DS-2024-11: Pinto Prieto, Daira (2024) Combining Uncertain Evidence: Logic and Complexity. Doctoral thesis, Universiteit van Amsterdam.
![[thumbnail of DS-2024-11.text.pdf]](https://eprints.illc.uva.nl/style/images/fileicons/text.png) |
Text
DS-2024-11.text.pdf - Published Version Download (1MB) |
|
Text (Samenvatting)
DS-2024-11.samenvatting.txt - Other Download (0B) |
Abstract
This dissertation addresses the challenge of combining uncertain, partial and possibly mutually contradictory evidence with a focus on logic and computational complexity. In this context, 'evidence' is represented as a subset of a universe; 'uncertainty' as values between 0 and 1; 'partiality' as ignorance about subsets that are not presented as evidence; and 'mutual contradiction' as empty intersection. The main problem is (1) to combine such evidence to obtain a normalized body of evidence, where certainty values sum up to 1. A relevant extension is (2) to compute degrees of belief based on that combined evidence. We explore problems (1) and (2) via three different approaches.
First, we study formal methods that address (1) and (2). In Chapter 2, we introduce some solutions from Dempster-Shafer theory---that relaxes probability axioms---and topological models of evidence---models for epistemic logic based on topological semantics. We establish a common vocabulary between both frameworks and use them as the basis of our solution for (1) and (2), developed in Chapter 3.
Second, we present a modal logic in Chapter 4 to compare propositions in terms of (a) their degree of belief based on Chapter 3, and (b) the certainty of their evidential support. Syntactically, it includes a binary modal operator for each type of comparison. Semantically, we make use of order liftings to interpret (b).
Lastly, we analyze the computational complexity of (1) and (2). In Chapter 5, we focus on the solution for (1) named Dempster's rule of combination, the belief operator of topological models of evidence, and the formal method developed in Chapter 3. In Chapter 6, we propose applying knowledge compilation techniques to compute Dempster's rule of combination.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Report Nr: | DS-2024-11 |
| Series Name: | ILLC Dissertation (DS) Series |
| Year: | 2024 |
| Subjects: | Computation Logic |
| Divisions: | Faculteit der Natuurwetenschappen, Wiskunde en Informatica |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 13 Sep 2024 14:10 |
| Last Modified: | 13 Nov 2025 17:14 |
| URI: | https://eprints.illc.uva.nl/id/eprint/2324 |
Actions (login required)
 |
View Item |
