Connecting Justifications, Belief, and Knowledge
The following is a fundamental connection between justification terms and the accessibility relation in a modular model.
It is not part of the general definition—we specify explicitly when we have a modular model meeting this condition.Definition 3.29 (Justification Yields Belief) We say that justification yields
Example 3.30 Model M1 from Example 3.25 enjoys JYB, whereas M2 from Example 3.28 does not.
We have soundness of modular models with JYB for the corresponding justification logics J, J4, J45, JT, LP, etc. This is because each of the worlds is a basic model. Completeness immediately follows from the corresponding completeness theorems for basic models because each basic model may be regarded as a modular model
with a singleton G and empty R.
3.8
More on the topic Connecting Justifications, Belief, and Knowledge:
- Artemov S., Fitting M.. Justification Logic: Reasoning with Reasons. Cambridge: Cambridge University Press,2019. — 271 p., 2019
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