledge engineer must learn to work with. In this paper, we continue work on an argumentation-based framework that extends the well-known Defeasible Logic Programming (DeLP) language with probabilistic uncertainty, giving rise to the Defeasible Logic Programming with Presumptions and Probabilistic Environments (DeLP3E) model. Our prior work focused on the problem of belief revision in DeLP3E, where we proposed a non-prioritized class of revision operators called AFO (Annotation Function-based Operators) to solve this problem. In this paper, we further study this class and argue that in some cases it may be desirable to define revision operators that take quantitative aspects into account, such as how the probabilities of certain literals or formulas of interest change after the revision takes place. To the best of our knowledge, this problem has not been addressed in the argumentation literature to date. We propose the QAFO (Quantitative Annotation Function-based Operators) class of operators, a subclass of AFO, and then go on to study the complexity of several problems related to their specification and application in revising knowledge bases. Finally, we present an algorithm for computing the probability that a literal is warranted in a DeLP3E knowledge base, and discuss how it could be applied towards implementing QAFO-style operators that compute approximations rather than exact operations.

KW - Belief revision

KW - Reasoning under probabilistic uncertainty

KW - Structured argumentation

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UR - http://www.scopus.com/inward/citedby.url?scp=84942042928&partnerID=8YFLogxK

U2 - 10.1007/s10472-015-9476-4

DO - 10.1007/s10472-015-9476-4

M3 - Article

JO - Annals of Mathematics and Artificial Intelligence

JF - Annals of Mathematics and Artificial Intelligence

SN - 1012-2443

ER -