Evidence and plausibility in neighborhood structures

TL;DR

This paper develops an evidence logic for epistemic agents using neighborhood semantics, modeling evidence, belief, and plausibility, with completeness results and potential for dynamic evidence change logics.

Contribution

It introduces a neighborhood semantics-based evidence logic with representation theorems and completeness results for various model classes, advancing formal modeling of evidence and belief.

Findings

Sound and complete axiomatizations for four major model classes.

Representation theorem linking general models to intended neighborhood models.

Structural analysis of uniform and flat models.

Abstract

The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an {\em evidence logic} for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a neighborhood semantics, where a neighborhood $N$ indicates that the agent has reason to believe that the true state of the world lies in $N$. Further notions of relative plausibility between worlds and beliefs based on the latter ordering are then defined in terms of this evidence structure, yielding our intended models for evidence-based beliefs. In addition, we also consider a second more general flavor, where belief and plausibility are modeled using additional primitive relations, and we prove a representation theorem showing that each such general model is a $p$-morphic image of an intended one. This semantics invites a number of natural special cases, depending on how uniform we make the evidence sets, and how coherent their total structure. We give a structural study of the resulting `uniform' and `flat' models. Our main result are sound and complete axiomatizations for the logics of all four major model classes with respect to the modal language of evidence, belief and safe belief. We conclude with an outlook toward logics for the dynamics of changing evidence, and the resulting language extensions and connections with logics of plausibility change.