Proof-Theoretic Approach to Description-Logic

2006 ◽  
Author(s):  
M. Hofmann
Keyword(s):  
Description Logic ◽  
Theoretic Approach

A Set-theoretic Approach to Reasoning Services for the Description Logic 𝒟 ℒ D 4,×

2020 ◽  
Vol 176 (3-4) ◽  
pp. 349-384
Author(s):  
Domenico Cantone ◽  
Marianna Nicolosi-Asmundo ◽  
Daniele Francesco Santamaria
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Theoretic Approach ◽  
The Novel ◽  
Data Types ◽  
Left Hand ◽  
Rule Languages ◽  
Tableau System ◽  
High Scalability ◽  
Better Than

In this paper we consider the most common TBox and ABox reasoning services for the description logic 𝒟ℒ〈4LQSR,x〉(D) ( 𝒟 ℒ D 4,× , for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment 4LQSR. 𝒟 ℒ D 4,× is a very expressive description logic. It combines the high scalability and efficiency of rule languages such as the SemanticWeb Rule Language (SWRL) with the expressivity of description logics. In fact, among other features, it supports Boolean operations on concepts and roles, role constructs such as the product of concepts and role chains on the left-hand side of inclusion axioms, role properties such as transitivity, symmetry, reflexivity, and irreflexivity, and data types. We further provide a KE-tableau-based procedure that allows one to reason on the main TBox and ABox reasoning tasks for the description logic 𝒟 ℒ D 4,× . Our algorithm is based on a variant of the KE-tableau system for sets of universally quantified clauses, where the KE-elimination rule is generalized in such a way as to incorporate the γ-rule. The novel system, called KEγ-tableau, turns out to be an improvement of the system introduced in [1] and of standard first-order KE-tableaux [2]. Suitable benchmark test sets executed on C++ implementations of the three mentioned systems show that in several cases the performances of the KEγ-tableau-based reasoner are up to about 400% better than the ones of the other two systems.

scholarly journals Towards a Practical Decision Procedure for Uniform Interpolants of EL-TBoxes - a Proof-Theoretic Approach

10.29007/bsqm ◽  
2018 ◽  
Author(s):  
Michel Ludwig ◽  
Dirk Walther
Keyword(s):  
Decision Procedure ◽  
Description Logic ◽  
Graph Representation ◽  
Theoretic Approach ◽  
Biomedical Ontologies ◽  
Prototype Implementation

We show how the problem of deciding the existence of uniform interpolants of TBoxes formulated in the Description Logic \EL can be divided into three subproblems based on a characterisation of the logical difference between \EL-TBoxes. We propose a proof-theoretic decision procedure for subsumer interpolants of general TBoxes formulated in the Description Logic \EL, solving one of these subproblems. A subsumer interpolant of a TBox depends on a signature and on a concept name. It is a TBox formulated using symbols from the signature only such that, both, it follows from the original TBox and it exactly entails the subsumers formulated in the signature that follow from the concept name \wrt~the original TBox. Our decision procedure first constructs a graph that exactly represents the part of original TBox that is describable using signature symbols only. Subsequently, it is checked whether a graph-representation of the original TBox can be simulated by the constructed graph, in which case a subsumer interpolant exists. We also evaluate our procedure by applying a prototype implementation on several biomedical ontologies.

scholarly journals DL-Lite Contraction and Revision

2016 ◽  
Vol 56 ◽  
pp. 329-378 ◽  
Author(s):  
Zhiqiang Zhuang ◽  
Zhe Wang ◽  
Kewen Wang ◽  
Guilin Qi
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Description Logic ◽  
Belief Change ◽  
Knowledge Bases ◽  
Theoretic Approach ◽  
Alternative Semantics ◽  
Representation Theorems ◽  
Standard Description ◽  
Model Based

Two essential tasks in managing description logic knowledge bases are eliminating problematic axioms and incorporating newly formed ones. Such elimination and incorporation are formalised as the operations of contraction and revision in belief change. In this paper, we deal with contraction and revision for the DL-Lite family through a model-theoretic approach. Standard description logic semantics yields an infinite number of models for DL-Lite knowledge bases, thus it is difficult to develop algorithms for contraction and revision that involve DL models. The key to our approach is the introduction of an alternative semantics called type semantics which can replace the standard semantics in characterising the standard inference tasks of DL-Lite. Type semantics has several advantages over the standard one. It is more succinct and importantly, with a finite signature, the semantics always yields a finite number of models. We then define model-based contraction and revision functions for DL-Lite knowledge bases under type semantics and provide representation theorems for them. Finally, the finiteness and succinctness of type semantics allow us to develop tractable algorithms for instantiating the functions.

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