University of Groningen
Evidence-Based Beliefs in Many-Valued Modal Logics David Santos, Yuri
DOI:
10.33612/diss.155882457
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Publication date: 2021
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David Santos, Y. (2021). Evidence-Based Beliefs in Many-Valued Modal Logics. University of Groningen. https://doi.org/10.33612/diss.155882457
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Propositions accompanying the thesis
Evidence-Based Beliefs in Many-Valued Modal Logics
1. Many-valued modal logics are suitable formalisms to model scenarios where agents possess evidence and form evidence-based beliefs.
2. Even in many-valued modal logics, with possibly conflicting evidence, there are rational and irrational ways of consolidating evidence into belief, as shown by the postulates of Chapter 3.
3. The ability to make good consolidations has become more important since the advent of social media platforms.
4. Cautious consolidation is a rational way of forming beliefs, given a limited representation of evidence such as the one used by Four-Valued Epistemic Logic.
5. The postulates of Chapter 4 impose rational constraints for social
consolidations, given a limited representation of evidence such as the one of that chapter.
6. When the evidence is private and opinions are public, rational consolidations must be iterative. We need to revisit our first consolidated opinions.
7. The combination of private evidence and public opinions can also lead to undesirable informational cascades. Here, an informational cascade is a
phenomenon in which a number of agents make decisions on the same topic in a sequential fashion, and each agent can observe the choices of the previous ones; the problem is that in such setups, even if each agent acts rationally, an irrational collective outcome is possible.
8. This thesis proposes some principles of rationality. There are many other principles of rationality studied by other authors. Ignore all of them and you might end up being president of more than 200 million people.
