We introduce a logic for a class of probabilistic Kripke structures that we call type structures, as they are inspired by Harsanyi type spaces. The latter structures are used in theoretical economics and game theory. A strong completeness theorem for an associated infinitary propositional logic with probabilistic operators was proved by Meier. By simplifying Meier’sproof, we prove that our logic is strongly complete with respect to the class of type structures. In order to do that, we define a canonical model (in the sense of modal logics), which turns out to be a terminal object in a suitable category. Furthermore, we extend some standard model-theoretic constructions to type structures and we prove analogues of first-order results for those constructions.

An infinitary propositional probability logic / Baratella, Stefano. - In: ARCHIVE FOR MATHEMATICAL LOGIC. - ISSN 1432-0665. - ELETTRONICO. - 2022:(2022), pp. [1-30]. [10.1007/s00153-022-00835-5]

An infinitary propositional probability logic

Baratella Stefano
2022

Abstract

We introduce a logic for a class of probabilistic Kripke structures that we call type structures, as they are inspired by Harsanyi type spaces. The latter structures are used in theoretical economics and game theory. A strong completeness theorem for an associated infinitary propositional logic with probabilistic operators was proved by Meier. By simplifying Meier’sproof, we prove that our logic is strongly complete with respect to the class of type structures. In order to do that, we define a canonical model (in the sense of modal logics), which turns out to be a terminal object in a suitable category. Furthermore, we extend some standard model-theoretic constructions to type structures and we prove analogues of first-order results for those constructions.
Baratella, Stefano
An infinitary propositional probability logic / Baratella, Stefano. - In: ARCHIVE FOR MATHEMATICAL LOGIC. - ISSN 1432-0665. - ELETTRONICO. - 2022:(2022), pp. [1-30]. [10.1007/s00153-022-00835-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/349139
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