Bayesianism without Learning

According to the standard definition, a Bayesian agent is one who forms his posterior belief by conditioning his prior belief on what he has learned, that is, on facts of which he has become certain. Here it is shown that Bayesianism can be described without assuming that the agent acquires any certain information; an agent is Bayesian if his prior, when conditioned on his posterior belief, agrees with the latter. This condition is shown to characterize Bayesian models.Bayesian updating, prior and posterior

THE LOGIC OF BELIEF PERSISTENCY

The interaction bietween knowledge and belief in a temporal context is analyzed. An axiomatic formulation and semantic characterization of the principle of belief persistency implied by the standard conditionalization rule are provided. This principle says that an individual does not change her mind unless new evidence forces her to do so. It is shown that if beliefs are conscious (or stateindependent) and satisfy negative introspection then the principle of persistency of beliefs is characterized by the following axiom schema: the individual believes that 9 at date t if and orilly if she believes at date t that she will believe that 4 at date t+l.

INTERSUBJECTIVE CONSISTENCY OF KNOWLEDGE AND BELIEF

We consider interactive epistemic models where individuals are described by both their ""knowledge"" and their ""beliefs."" Three intersubjective consistency conditions are examined: Intersubjective Caution (if an individual believes something to be common belief then he knows it to be common belief), Truth of Common Belief (only true facts are commonly believed) and Qualitative Agreement. These conditions are employed in characterizations of the following properties which describe either the extent of intersubjective truth and/or the logic of common belief: common belief in no error, common knowledge of common belief, negative introspection of common belief, coincidence of common knowledge and common belief, and collapse of individual belief and knowledge. We also discuss to what extent the three fundamental conditions can be viewed as intersubjective rationality conditions.

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 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

シャカイネットワークニオケルオピニオンダイナミクスノゴシップベースモデル

Emerico Aguilar & Yasumasa Fujisaki. "Reaching consensus via coordinated groups", SICE Journal of Control, Measurement, and System Integration, 14(1), 20-26 (2021). DOI: 10.1080/18824889.2021.1874673

Quantum information vs. epistemic logic: An analysis of the Frauchiger-Renner theorem

A recent no-go theorem establishes a contradiction from a specific application of quantum theory to a multi-agent setting. The proof of this theorem relies heavily on notions such as ‘knows’ or ‘is certain that’. This has stimulated an analysis of the theorem by Nurgalieva and del Rio, in which they claim that it shows the “[i]nadequacy of modal logic in quantum settings”. In this paper, we will offer a significantly extended and refined reconstruction of the theorem in multi-agent modal logic. We will then show that a thorough reconstruction of the proof as given by Frauchiger and Renner requires the reflexivity of access relations (system T). However, a stronger theorem is possible that already follows in serial frames, and hence also holds in systems of doxastic logic (such as KD45). After proving this, we will discuss the general implications for different interpretations of quantum probabilities as well as several options for dealing with the result