4,984 research outputs found
Requirements modelling and formal analysis using graph operations
The increasing complexity of enterprise systems requires a more advanced
analysis of the representation of services expected than is currently possible.
Consequently, the specification stage, which could be facilitated by formal
verification, becomes very important to the system life-cycle. This paper presents
a formal modelling approach, which may be used in order to better represent
the reality of the system and to verify the awaited or existing system’s properties,
taking into account the environmental characteristics. For that, we firstly propose
a formalization process based upon properties specification, and secondly we
use Conceptual Graphs operations to develop reasoning mechanisms of verifying
requirements statements. The graphic visualization of these reasoning enables us
to correctly capture the system specifications by making it easier to determine if
desired properties hold. It is applied to the field of Enterprise modelling
Enterprise model verification and validation : an approach
This article presents a verification and validation approach which is used here in order to complete the classical tool box the industrial user may utilize in enterprise modeling and integration domain. This approach, which has been defined independently from any application domain is based on several formal concepts and tools presented in this paper. These concepts are property concepts, property reference matrix, properties graphs, enterprise modeling domain ontology, conceptual graphs and formal reasoning mechanisms
Goal driven theorem proving using conceptual graphs and Peirce logic
The thesis describes a rational reconstruction of Sowa's theory of Conceptual
Graphs. The reconstruction produces a theory with a firmer logical foundation than was
previously the case and which is suitable for computation whilst retaining the
expressiveness of the original theory. Also, several areas of incompleteness are
addressed. These mainly concern the scope of operations on conceptual graphs of
different types but include extensions for logics of higher orders than first order. An
important innovation is the placing of negation onto a sound representational basis.
A comparison of theorem proving techniques is made from which the principles of
theorem proving in Peirce logic are identified. As a result, a set of derived inference rules,
suitable for a goal driven approach to theorem proving, is developed from Peirce's beta
rules. These derived rules, the first of their kind for Peirce logic and conceptual graphs,
allow the development of a novel theorem proving approach which has some similarities
to a combined semantic tableau and resolution methodology. With this methodology it is
shown that a logically complete yet tractable system is possible. An important result is the
identification of domain independent heuristics which follow directly from the
methodology. In addition to the theorem prover, an efficient system for the detection of
selectional constraint violations is developed.
The proof techniques are used to build a working knowledge base system in Prolog
which can accept arbitrary statements represented by conceptual graphs and test their
semantic and logical consistency against a dynamic knowledge base. The same proof
techniques are used to find solutions to arbitrary queries. Since the system is logically
complete it can maintain the integrity of its knowledge base and answer queries in a fully
automated manner. Thus the system is completely declarative and does not require any
programming whatever by a user with the result that all interaction with a user is
conversational. Finally, the system is compared with other theorem proving systems
which are based upon Conceptual Graphs and conclusions about the effectiveness of the
methodology are drawn
An Algebraic Framework for Compositional Program Analysis
The purpose of a program analysis is to compute an abstract meaning for a
program which approximates its dynamic behaviour. A compositional program
analysis accomplishes this task with a divide-and-conquer strategy: the meaning
of a program is computed by dividing it into sub-programs, computing their
meaning, and then combining the results. Compositional program analyses are
desirable because they can yield scalable (and easily parallelizable) program
analyses.
This paper presents algebraic framework for designing, implementing, and
proving the correctness of compositional program analyses. A program analysis
in our framework defined by an algebraic structure equipped with sequencing,
choice, and iteration operations. From the analysis design perspective, a
particularly interesting consequence of this is that the meaning of a loop is
computed by applying the iteration operator to the loop body. This style of
compositional loop analysis can yield interesting ways of computing loop
invariants that cannot be defined iteratively. We identify a class of
algorithms, the so-called path-expression algorithms [Tarjan1981,Scholz2007],
which can be used to efficiently implement analyses in our framework. Lastly,
we develop a theory for proving the correctness of an analysis by establishing
an approximation relationship between an algebra defining a concrete semantics
and an algebra defining an analysis.Comment: 15 page
From Euclidean Geometry to Knots and Nets
This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.Peer reviewe
Wheeled pro(p)file of Batalin-Vilkovisky formalism
Using technique of wheeled props we establish a correspondence between the
homotopy theory of unimodular Lie 1-bialgebras and the famous
Batalin-Vilkovisky formalism. Solutions of the so called quantum master
equation satisfying certain boundary conditions are proven to be in 1-1
correspondence with representations of a wheeled dg prop which, on the one
hand, is isomorphic to the cobar construction of the prop of unimodular Lie
1-bialgebras and, on the other hand, is quasi-isomorphic to the dg wheeled prop
of unimodular Poisson structures. These results allow us to apply properadic
methods for computing formulae for a homotopy transfer of a unimodular Lie
1-bialgebra structure on an arbitrary complex to the associated quantum master
function on its cohomology. It is proven that in the category of quantum BV
manifolds associated with the homotopy theory of unimodular Lie 1-bialgebras
quasi-isomorphisms are equivalence relations.
It is shown that Losev-Mnev's BF theory for unimodular Lie algebras can be
naturally extended to the case of unimodular Lie 1-bialgebras (and, eventually,
to the case of unimodular Poisson structures). Using a finite-dimensional
version of the Batalin-Vilkovisky quantization formalism it is rigorously
proven that the Feynman integrals computing the effective action of this new BF
theory describe precisely homotopy transfer formulae obtained within the
wheeled properadic approach to the quantum master equation. Quantum corrections
(which are present in our BF model to all orders of the Planck constant)
correspond precisely to what are often called "higher Massey products" in the
homological algebra.Comment: 42 pages. The journal versio
- …