1,619 research outputs found
Expressiveness and Completeness in Abstraction
We study two notions of expressiveness, which have appeared in abstraction
theory for model checking, and find them incomparable in general. In
particular, we show that according to the most widely used notion, the class of
Kripke Modal Transition Systems is strictly less expressive than the class of
Generalised Kripke Modal Transition Systems (a generalised variant of Kripke
Modal Transition Systems equipped with hypertransitions). Furthermore, we
investigate the ability of an abstraction framework to prove a formula with a
finite abstract model, a property known as completeness. We address the issue
of completeness from a general perspective: the way it depends on certain
abstraction parameters, as well as its relationship with expressiveness.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
Quantified CTL: Expressiveness and Complexity
While it was defined long ago, the extension of CTL with quantification over
atomic propositions has never been studied extensively. Considering two
different semantics (depending whether propositional quantification refers to
the Kripke structure or to its unwinding tree), we study its expressiveness
(showing in particular that QCTL coincides with Monadic Second-Order Logic for
both semantics) and characterise the complexity of its model-checking and
satisfiability problems, depending on the number of nested propositional
quantifiers (showing that the structure semantics populates the polynomial
hierarchy while the tree semantics populates the exponential hierarchy)
Complexity of ITL model checking: some well-behaved fragments of the interval logic HS
Model checking has been successfully used in many computer science fields,
including artificial intelligence, theoretical computer science, and databases.
Most of the proposed solutions make use of classical, point-based temporal
logics, while little work has been done in the interval temporal logic setting.
Recently, a non-elementary model checking algorithm for Halpern and Shoham's
modal logic of time intervals HS over finite Kripke structures (under the
homogeneity assumption) and an EXPSPACE model checking procedure for two
meaningful fragments of it have been proposed. In this paper, we show that more
efficient model checking procedures can be developed for some expressive enough
fragments of HS
State/event based versus purely Action or State based Logics
Although less studied than purely action or state based logics, state/event
based logics are becoming increasingly important. Some systems are best studied
using structures with information on both states and transitions, and it is
these structures over which state/event based logics are defined. The logic
UCTL and its variants are perhaps the most widely studied and implemented of
these logics to date. As yet, however, no-one seems to have defined UCTL*, a
trivial step but a worthwhile one. Here we do just that, but prove in the cases
of both UCTL and UCTL* that these logics are no more expressive than their more
commonplace fragments. Also, acknowledging the importance of modal transition
systems, we define a state/event based logic over a modified modal transition
system as a precursor to further work.Comment: 9 pages, 6 figure
Logic Programming for Finding Models in the Logics of Knowledge and its Applications: A Case Study
The logics of knowledge are modal logics that have been shown to be effective
in representing and reasoning about knowledge in multi-agent domains.
Relatively few computational frameworks for dealing with computation of models
and useful transformations in logics of knowledge (e.g., to support multi-agent
planning with knowledge actions and degrees of visibility) have been proposed.
This paper explores the use of logic programming (LP) to encode interesting
forms of logics of knowledge and compute Kripke models. The LP modeling is
expanded with useful operators on Kripke structures, to support multi-agent
planning in the presence of both world-altering and knowledge actions. This
results in the first ever implementation of a planner for this type of complex
multi-agent domains.Comment: 16 pages, 1 figure, International Conference on Logic Programming
201
Checking Interval Properties of Computations
Model checking is a powerful method widely explored in formal verification.
Given a model of a system, e.g., a Kripke structure, and a formula specifying
its expected behaviour, one can verify whether the system meets the behaviour
by checking the formula against the model.
Classically, system behaviour is expressed by a formula of a temporal logic,
such as LTL and the like. These logics are "point-wise" interpreted, as they
describe how the system evolves state-by-state. However, there are relevant
properties, such as those constraining the temporal relations between pairs of
temporally extended events or involving temporal aggregations, which are
inherently "interval-based", and thus asking for an interval temporal logic.
In this paper, we give a formalization of the model checking problem in an
interval logic setting. First, we provide an interpretation of formulas of
Halpern and Shoham's interval temporal logic HS over finite Kripke structures,
which allows one to check interval properties of computations. Then, we prove
that the model checking problem for HS against finite Kripke structures is
decidable by a suitable small model theorem, and we provide a lower bound to
its computational complexity.Comment: In Journal: Acta Informatica, Springer Berlin Heidelber, 201
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