On the consistency among prior, posteriors, and information sets (Extended Abstract)
| Autor: | Satoshi Fukuda |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Logic in Computer Science INFORMATION SETS POSTERIORS Consistency (knowledge bases) lcsh:QA75.5-76.95 Bayes' theorem Computer Science - Computer Science and Game Theory 0502 economics and business ADDITIVITY Almost surely Computer Science - Multiagent Systems 050207 economics INFORMATION SETS PRIOR POSTERIORS BAYES CONDITIONAL PROBABILITY TRUTH AXIOM ADDITIVITY Axiom Mathematics Information set BAYES CONDITIONAL PROBABILITY lcsh:Mathematics 05 social sciences Conditional probability TRUTH AXIOM State (functional analysis) lcsh:QA1-939 Partition (database) Logic in Computer Science (cs.LO) 050206 economic theory lcsh:Electronic computers. Computer science PRIOR Mathematical economics Computer Science and Game Theory (cs.GT) Multiagent Systems (cs.MA) |
| Zdroj: | Electronic Proceedings in Theoretical Computer Science, Vol 297, Iss Proc. TARK 2019, Pp 189-205 (2019) TARK |
| Popis: | This paper studies implications of the consistency conditions among prior, posteriors, and information sets on introspective properties of qualitative belief induced from information sets. The main result reformulates the consistency conditions as: (i) the information sets, without any assumption, almost surely form a partition; and (ii) the posterior at a state is equal to the Bayes conditional probability given the corresponding information set. Implications are as follows. First, each posterior is uniquely determined. Second, qualitative belief reduces to fully introspective knowledge in a ``standard'' environment. Thus, a care must be taken when one studies non-veridical belief or non-introspective knowledge. Third, an information partition compatible with the consistency conditions is uniquely determined by the posteriors. Fourth, qualitative and probability-one beliefs satisfy truth axiom almost surely. The paper also sheds light on how the additivity of the posteriors yields negative introspective properties of beliefs. In Proceedings TARK 2019, arXiv:1907.08335 |
| Databáze: | OpenAIRE |
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