Xinyu Wang

Xinyu Wang, Momoka Fujieda

This paper establishes a dual theory about knowledge and argumentation. Our idea is rooted at both epistemic logic and argumentation theory, and we aim to merge these two fields, not just in a superficial way but to thoroughly disclose the intrinsic relevance between knowledge and argumentation. Specifically, we define epistemic Kripke models and argument Kripke models as a dual pair, and then work out a two-way generation method between these two types of Kripke models. Such generation is rigorously justified by a duality theorem on modal formulae's invariance. We also provide realistic examples to demonstrate our generation, through which our framework's practical utility gets strongly advocated. We finally propose a philosophical thesis that knowledge is essentially dynamic, and we draw certain connection to Maxwell's demon as well as the well-known proverb "knowledge is power".

Xinyu Wang

Bayesian reasoning plays a significant role both in human rationality and in machine learning. In this paper, we introduce transfinite modal logic, which combines modal logic with ordinal arithmetic, in order to formalize Bayesian reasoning semi-quantitatively. Technically, we first investigate some nontrivial properties of ordinal arithmetic, which then enable us to expand normal modal logic's semantics naturally and elegantly onto the novel transfinite modal logic, while still keeping the ordinary definition of Kripke models totally intact. Despite all the transfinite mathematical definition, we argue that in practice, this logic can actually fit into a completely finite interpretation as well. We suggest that transfinite modal logic captures the essence of Bayesian reasoning in a rather clear and simple form, in particular, it provides a perfect explanation for Sherlock Holmes' famous saying, "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." We also prove a counterpart of finite model property theorem for our logic.

Hanqi Yan, Qinglin Zhu, Xinyu Wang et al.

While Large language models (LLMs) have the capability to iteratively reflect on their own outputs, recent studies have observed their struggles with knowledge-rich problems without access to external resources. In addition to the inefficiency of LLMs in self-assessment, we also observe that LLMs struggle to revisit their predictions despite receiving explicit negative feedback. Therefore, We propose Mirror, a Multiple-perspective self-reflection method for knowledge-rich reasoning, to avoid getting stuck at a particular reflection iteration. Mirror enables LLMs to reflect from multiple-perspective clues, achieved through a heuristic interaction between a Navigator and a Reasoner. It guides agents toward diverse yet plausibly reliable reasoning trajectory without access to ground truth by encouraging (1) diversity of directions generated by Navigator and (2) agreement among strategically induced perturbations in responses generated by the Reasoner. The experiments on five reasoning datasets demonstrate that Mirror's superiority over several contemporary self-reflection approaches. Additionally, the ablation study studies clearly indicate that our strategies alleviate the aforementioned challenges.