A simple logic for reasoning about incomplete knowledge

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...

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Bibliographic Details
Published in:Accounting horizons 2014-01, Vol.55 (2), p.639-653
Main Authors: Banerjee, Mohua, Dubois, Didier
Format: Article
Language:English
Subjects:
Applied sciences
Artificial Intelligence
Computation and Language
Computer Science
Computer science
control theory
systems
Epistemic logic
Evidence theory
Exact sciences and technology
Incomplete information
Learning and adaptive systems
Logic in Computer Science
Logical, boolean and switching functions
Machine Learning
Possibility theory
Theoretical computing
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Summary: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. •The simplest possible logic of uncertainty capable of accounting for unknown propositions in the language.•A new simple completeness proof that does not borrow from modal logic methods.•The connection with uncertainty theories like possibility and belief functions.•The connection with the Möbius transform.
ISSN:0888-613X
0888-7993
1873-4731
DOI:10.1016/j.ijar.2013.11.003