scholarly journals Query Answering with Transitive and Linear-Ordered Data

2018 ◽  
Vol 63 ◽  
pp. 191-264
Author(s):  
Antone Amarilli ◽  
Michael Benedikt ◽  
Pierre Bourhis ◽  
Michael Vanden Boom
Keyword(s):  
Linear Order ◽  
Transitive Closure ◽  
Query Answering ◽  
Decision Problems ◽  
Natural Variants ◽  
Powerful Constraint ◽  
Ordered Data ◽  
Constraint Languages

We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation to be transitive, restricting a relation to be the transitive closure of another relation, and restricting a relation to be a linear order. We give some natural variants of guardedness that allow inference to be decidable in each case, and isolate the complexity of the corresponding decision problems. Finally we show that slight changes in these conditions lead to undecidability.

scholarly journals Explanations for Query Answers under Existential Rules

2019 ◽  
Author(s):  
İsmail İlkan Ceylan ◽  
Thomas Lukasiewicz ◽  
Enrico Malizia ◽  
Andrius Vaicenavičius
Keyword(s):  
Complexity Analysis ◽  
Query Answering ◽  
Decision Problems ◽  
Logical Theory ◽  
Logical Entailment ◽  
Ontology Languages

Ontology-mediated query answering is an extensively studied paradigm, which aims at improving query answers with the use of a logical theory. As a form of logical entailment, ontology-mediated query answering is fully interpretable, which makes it possible to derive explanations for query answers. Surprisingly, however, explaining answers for ontology-mediated queries has received little attention for ontology languages based on existential rules. In this paper, we close this gap, and study the problem of explaining query answers in terms of minimal subsets of database facts. We provide a thorough complexity analysis for several decision problems associated with minimal explanations under existential rules.

scholarly journals Relating timed and register automata

2014 ◽  
Vol 26 (6) ◽  
pp. 993-1021 ◽  
Author(s):  
DIEGO FIGUEIRA ◽  
PIOTR HOFMAN ◽  
SŁAWOMIR LASOTA
Keyword(s):  
Decision Problems ◽  
Models Of Computation ◽  
Exponential Time ◽  
Infinite Words ◽  
Complexity Results ◽  
Ordered Data ◽  
Decidability And Complexity ◽  
Alternating Automata ◽  
Primitive Recursive ◽  
Timed Automaton

Timed and register automata are well-known models of computation over timed and data words, respectively. The former has clocks that allow to test the lapse of time between two events, whilst the latter includes registers that can store data values for later comparison. Although these two models behave differently in appearance, several decision problems have the same (un)decidability and complexity results for both models. As a prominent example, emptiness is decidable for alternating automata with one clock or register, both with non-primitive recursive complexity. This is not by chance.This work confirms that there is indeed a tight relationship between the two models. We show that a run of a timed automaton can be simulated by a register automaton over ordered data domain, and conversely that a run of a register automaton can be simulated by a timed automaton. These are exponential time reductions hold both in the finite and infinite words settings. Our results allow to transfer decidability results back and forth between these two kinds of models, as well complexity results modulo an exponential time reduction. We justify the usefulness of these reductions by obtaining new results on register automata.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

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.

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