Probability Logic for Harsanyi Type Spaces
Probability logic has contributed to significant developments in belief types for game-theoretical economics. We present a new probability logic for Harsanyi Type spaces, show its completeness, and prove both a de-nesting property and a unique extension theorem. We then prove that multi-agent intera...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2014-06-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/898/pdf |
| _version_ | 1797268685530857472 |
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| author | Chunlai Zhou |
| author_facet | Chunlai Zhou |
| author_sort | Chunlai Zhou |
| collection | DOAJ |
| description | Probability logic has contributed to significant developments in belief types
for game-theoretical economics. We present a new probability logic for Harsanyi
Type spaces, show its completeness, and prove both a de-nesting property and a
unique extension theorem. We then prove that multi-agent interactive
epistemology has greater complexity than its single-agent counterpart by
showing that if the probability indices of the belief language are restricted
to a finite set of rationals and there are finitely many propositional letters,
then the canonical space for probabilistic beliefs with one agent is finite
while the canonical one with at least two agents has the cardinality of the
continuum. Finally, we generalize the three notions of definability in
multimodal logics to logics of probabilistic belief and knowledge, namely
implicit definability, reducibility, and explicit definability. We find that
S5-knowledge can be implicitly defined by probabilistic belief but not reduced
to it and hence is not explicitly definable by probabilistic belief. |
| first_indexed | 2024-04-25T01:36:25Z |
| format | Article |
| id | doaj.art-399602e14fe447bcb7a2afa5b379a504 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:36:25Z |
| publishDate | 2014-06-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-399602e14fe447bcb7a2afa5b379a5042024-03-08T09:36:22ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742014-06-01Volume 10, Issue 210.2168/LMCS-10(2:13)2014898Probability Logic for Harsanyi Type SpacesChunlai ZhouProbability logic has contributed to significant developments in belief types for game-theoretical economics. We present a new probability logic for Harsanyi Type spaces, show its completeness, and prove both a de-nesting property and a unique extension theorem. We then prove that multi-agent interactive epistemology has greater complexity than its single-agent counterpart by showing that if the probability indices of the belief language are restricted to a finite set of rationals and there are finitely many propositional letters, then the canonical space for probabilistic beliefs with one agent is finite while the canonical one with at least two agents has the cardinality of the continuum. Finally, we generalize the three notions of definability in multimodal logics to logics of probabilistic belief and knowledge, namely implicit definability, reducibility, and explicit definability. We find that S5-knowledge can be implicitly defined by probabilistic belief but not reduced to it and hence is not explicitly definable by probabilistic belief.https://lmcs.episciences.org/898/pdfmathematics - logic |
| spellingShingle | Chunlai Zhou Probability Logic for Harsanyi Type Spaces Logical Methods in Computer Science mathematics - logic |
| title | Probability Logic for Harsanyi Type Spaces |
| title_full | Probability Logic for Harsanyi Type Spaces |
| title_fullStr | Probability Logic for Harsanyi Type Spaces |
| title_full_unstemmed | Probability Logic for Harsanyi Type Spaces |
| title_short | Probability Logic for Harsanyi Type Spaces |
| title_sort | probability logic for harsanyi type spaces |
| topic | mathematics - logic |
| url | https://lmcs.episciences.org/898/pdf |
| work_keys_str_mv | AT chunlaizhou probabilitylogicforharsanyitypespaces |