95 research outputs found
A Formally Verified Prover for the ALC Description Logic
The Ontology Web Language (OWL) is a language used for
the Semantic Web. OWL is based on Description Logics (DLs), a family
of logical formalisms for representing and reasoning about conceptual
and terminological knowledge. Among these, the logic ALC is a ground
DL used in many practical cases. Moreover, the Semantic Web appears
as a new field for the application of formal methods, that could be used
to increase its reliability. A starting point could be the formal verification
of satisfiability provers for DLs. In this paper, we present the PVS
specification of a prover for ALC , as well as the proofs of its termination,
soundness and completeness. We also present the formalization of
the well–foundedness of the multiset relation induced by a well–founded
relation. This result has been used to prove the termination and the
completeness of the ALC prover.Ministerio de Educación y Ciencia TIN2004–0388
Formally Verified Tableau-Based Reasoners for a Description Logic
Description Logics are a family of logics used to represent and reason
about conceptual and terminological knowledge. One of the most basic description
logics is ALC , used as a basis from which to obtain others. Description logics are
particularly important to provide a logical basis for the web ontology languages (such
as OWL) used in the Semantic Web. In order to increase the reliability of the Semantic
Web, formal methods can be applied, and in particular formal verification of its
reasoning services can be carried out. In this paper, we present the formal verification
of a tableau-based satisfiability algorithm for the logic ALC . The verification has
been completed in several stages. First, we develop an abstract formalization of
satisfiability-checking of ALC -concepts. Secondly, we define and formally verify a
tableau-based algorithm in which the order of rule application and branch selection
can be flexibly specified, using a methodology of refinements to transfer the main
properties from the ALC abstract formalization. Finally, we obtain verified and
executable reasoners from the algorithm via a process of instantiation.Ministerio de Ciencia e Innovación TIN2009-09492Junta de Andalucía TIC-0606
Verified Decision Procedures for Modal Logics
We describe a formalization of modal tableaux with histories for the modal logics K, KT and S4 in Lean. We describe how we formalized the static and transitional rules, the non-trivial termination and the correctness of loop-checks. The formalized tableaux are essentially executable decision procedures with soundness and completeness proved. Termination is also proved in order to define them as functions in Lean. All of these decision procedures return a concrete Kripke model in cases where the input set of formulas is satisfiable, and a proof constructed via the tableau rules witnessing unsatisfiability otherwise. We also describe an extensible formalization of backjumping and its verified implementation for the modal logic K. As far as we know, these are the first verified decision procedures for these modal logics
Proceedings of the Automated Reasoning Workshop (ARW 2019)
Preface
This volume contains the proceedings of ARW 2019, the twenty sixths Workshop on Automated Rea-
soning (2nd{3d September 2019) hosted by the Department of Computer Science, Middlesex University,
England (UK). Traditionally, this annual workshop which brings together, for a two-day intensive pro-
gramme, researchers from different areas of automated reasoning, covers both traditional and emerging
topics, disseminates achieved results or work in progress. During informal discussions at workshop ses-
sions, the attendees, whether they are established in the Automated Reasoning community or are only at
their early stages of their research career, gain invaluable feedback from colleagues. ARW always looks
at the ways of strengthening links between academia, industry and government; between theoretical and
practical advances. The 26th ARW is affiliated with TABLEAUX 2019 conference.
These proceedings contain forteen extended abstracts contributed by the participants of the workshop
and assembled in order of their presentations at the workshop. The abstracts cover a wide range of topics
including the development of reasoning techniques for Agents, Model-Checking, Proof Search for classical
and non-classical logics, Description Logics, development of Intelligent Prediction Models, application of
Machine Learning to theorem proving, applications of AR in Cloud Computing and Networking.
I would like to thank the members of the ARW Organising Committee for their advice and assis-
tance. I would also like to thank the organisers of TABLEAUX/FroCoS 2019, and Andrei Popescu, the
TABLEAUX Conference Chair, in particular, for the enormous work related to the organisation of this
affiliation. I would also like to thank Natalia Yerashenia for helping in preparing these proceedings.
London Alexander Bolotov
September 201
A cookbook for temporal conceptual data modelling with description logic
We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z,<), satisfying the constant domain assumption. We prove that the most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turn out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we obtain logics whose complexity ranges between PSpace and NLogSpace. These positive results were obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL
, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established
Context-Aware Modeling Using Semantic Web and Z Notation
Surveys in user context modeling have shown that the semantic web is one of
the promising approach to represent and structure the contextual information captured
from user’s surrounding environment in a context-aware application. A benefit of
using semantic web language is that it enables application to reason user contextual
information in order to get the knowledge of user’s behavior. However, regarding its
notation format, semantic web is suitable for implementation level or to be consumed
by application run-time.
Context-aware application is a part of distributed computing system. In distributed
computing system, the language used for specification should be distinguished from
the implementation / run-time purpose. This is known as separation of modeling language.
Regarding the context-aware application, for those who are concerned with
specification of context modeling, the language that is used for specification should
also be distinguished from the implementation one.
This thesis aims at proposing the use of formal specification technique to develop
a generic context ontology model of user’s behavior at the Computer and Information
Sciences Department, Universiti Teknologi PETRONAS. Initially, the context ontology
was written in OWL semantic web language. The further process is mapping onto
a formal specification language, i.e. onto Z notation. As a result, specification of context
ontology and its consistency checking have been developed and verified beyond
the semantic web language environment. An inconsistency of context model has been
detected during the verification of Z model, which cannot be revealed by current OWL
DL reasoner.
The context-aware designers might benefit from the formal specification of context
ontology, where the designers could fully use formal verification technique to check
the correctness of context ontology. Thus, the modeling approach in this thesis has
shown that it could complement the context ontology development process, where the
checking and refinement are performed beyond the semantic web reasone
Proceedings of the Joint Automated Reasoning Workshop and Deduktionstreffen: As part of the Vienna Summer of Logic – IJCAR 23-24 July 2014
Preface
For many years the British and the German automated reasoning communities have successfully run independent series of workshops for anybody working in the area of automated reasoning. Although open to the general
public they addressed in the past primarily the British and the German communities, respectively. At the occasion of the Vienna Summer of Logic the two series have a joint event in Vienna as an IJCAR workshop. In the spirit of the two series there will be only informal proceedings with abstracts of the works presented. These are collected in this document. We have tried to maintain the informal open atmosphere of the two series and have welcomed in particular research students to present their work. We have solicited for all work related to automated reasoning and its applications with a particular interest in work-in-progress and the presentation of half-baked ideas.
As in the previous years, we have aimed to bring together researchers from all areas of automated reasoning in order to foster links among researchers from various disciplines; among theoreticians, implementers and users alike, and among international communities, this year not just the British and German communities
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