Logical Omniscience and Inconsistent Belief

The dynamic epistemic logic for actual knowledge models the phenomenon of actual knowledge change when new information is received. In contrast to the systems of dynamic epistemic logic which have been discussed in the past literature, our system is not burdened with the problem of logical omniscience, that is, an idealized assumption that the agent explicitly knows all classical tautologies and all logical consequences of his or her knowledge. We provide a sound and complete axiomatization for this logic.

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A Dynamic Solution to the Problem of Logical Omniscience

Journal of Philosophical Logic ◽

10.1007/s10992-018-9473-2 ◽

2018 ◽

Vol 48 (3) ◽

pp. 501-521 ◽

Cited By ~ 8

Author(s):

Jens Christian Bjerring ◽

Mattias Skipper

Keyword(s):

Logical Omniscience ◽

Dynamic Solution

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A logic of knowledge based on abstract arguments

Journal of Logic and Computation ◽

10.1093/logcom/exab002 ◽

2021 ◽

Author(s):

Yì N Wáng ◽

Xu Li

Keyword(s):

Computational Complexity ◽

Model Checking ◽

True Belief ◽

Logical Omniscience ◽

Knowledge Based ◽

Logic Of Knowledge ◽

Multi Agent ◽

Soundness And Completeness ◽

Base Logic

Abstract We introduce a logic of knowledge in a framework in which knowledge is treated as a kind of belief. The framework is based on a standard KD45 characterization of belief, and the characterization of knowledge undergoes the classical tripartite analysis that knowledge is justified true belief, which has a natural link to the studies of logics of evidence and justification. The interpretation of knowledge avoids the unwanted properties of logical omniscience, independent of the choice of the base logic of belief. We axiomatize the logic, prove its soundness and completeness and study the computational complexity results of the model checking and satisfiability problems. We extend the logic to a multi-agent setting and introduce a variant in which belief is characterized in a weaker system to avoid the problem of logical omniscience.

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