Model Change for Description Logic Concepts

Belief revision is a process in which an agent begins to believe in something she previously did not. I begin the paper by presenting, based on (Gärdenfors, 1998; Hansson, 1999), postulates for belief revision that constitute the basis of the AGM theory. I will then briefly show the semantics of a modal logic introduced in (van Ditmarsch, 2005), which I call $P$'. This logic formalizes static epistemic states and has greater expressive power than AGM in doing so because it captures the quantitative notion of "degrees of conviction". The third step is to introduce revision operators on $P$ and, mostly following (van Ditmarsch, 2005), obtain the Dynamic Epistemic Logic (DEL) I call $P*$'. It models processes of belief revision in several ways. Original results are presented in the following two sections. The first one of these sections revolves around a formalization of AGM postulates within $P*$ by proving some theorems related to the satisfaction of those postulates by revisions defined in $P*$. The last section features an analysis of $P*$'s revisions that go beyond the mere satisfaction of postulates. I compare their formal behavior with respect to some philosophical criteria. At last, I conclude that the functions presented in (van Ditmarsch, 2005) are not good formalizations of the philosophical intuition behind AGM. Instead, it is captured by the function $*^0$ originally defined in this paper (but highly inspired by (van Benthem, 2007)). An implementation of this function is also provided.

Reasoning benchmarks typically evaluate whether a model derives the correct answer from a fixed premise set, but they under-measure a closely related capability that matters in dynamic environments: belief revision under minimal evidence change. We introduce DeltaLogic, a benchmark transformation protocol that converts natural-language reasoning examples into short revision episodes. Each episode first asks for an initial conclusion under premises P, then applies a minimal edit δ(P), and finally asks whether the previous conclusion should remain stable or be revised. We instantiate DeltaLogic from FOLIO and ProofWriter and evaluate small causal language models with constrained label scoring. On a completed 30-episode Qwen evaluation subset, stronger initial reasoning still does not imply stronger revision behavior: Qwen3-1.7B reaches 0.667 initial accuracy but only 0.467 revision accuracy, with inertia rising to 0.600 on episodes where the gold label should change, while Qwen3-0.6B collapses into near universal abstention. There, Qwen3-4B preserves the same inertial failure pattern (0.650 initial, 0.450 revised, 0.600 inertia), whereas Phi-4-mini-instruct is substantially stronger (0.950 initial, 0.850 revised) but still exhibits non-trivial abstention and control instability. These results suggest that logical competence under fixed premises does not imply disciplined belief revision after local evidence edits. DeltaLogic therefore targets a distinct and practically important reasoning capability that complements existing logical inference and belief-updating benchmarks.

This article proposes a set-theoretic framework for belief change, called Abstract Worlds Semantics, in which no logical syntax is assumed. Inspired by Grove's (1988) results, our approach treats worlds as primitive elements, over which world contraction and world revision operators are defined. This semantic framework enables a unified analysis of belief change models. Within this framework, we unify classical and non-prioritized belief change constructions by defining versatile operators. When classical propositional logic is considered, our framework provides a homogeneous account of AGM, KM, and Multiple Change models. In summary, AWS systematizes belief change frameworks and operators, simplifying and generalizing belief change theory over belief sets.