Papers for

epistemic game designers

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Moorean phenomena explain unknowability and self-refutation in logic

The Sources of Unknowability and Self-refutation in Epistemic and Dynamic Epistemic Logic

Abstract: In this paper, we define a formula $\varphi$ to be unbelievable if $\Box\varphi$ is unsatisfiable, and unknowable if $\Box\varphi\land\varphi$ is unsatisfiable. We then analyze the sources of unknowability and unbelievability in different classes of frames K, KD, KD45, and S5. We first show that any unbelievable formula is a fixed point of the Moore function defined by $f(\varphi)=\varphi\land\lnot\Box\varphi.$ Our main result shows that in S5, the static notions of unknowability and unbelievability in epistemic logic, and the dynamic notions of always informativeness and eventual self-refutation in dynamic epistemic logic are all equivalent to ``Moorean phenomena.'' We also generalize the result to the multi-agent case, showing that although all unknowable formulas still manifest Moorean phenomena, new mechanisms arise due to their interactive nature. Finally, we briefly analyze whether the Brandenburger-Keisler paradox in epistemic game theory can be considered Moorean.

Fri 18 SeptLogic in Computer Science

The gist

This paper looks at why some statements can't be believed or known within certain logical systems. The authors show that these tricky statements, called unbelievable or unknowable, are connected to self-contradictory patterns known as Moorean phenomena. They also find that these patterns appear in both single and multiple person scenarios, and relate these ideas to well-known logical puzzles in game theory. Overall, the work helps clarify the logic behind knowing and believing statements that contradict themselves.

Open → 2609.21317v1