A simple logic for reasoning about incomplete knowledge

Abstract : The semantics of modal logics for reasoning about belief or knowledge is often described in terms of accessibility relations, which is too expressive to account for mere epistemic states of an agent. This paper proposes a simple logic whose atoms express epistemic attitudes about formulae expressed in another basic propositional language, and that allows for conjunctions, disjunctions and negations of belief or knowledge statements. It allows an agent to reason about what is known about the beliefs held by another agent. This simple epistemic logic borrows its syntax and axioms from the modal logic KD. It uses only a fragment of the S5 language, which makes it a two-tiered propositional logic rather than as an extension thereof. Its semantics is given in terms of epistemic states understood as subsets of mutually exclusive propositional interpretations. Our approach offers a logical grounding to uncertainty theories like possibility theory and belief functions. In fact, we define the most basic logic for possibility theory as shown by a completeness proof that does not rely on accessibility relations.
Complete list of metadatas

Cited literature [49 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01119806
Contributor : Open Archive Toulouse Archive Ouverte (oatao) <>
Submitted on : Tuesday, February 24, 2015 - 10:01:39 AM
Last modification on : Friday, June 14, 2019 - 6:31:07 PM
Long-term archiving on : Monday, May 25, 2015 - 10:25:46 AM

File

Banerjee_12870.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Mohua Banerjee, Didier Dubois. A simple logic for reasoning about incomplete knowledge. Accounting Horizons, American Accounting Association, 2014, vol. 55 (n° 2), pp. 639-653. ⟨10.1016/j.ijar.2013.11.003⟩. ⟨hal-01119806⟩

Share

Metrics

Record views

167

Files downloads

145