170 research outputs found
Type-elimination-based reasoning for the description logic SHIQbs using decision diagrams and disjunctive datalog
We propose a novel, type-elimination-based method for reasoning in the
description logic SHIQbs including DL-safe rules. To this end, we first
establish a knowledge compilation method converting the terminological part of
an ALCIb knowledge base into an ordered binary decision diagram (OBDD) which
represents a canonical model. This OBDD can in turn be transformed into
disjunctive Datalog and merged with the assertional part of the knowledge base
in order to perform combined reasoning. In order to leverage our technique for
full SHIQbs, we provide a stepwise reduction from SHIQbs to ALCIb that
preserves satisfiability and entailment of positive and negative ground facts.
The proposed technique is shown to be worst case optimal w.r.t. combined and
data complexity and easily admits extensions with ground conjunctive queries.Comment: 38 pages, 3 figures, camera ready version of paper accepted for
publication in Logical Methods in Computer Scienc
Solving Set Optimization Problems by Cardinality Optimization with an Application to Argumentation
Optimization—minimization or maximization—in the lattice of subsets is a frequent operation in Artificial Intelligence tasks. Examples are subset-minimal model-based diagnosis, nonmonotonic reasoning by means of circumscription, or preferred extensions in abstract argumentation. Finding the optimum among many admissible solutions is often harder than finding admissible solutions with respect to both computational complexity and methodology. This paper addresses the former issue by means of an effective method for finding subset-optimal solutions. It is based on the relationship between cardinality-optimal and subset-optimal solutions, and the fact that many logic-based declarative programming systems provide constructs for finding cardinality-optimal solutions, for example maximum satisfiability (MaxSAT) or weak constraints in Answer Set Programming (ASP). Clearly each cardinality-optimal solution is also a subset-optimal one, and if the language also allows for the addition of particular restricting constructs (both MaxSAT and ASP do) then all subset-optimal solutions can be found by an iterative computation of cardinality-optimal solutions. As a showcase, the computation of preferred extensions of abstract argumentation frameworks using the proposed method is studied
Algorithms for computational argumentation in artificial intelligence
Argumentation is a vital aspect of intelligent behaviour by humans. It provides the means for comparing
information by analysing pros and cons when trying to make a decision. Formalising argumentation in
computational environment has become a topic of increasing interest in artificial intelligence research
over the last decade.
Computational argumentation involves reasoning with uncertainty by making use of logic in order
to formalize the presentation of arguments and counterarguments and deal with conflicting information.
A common assumption for logic-based argumentation is that an argument is a pair where Φ is
a consistent set which is minimal for entailing a claim α. Different logics provide different definitions
for consistency and entailment and hence give different options for formalising arguments and counterarguments.
The expressivity of classical propositional logic allows for complicated knowledge to be
represented but its computational cost is an issue. This thesis is based on monological argumentation
using classical propositional logic [12] and aims in developing algorithms that are viable despite the
computational cost. The proposed solution adapts well established techniques for automated theorem
proving, based on resolution and connection graphs. A connection graph is a graph where each node is
a clause and each arc denotes there exist complementary disjuncts between nodes. A connection graph
allows for a substantially reduced search space to be used when seeking all the arguments for a claim
from a given knowledgebase. In addition, its structure provides information on how its nodes can be linked
with each other by resolution, providing this way the basis for applying algorithms which search for
arguments by traversing the graph. The correctness of this approach is supported by theoretical results,
while experimental evaluation demonstrates the viability of the algorithms developed. In addition, an
extension of the theoretical work for propositional logic to first-order logic is introduced
Foundations of implementations for formal argumentation
We survey the current state of the art of general techniques, as well as specific software systems for solving tasks in abstract argumentation frameworks, structured argumentation frameworks, and approaches for visualizing and analysing argumentation. Furthermore, we discuss challenges and promising techniques such as parallel processing and approximation approaches. Finally, we address the issue of evaluating software systems empirically with links to the International Competition on Computational Models of Argumentation
Foundations of SPARQL Query Optimization
The SPARQL query language is a recent W3C standard for processing RDF data, a
format that has been developed to encode information in a machine-readable way.
We investigate the foundations of SPARQL query optimization and (a) provide
novel complexity results for the SPARQL evaluation problem, showing that the
main source of complexity is operator OPTIONAL alone; (b) propose a
comprehensive set of algebraic query rewriting rules; (c) present a framework
for constraint-based SPARQL optimization based upon the well-known chase
procedure for Conjunctive Query minimization. In this line, we develop two
novel termination conditions for the chase. They subsume the strongest
conditions known so far and do not increase the complexity of the recognition
problem, thus making a larger class of both Conjunctive and SPARQL queries
amenable to constraint-based optimization. Our results are of immediate
practical interest and might empower any SPARQL query optimizer
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