This paper investigates the relationship between the theory of belief revision and Lindenbaum-Tarski algebras for propositional logic. The intent is to represent the revision function described by the AGM-postulates algebraically. The AGM theory is based on deductively closed sets, which are characterizable as generated filters in the algebra as well as depictable in the corresponding Hasse diagram. This fact is shown by proving that a partial order is definable for the algebra, that this order is the consequence relation of propositional calculus and that the generated filters are deductively closed.
Furthermore, an alternative, but equivalent approach to the AGM theory is introduced, the revision proposed by Katsuno and Mendelzon, which characterizes the deductively closed sets as propositional formulae. This correspondence follows naturally from the behaviour of filters and can be applied without problems to define the functions of the AGM framework in the Lindenbaum-Tarski algebra.
The visualization of partially ordered sets as a Hasse diiagram is used to depict an example of a belief revision. Lastly, some combinatorical calculations are introduced to determine the number of possible solution candidates for a belief revision.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:77662 |
| Date | 28 January 2022 |
| Creators | Schönau, Tobias |
| Contributors | Baumann, Ringo, Max, Ingolf, Universität Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/acceptedVersion, doc-type:masterThesis, info:eu-repo/semantics/masterThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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