Query answering in nondeterministic, nonmonotonic logic databases

1998 ◽  
pp. 175-187 ◽  
Author(s):  
Fosca Giannotti ◽  
Giuseppe Manco ◽  
Mirco Nanni ◽  
Dino Pedreschi
Keyword(s):  
Nonmonotonic Logic ◽  
Query Answering

Computing Cores for Existential Rules with the Standard Chase and ASP

2020 ◽  
Author(s):  
Markus Krötzsch
Keyword(s):  
Large Class ◽  
Data Exchange ◽  
Answer Set Programming ◽  
Query Answering ◽  
Universal Model ◽  
The Core ◽  
Universal Models ◽  
General Terms ◽  
Special Cases ◽  
The Many

To reason with existential rules (a.k.a. tuple-generating dependencies), one often computes universal models. Among the many such models of different structure and cardinality, the core is arguably the “best”. Especially for finitely satisfiable theories, where the core is the unique smallest universal model, it has advantages in query answering, non-monotonic reasoning, and data exchange. Unfortunately, computing cores is difficult and not supported by most reasoners. We therefore propose ways of computing cores using practically implemented methods from rule reasoning and answer set programming. Our focus is on cases where the standard chase algorithm produces a core. We characterise this desirable situation in general terms that apply to a large class of cores, derive concrete approaches for decidable special cases, and generalise these approaches to non-monotonic extensions of existential rules.

scholarly journals More on Modal Aspects of Default Logic1

1992 ◽  
Vol 17 (1-2) ◽  
pp. 99-116
Author(s):  
V. Wiktor Marek ◽  
Miroslaw Truszczynski
Keyword(s):  
Modal Logic ◽  
Default Logic ◽  
Nonmonotonic Logic ◽  
Default Reasoning ◽  
Default Theory ◽  
Autoepistemic Logic ◽  
The Relationship ◽  
Natural Classes ◽  
Weak Extension

Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we introduce the concept of a weak extension and study its properties. It has long been suspected that there are close connections between default and autoepistemic logics. The notion of weak extension allows us to precisely describe the relationship between these two formalisms. In particular, we show that default logic with weak extensions is essentially equivalent to autoepistemic logic, that is, nonmonotonic logic KD45. In the paper we also study the notion of a set of formulas closed under a default theory. These objects are shown to correspond to stable theories and to modal logic S5. In particular, we show that skeptical reasoning with sets closed under default theories is closely related with provability in S5. As an application of our results we determine the complexity of reasoning with weak extensions and sets closed under default theories.

An Improved Set-based Reasoner for the Description Logic 𝒟ℒD4,׆

2021 ◽  
Vol 178 (4) ◽  
pp. 315-346
Author(s):  
Domenico Cantone ◽  
Marianna Nicolosi-Asmundo ◽  
Daniele Francesco Santamaria
Keyword(s):  
Semantic Web ◽  
Set Theory ◽  
Description Logic ◽  
Knowledge Bases ◽  
Query Answering ◽  
Conjunctive Query ◽  
Classification Problems ◽  
Previous Version ◽  
Decidable Fragment ◽  
Stratified Set

We present a KE-tableau-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic 𝒟ℒ〈4LQSR,×〉(D) (𝒟ℒD4,×, for short). Our application solves the main TBox and ABox reasoning problems for 𝒟ℒD4,×. In particular, it solves the consistency and the classification problems for 𝒟ℒD4,×-knowledge bases represented in set-theoretic terms, and a generalization of the Conjunctive Query Answering problem in which conjunctive queries with variables of three sorts are admitted. The reasoner, which extends and improves a previous version, is implemented in C++. It supports 𝒟ℒD4,×-knowledge bases serialized in the OWL/XML format and it admits also rules expressed in SWRL (Semantic Web Rule Language).

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