Subset Semantics for Justifications - PhDData

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Subset Semantics for Justifications

The thesis was published by Lehmann, Eveline, in September 2022, University of Bern.


Justification logic is a variant of modal logic where the modal operators are replaced be justification terms. So we deal with formulas like t:A where t is a term denoting some justification that justifies the formula A.

There are many justification logics among which the Logic of Proof established by Artemov was the first. However, since a long time the framework of justification logic is also used in a wide range of epistemic logics. In this field justification terms represent reasons to belief or know something. A standard interpretation of a justification term t is then the set of formulas that are supported by the reason t.
This thesis establishes in the first part another way to interpret terms, namely as sets of worlds. We use so-called subset models in which t:A is true in a normal world, when the interpretation of t in this world is a subset of the truthset of A. These models are shown to be sound and complete towards a whole family of justification logics, including the Logic of Proof.

As is shown in the second part of this thesis, subset models can easily be adapted to model new kinds of justification terms and operations: finer distinctions between several variants of combining justifications, justifications with presumptions, probabilistic evidence. Furthermore, it is shown, how subset models can be used to model dynamic reasoning and forgetting.

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