824 research outputs found
A set-based reasoner for the description logic \shdlssx (Extended Version)
We present a \ke-based implementation of a reasoner for a decidable fragment
of (stratified) set theory expressing the description logic \dlssx
(\shdlssx, for short). Our application solves the main TBox and ABox
reasoning problems for \shdlssx. In particular, it solves the consistency
problem for \shdlssx-knowledge bases represented in set-theoretic terms, and
a generalization of the \emph{Conjunctive Query Answering} problem in which
conjunctive queries with variables of three sorts are admitted. The reasoner,
which extends and optimizes a previous prototype for the consistency checking
of \shdlssx-knowledge bases (see \cite{cilc17}), is implemented in
\textsf{C++}. It supports \shdlssx-knowledge bases serialized in the OWL/XML
format, and it admits also rules expressed in SWRL (Semantic Web Rule
Language).Comment: arXiv admin note: text overlap with arXiv:1804.11222,
arXiv:1707.07545, arXiv:1702.0309
A \textsf{C++} reasoner for the description logic \shdlssx (Extended Version)
We present an ongoing implementation of a \ke\space based reasoner for a
decidable fragment of stratified elementary set theory expressing the
description logic \dlssx (shortly \shdlssx). The reasoner checks the
consistency of \shdlssx-knowledge bases (KBs) represented in set-theoretic
terms. It is implemented in \textsf{C++} and supports \shdlssx-KBs serialized
in the OWL/XML format. To the best of our knowledge, this is the first attempt
to implement a reasoner for the consistency checking of a description logic
represented via a fragment of set theory that can also classify standard OWL
ontologies.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1702.03096,
arXiv:1804.1122
Web ontology representation and reasoning via fragments of set theory
In this paper we use results from Computable Set Theory as a means to
represent and reason about description logics and rule languages for the
semantic web.
Specifically, we introduce the description logic \mathcal{DL}\langle
4LQS^R\rangle(\D)--admitting features such as min/max cardinality constructs
on the left-hand/right-hand side of inclusion axioms, role chain axioms, and
datatypes--which turns out to be quite expressive if compared with
\mathcal{SROIQ}(\D), the description logic underpinning the Web Ontology
Language OWL. Then we show that the consistency problem for
\mathcal{DL}\langle 4LQS^R\rangle(\D)-knowledge bases is decidable by
reducing it, through a suitable translation process, to the satisfiability
problem of the stratified fragment of set theory, involving variables
of four sorts and a restricted form of quantification. We prove also that,
under suitable not very restrictive constraints, the consistency problem for
\mathcal{DL}\langle 4LQS^R\rangle(\D)-knowledge bases is
\textbf{NP}-complete. Finally, we provide a -translation of rules
belonging to the Semantic Web Rule Language (SWRL)
Analytic Tableaux for Simple Type Theory and its First-Order Fragment
We study simple type theory with primitive equality (STT) and its first-order
fragment EFO, which restricts equality and quantification to base types but
retains lambda abstraction and higher-order variables. As deductive system we
employ a cut-free tableau calculus. We consider completeness, compactness, and
existence of countable models. We prove these properties for STT with respect
to Henkin models and for EFO with respect to standard models. We also show that
the tableau system yields a decision procedure for three EFO fragments
An optimized KE-tableau-based system for reasoning in the description logic \shdlssx (Extended Version)
We present a \ke-based procedure for the main TBox and ABox reasoning tasks
for the description logic \dlssx, in short \shdlssx. The logic \shdlssx,
representable in the decidable multi-sorted quantified set-theoretic fragment
\flqsr, combines the high scalability and efficiency of rule languages such
as the Semantic Web Rule Language (SWRL) with the expressivity of description
logics. %In fact it supports, among other features, 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, and role properties such as
transitivity, symmetry, reflexivity, and irreflexivity.
Our algorithm is based on a variant of the \ke\space system for sets of
universally quantified clauses, where the KE-elimination rule is generalized in
such a way as to incorporate the -rule. The novel system, called \keg,
turns out to be an improvement of the system introduced in \cite{RR2017} and of
standard first-order \ke x \cite{dagostino94}. Suitable benchmark test sets
executed on C++ implementations of the three mentioned systems show that the
performances of the \keg-based reasoner are often up to about 400\% better than
the ones of the other two systems. This a first step towards the construction
of efficient reasoners for expressive OWL ontologies based on fragments of
computable set-theory.Comment: arXiv admin note: text overlap with arXiv:1702.03096,
arXiv:1805.0860
Deciding regular grammar logics with converse through first-order logic
We provide a simple translation of the satisfiability problem for regular
grammar logics with converse into GF2, which is the intersection of the guarded
fragment and the 2-variable fragment of first-order logic. This translation is
theoretically interesting because it translates modal logics with certain frame
conditions into first-order logic, without explicitly expressing the frame
conditions.
A consequence of the translation is that the general satisfiability problem
for regular grammar logics with converse is in EXPTIME. This extends a previous
result of the first author for grammar logics without converse. Using the same
method, we show how some other modal logics can be naturally translated into
GF2, including nominal tense logics and intuitionistic logic.
In our view, the results in this paper show that the natural first-order
fragment corresponding to regular grammar logics is simply GF2 without extra
machinery such as fixed point-operators.Comment: 34 page
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