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
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
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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Summary
With the advent of the internet and social media, we are exposed to more information than ever in human history. Being well-informed, however, is not an easy task, as the amount of untrustworthy information is also enormous. In our age, individuals need to be able to search, filter, combine and separate reliable from unreliable evidence, and draw sensible conclu-sions from it. All this has to be done with limited time and cognitive resources. The same hurdles are faced by software agents, which have an ever increasing presence in our times.
Rational agents, humans or otherwise, build their beliefs from evidence – a process which we call consolidation. But how should this process be carried out? In this thesis, we study a multi-agent logic of evidence and the question how agents should form beliefs in this logic.
We begin by formalising four-valued epistemic logic (FVEL), a multi-agent modal logic that describes public evidence and what multi-agents know about this evidence. A key concept in this logic is that propositions can take four values: true, false, both or none. The meaning of these values is not ontic, but epistemic: true means that there is only positive evidence for a proposition, false means that there is only negative evidence (evidence against the proposition), both means that there are both types of evidence, and none means that there is no evidence at all. We offer a complete tableau proof system, prove basic properties of this logic, and also add public announcements to it.
Based on the formalism developed for FVEL, the next step is to think about how agents can use the evidence they have to form beliefs. Some principles are discussed and methods for forming beliefs, the so-called consolidations, are presented. The properties of this operation are studied, and it is then compared with an “implicit” consolidation found in another evidence logic in the literature (by van Benthem and Pacuit).
After this, another dimension of evidence is considered: social evidence, that is, evidence coming from peers. Until this point, the evidence other
agents have was not very relevant for each individual agent in its consoli-dation process. Now, each agent will take not only its own evidence into account, but also the evidence of its peers. Here a new interpretation of FVEL is employed, where each state represents one agent. Ideas from the social epistemology literature on peer disagreement are used to guide the principles for these social consolidations. A set of rationality postulates inspired also by Social Choice Theory is devised, and we then show that some consolidations fail these postulates, while others can satisfy all of them.
Finally, a modification of the previous social consolidations is explored. There, an agent could access the evidence of its peers, as if it were public. In this final part of the thesis, the evidence of each agent is considered to be private, and what is used instead is the beliefs or testimony of the peers, plus each agent’s own evidence. This makes the consolidations iterative: in the first moment, each agent forms initial beliefs based on its own evidence only; subsequently, they change their beliefs based on their evidence plus their peers’ beliefs; and so on. Eventually, the process may reach an equilibrium, or it can go on forever. This is the problem of stabilisation, and is the main topic explored in the thesis with respect to this type of consolidations.
To put it simply, the main contributions of this thesis are twofold. First, we present and study a many-valued modal logic, and show how it can be suitable for modelling multi-agent scenarios where each agent has access to some evidence, which in turn can be processed into beliefs. This is a technical and practical contribution to many-valued modal logics. Second, we open new paths for research in the field of evidence logics: we show a new approach based on many-valued logics, we highlight the concept of consolidations and the importance of looking at their dynamic nature, and build a methodology based on rationality postulates to evaluate them.
With this work, we hope to have advanced the knowledge on the field of logics of evidence and consolidations, giving new insights on the requirements of proper “epistemic machinery”, which is essential for both human and artificial agents in dealing with the complex sea of information of the current era.
