Parametric Constructive Kripke-Semantics for Standard Multi-Agent Belief and Knowledge (Knowledge As Unbiased Belief)
Simon Kramer, Joshua Sack

TL;DR
This paper introduces a parametric constructive Kripke-semantics framework for multi-agent belief and knowledge, using set-theoretic functions to unify and generalize various epistemic concepts.
Contribution
It provides a novel semantic model linking belief and knowledge through bias and visibility functions, enabling a unified view of different epistemic modalities.
Findings
Defines accessibility relations via bias and visibility functions.
Shows how knowledge can be viewed as unbiased belief.
Provides a semantic complement to foundational results on belief and knowledge.
Abstract
We propose parametric constructive Kripke-semantics for multi-agent KD45-belief and S5-knowledge in terms of elementary set-theoretic constructions of two basic functional building blocks, namely bias (or viewpoint) and visibility, functioning also as the parameters of the doxastic and epistemic accessibility relation. The doxastic accessibility relates two possible worlds whenever the application of the composition of bias with visibility to the first world is equal to the application of visibility to the second world. The epistemic accessibility is the transitive closure of the union of our doxastic accessibility and its converse. Therefrom, accessibility relations for common and distributed belief and knowledge can be constructed in a standard way. As a result, we obtain a general definition of knowledge in terms of belief that enables us to view S5-knowledge as accurate (unbiased…
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Semantic Web and Ontologies · Bayesian Modeling and Causal Inference
