29,887 research outputs found
PSPACE Reasoning for Graded Modal Logics
We present a PSPACE algorithm that decides satisfiability of the graded modal
logic Gr(K_R)---a natural extension of propositional modal logic K_R by
counting expressions---which plays an important role in the area of knowledge
representation. The algorithm employs a tableaux approach and is the first
known algorithm which meets the lower bound for the complexity of the problem.
Thus, we exactly fix the complexity of the problem and refute an
ExpTime-hardness conjecture. We extend the results to the logic Gr(K_(R \cap
I)), which augments Gr(K_R) with inverse relations and intersection of
accessibility relations. This establishes a kind of ``theoretical benchmark''
that all algorithmic approaches can be measured against
On the evolution of the instance level of DL-lite knowledge bases
Recent papers address the issue of updating the instance level of knowledge
bases expressed in Description Logic following a model-based approach. One of
the outcomes of these papers is that the result of updating a knowledge base K
is generally not expressible in the Description Logic used to express K. In
this paper we introduce a formula-based approach to this problem, by revisiting
some research work on formula-based updates developed in the '80s, in
particular the WIDTIO (When In Doubt, Throw It Out) approach. We show that our
operator enjoys desirable properties, including that both insertions and
deletions according to such operator can be expressed in the DL used for the
original KB. Also, we present polynomial time algorithms for the evolution of
the instance level knowledge bases expressed in the most expressive Description
Logics of the DL-lite family
Understanding Opportunities in Social Entrepreneurship: A Critical Realist Abstraction
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This paper extends social entrepreneurship (SE) research by drawing upon a critical realist perspective to analyse dynamic structure/agency relations in SE opportunity emergence, illustrated by empirical evidence. Our findings demonstrate an agential aspect (opportunity actualisation following a path-dependent seeding-growing-shaping process) and a structural aspect (institutional, cognitive and embedded structures necessary for SE opportunity emergence) related to SE opportunities. These structures provide three boundary conditions for SE agency: institutional discrimination, an SE belief system and social feasibility. Within this paper, we develop a novel theoretical framework to analyse SE opportunities plus, an applicable tool to advance related empirical research
Inconsistency-tolerant Query Answering in Ontology-based Data Access
Ontology-based data access (OBDA) is receiving great attention as a new paradigm for managing information systems through semantic technologies. According to this paradigm, a Description Logic ontology provides an abstract and formal representation of the domain of interest to the information system, and is used as a sophisticated schema for accessing the data and formulating queries over them. In this paper, we address the problem of dealing with inconsistencies in OBDA. Our general goal is both to study DL semantical frameworks that are inconsistency-tolerant, and to devise techniques for answering unions of conjunctive queries under such inconsistency-tolerant semantics. Our work is inspired by the approaches to consistent query answering in databases, which are based on the idea of living with inconsistencies in the database, but trying to obtain only consistent information during query answering, by relying on the notion of database repair. We first adapt the notion of database repair to our context, and show that, according to such a notion, inconsistency-tolerant query answering is intractable, even for very simple DLs. Therefore, we propose a different repair-based semantics, with the goal of reaching a good compromise between the expressive power of the semantics and the computational complexity of inconsistency-tolerant query answering. Indeed, we show that query answering under the new semantics is first-order rewritable in OBDA, even if the ontology is expressed in one of the most expressive members of the DL-Lite family
Reasoning with Individuals for the Description Logic SHIQ
While there has been a great deal of work on the development of reasoning
algorithms for expressive description logics, in most cases only Tbox reasoning
is considered. In this paper we present an algorithm for combined Tbox and Abox
reasoning in the SHIQ description logic. This algorithm is of particular
interest as it can be used to decide the problem of (database) conjunctive
query containment w.r.t. a schema. Moreover, the realisation of an efficient
implementation should be relatively straightforward as it can be based on an
existing highly optimised implementation of the Tbox algorithm in the FaCT
system.Comment: To appear at CADE-1
Practical Reasoning for Very Expressive Description Logics
Description Logics (DLs) are a family of knowledge representation formalisms
mainly characterised by constructors to build complex concepts and roles from
atomic ones. Expressive role constructors are important in many applications,
but can be computationally problematical. We present an algorithm that decides
satisfiability of the DL ALC extended with transitive and inverse roles and
functional restrictions with respect to general concept inclusion axioms and
role hierarchies; early experiments indicate that this algorithm is well-suited
for implementation. Additionally, we show that ALC extended with just
transitive and inverse roles is still in PSPACE. We investigate the limits of
decidability for this family of DLs, showing that relaxing the constraints
placed on the kinds of roles used in number restrictions leads to the
undecidability of all inference problems. Finally, we describe a number of
optimisation techniques that are crucial in obtaining implementations of the
decision procedures, which, despite the worst-case complexity of the problem,
exhibit good performance with real-life problems
Specification Patterns for Robotic Missions
Mobile and general-purpose robots increasingly support our everyday life,
requiring dependable robotics control software. Creating such software mainly
amounts to implementing their complex behaviors known as missions. Recognizing
the need, a large number of domain-specific specification languages has been
proposed. These, in addition to traditional logical languages, allow the use of
formally specified missions for synthesis, verification, simulation, or guiding
the implementation. For instance, the logical language LTL is commonly used by
experts to specify missions, as an input for planners, which synthesize the
behavior a robot should have. Unfortunately, domain-specific languages are
usually tied to specific robot models, while logical languages such as LTL are
difficult to use by non-experts. We present a catalog of 22 mission
specification patterns for mobile robots, together with tooling for
instantiating, composing, and compiling the patterns to create mission
specifications. The patterns provide solutions for recurrent specification
problems, each of which detailing the usage intent, known uses, relationships
to other patterns, and---most importantly---a template mission specification in
temporal logic. Our tooling produces specifications expressed in the LTL and
CTL temporal logics to be used by planners, simulators, or model checkers. The
patterns originate from 245 realistic textual mission requirements extracted
from the robotics literature, and they are evaluated upon a total of 441
real-world mission requirements and 1251 mission specifications. Five of these
reflect scenarios we defined with two well-known industrial partners developing
human-size robots. We validated our patterns' correctness with simulators and
two real robots
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