2,509 research outputs found
An Axiomatic Approach to Liveness for Differential Equations
This paper presents an approach for deductive liveness verification for
ordinary differential equations (ODEs) with differential dynamic logic.
Numerous subtleties complicate the generalization of well-known discrete
liveness verification techniques, such as loop variants, to the continuous
setting. For example, ODE solutions may blow up in finite time or their
progress towards the goal may converge to zero. Our approach handles these
subtleties by successively refining ODE liveness properties using ODE
invariance properties which have a well-understood deductive proof theory. This
approach is widely applicable: we survey several liveness arguments in the
literature and derive them all as special instances of our axiomatic refinement
approach. We also correct several soundness errors in the surveyed arguments,
which further highlights the subtlety of ODE liveness reasoning and the utility
of our deductive approach. The library of common refinement steps identified
through our approach enables both the sound development and justification of
new ODE liveness proof rules from our axioms.Comment: FM 2019: 23rd International Symposium on Formal Methods, Porto,
Portugal, October 9-11, 201
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
RHLE: Modular Deductive Verification of Relational Properties
Relational program logics are used to prove that a desired relationship holds
between the execution of multiple programs. Existing relational program logics
have focused on verifying that all runs of a collection of programs do not fall
outside a desired set of behaviors. Several important relational properties,
including refinement and noninterference, do not fit into this category, as
they require the existence of specific desirable executions. This paper
presents RHLE, a logic for verifying a class of relational properties which we
term properties. properties assert that for
all executions of a collection of programs, there exist executions of another
set of programs exhibiting some intended behavior. Importantly, RHLE can reason
modularly about programs which make library calls, ensuring that
properties are preserved when the programs are linked with any
valid implementation of the library. To achieve this, we develop a novel form
of function specification that requires the existence of certain behaviors in
valid implementations. We have built a tool based on RHLE which we use to
verify a diverse set of relational properties drawn from the literature,
including refinement and generalized noninterference
A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time
Interval Temporal Logic (ITL) is an established temporal formalism for
reasoning about time periods. For over 25 years, it has been applied in a
number of ways and several ITL variants, axiom systems and tools have been
investigated. We solve the longstanding open problem of finding a complete
axiom system for basic quantifier-free propositional ITL (PITL) with infinite
time for analysing nonterminating computational systems. Our completeness proof
uses a reduction to completeness for PITL with finite time and conventional
propositional linear-time temporal logic. Unlike completeness proofs of equally
expressive logics with nonelementary computational complexity, our semantic
approach does not use tableaux, subformula closures or explicit deductions
involving encodings of omega automata and nontrivial techniques for
complementing them. We believe that our result also provides evidence of the
naturalness of interval-based reasoning
An extended interval temporal logic and a framing technique for temporal logic programming
PhD ThesisTemporal logic programming is a paradigm for specification and verification of concurrent programs
in which a program can be written, and the properties of the program can be described
and verified in a same notation. However, there are many aspects of programming in temporal
logics that are not well-understood. One such an aspect is concurrent programming, another is
framing and the third is synchronous communication for parallel processes.
This thesis extends the original Interval Temporal Logic (ITL) to include infinite models,
past operators, and a new projection operator for dealing with concurrent computation, synchronous
communication, and framing in the context of temporal logic programming.
The thesis generalizes the original ITL to include past operators such as previous and past
chop, and extends the model to include infinite intervals. A considerable collection of logic laws
regarding both propositional and first order logics is formalized and proved within model theory.
After that, a subset of the extended ITL is formalized as a programming language, called
extended Tempura. These extensions, as in their logic basis, include infinite models, the previous
operator, projection and framing constructs. A normal form for programs within the extended
Tempura is demonstrated.
Next, a new projection operator is introduced. In the new construct, the sub-processes are
autonomous; each process has the right to specify its own interval over which it is executed.
The thesis presents a framing technique for temporal logic programming, which includes the
definitions of new assignments, the assignment flag and the framing operator, the formalization
of algebraic properties of the framing operator, the minimal model semantics of framed programs,
as well as an executable framed interpreter.
The synchronous communication operator await is based directly on the proposed framing
technique. It enables us to deal with concurrent computation. Based on EITL and await
operator, a framed concurrent temporal logic programming language, FTLL, is formally defined
within EITL.
Finally, the thesis describes a framed interpreter for the extended Tempura which has been
developed in SICSTUS prolog. In the new interpreter, the implementation of new assignments,
the frame operator, the await operator, and the new projection operator are all included
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