Relevance Sensitive Non-Monotonic Inference on Belief Sequences

TL;DR

This paper introduces a relevance-sensitive non-monotonic inference method for belief sequences, enabling consistent, context-aware reasoning that handles belief revision and distinguishes explicit from implicit beliefs.

Contribution

It proposes a novel inference framework using ternary relevance relations and belief sequences, improving reasoning robustness and handling iterated revisions.

Findings

Handles belief revision with a finite, ordered belief sequence

Blocks inconsistent inferences from belief sequences

Maintains explicit and implicit belief distinctions

Abstract

We present a method for relevance sensitive non-monotonic inference from belief sequences which incorporates insights pertaining to prioritized inference and relevance sensitive, inconsistency tolerant belief revision. Our model uses a finite, logically open sequence of propositional formulas as a representation for beliefs and defines a notion of inference from maxiconsistent subsets of formulas guided by two orderings: a temporal sequencing and an ordering based on relevance relations between the conclusion and formulas in the sequence. The relevance relations are ternary (using context as a parameter) as opposed to standard binary axiomatizations. The inference operation thus defined easily handles iterated revision by maintaining a revision history, blocks the derivation of inconsistent answers from a possibly inconsistent sequence and maintains the distinction between explicit and implicit beliefs. In doing so, it provides a finitely presented formalism and a plausible model of reasoning for automated agents.