Model Change for Description Logic Concepts

Ana Ozaki; Jandson S. Ribeiro

cs.LOMar 5, 2026

Model Change for Description Logic Concepts

Authors: Ana Ozaki, Jandson S. Ribeiro

Organizations: University of Oslo, Norway · Cardiff University, UK

Abstract

We consider the problem of modifying a description logic concept in light of models represented as pointed interpretations. We call this setting model change, and distinguish three main kinds of changes: eviction, which consists of only removing models; reception, which incorporates models; and revision, which combines removal with incorporation of models in a single operation. We introduce a formal notion of revision and argue that it does not reduce to a simple combination of eviction and reception, contrary to intuition. We provide positive and negative results on the compatibility of eviction and reception for EL and ALC description logic concepts and on the compatibility of revision for ALC concepts.

Figures & tables

Sat. System	Eviction	Reception
${\Lambda}({\cal E\!L}_{\bot con.})$	yes ( Thm. 11 )	no ( Thm. 13 )
${\Lambda}({\cal E\!L}_{\bot con.})^{\dagger}$	yes ( Thm. 11 )	yes ( Thm. 14 )
${\Lambda}({\cal ALC}_{con.})$	no ( Thm. 12 )	no ( Thm. 13 )
${\Lambda}({\cal ALC}_{con.})^{\ddagger}$	yes ( Thm. 16 )	yes ( Thm. 16 )

Table 1: Eviction and reception-compatibility for DL concepts.

\dagger

is for the case pointed interpretations can only be tree-shaped and

\ddagger

is for the case they can only be tree-shaped, over finite signatures, and sets of models can only be finite.

Description Logic

Description logic provides formal languages for representing ontologies and reasoning about concepts, relations, and their instances.

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Study on Quantitative Dynamic Epistemic Logic for Belief Revision

Felipe Nunes de Souza Camargo

State University of Campinas (UNICAMP), Campinas-SP, Brasil

Belief Revision Dynamic Epistemic Logic Epistemic Logic

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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.

Abstract

Description Logic

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