30 research outputs found
Complexity Jumps In Multiagent Justification Logic Under Interacting Justifications
The Logic of Proofs, LP, and its successor, Justification Logic, is a
refinement of the modal logic approach to epistemology in which
proofs/justifications are taken into account. In 2000 Kuznets showed that
satisfiability for LP is in the second level of the polynomial hierarchy, a
result which has been successfully repeated for all other one-agent
justification logics whose complexity is known.
We introduce a family of multi-agent justification logics with interactions
between the agents' justifications, by extending and generalizing the two-agent
versions of the Logic of Proofs introduced by Yavorskaya in 2008. Known
concepts and tools from the single-agent justification setting are adjusted for
this multiple agent case. We present tableau rules and some preliminary
complexity results. In several cases the satisfiability problem for these
logics remains in the second level of the polynomial hierarchy, while for
others it is PSPACE or EXP-hard. Furthermore, this problem becomes PSPACE-hard
even for certain two-agent logics, while there are EXP-hard logics of three
agents
Counting Computations with Formulae: Logical Characterisations of Counting Complexity Classes
We present quantitative logics with two-step semantics based on the framework of quantitative logics introduced by Arenas et al. (2020) and the two-step semantics defined in the context of weighted logics by Gastin & Monmege (2018). We show that some of the fragments of our logics augmented with a least fixed point operator capture interesting classes of counting problems. Specifically, we answer an open question in the area of descriptive complexity of counting problems by providing logical characterisations of two subclasses of #P, namely SpanL and TotP, that play a significant role in the study of approximable counting problems. Moreover, we define logics that capture FPSPACE and SpanPSPACE, which are counting versions of PSPACE
Monitoring for Silent Actions
Silent actions are an essential mechanism for system modelling and specification. They are used to abstractly report the occurrence of computation steps without divulging their precise details, thereby enabling the description of important aspects such as the branching structure of a system. Yet, their use rarely features in specification logics used in runtime verification. We study monitorability aspects of a branching-time logic that employs silent actions, identifying which formulas are monitorable for a number of instrumentation setups. We also consider defective instrumentation setups that imprecisely report silent events, and establish monitorability results for tolerating these imperfections
If At First You Don't Succeed: Extended Monitorability through Multiple Executions
This paper investigates the observational capabilities of monitors that can
observe a system over multiple runs. We study how the augmented monitoring
setup affect the class of properties that can be verified at runtime, focussing
on branching-time properties expressed in the modal mu-calculus. Our results
show that the setup can be used to systematically extend previously established
monitorability limits. We also prove bounds that capture the correspondence
between the syntactic structure of a branching-time property and the number of
system runs required to conduct the verification
An axiomatization of verdict equivalence over regular monitors
Monitors are a key tool in the field of runtime verification, where they are
used to check for system properties by analysing execution traces generated by
processes. Work on runtime monitoring carried out in a series of papers by
Aceto et al. has specified monitors using a variation on the regular fragment
of Milner's CCS and studied two trace-based notions of equivalence over
monitors, namely verdict and -verdict equivalence. This article is
devoted to the study of the equational logic of monitors modulo those two
notions of equivalence. It presents complete equational axiomatizations of
verdict and -verdict equivalence for closed and open terms over
recursion-free monitors.Comment: Preprint submitted to Journal of logical and algebraic methods in
programing 202
The Best a Monitor Can Do
Existing notions of monitorability for branching-time properties are fairly restrictive. This, in turn, impacts the ability to incorporate prior knowledge about the system under scrutiny - which corresponds to a branching-time property - into the runtime analysis. We propose a definition of optimal monitors that verify the best monitorable under- or over-approximation of a specification, regardless of its monitorability status. Optimal monitors can be obtained for arbitrary branching-time properties by synthesising a sound and complete monitor for their strongest monitorable consequence. We show that the strongest monitorable consequence of specifications expressed in Hennessy-Milner logic with recursion is itself expressible in this logic, and present a procedure to find it. Our procedure enables prior knowledge to be optimally incorporated into runtime monitors
Complexity results for modal logic with recursion via translations and tableaux
This paper studies the complexity of classical modal logics and of their
extension with fixed-point operators, using translations to transfer results
across logics. In particular, we show several complexity results for
multi-agent logics via translations to and from the -calculus and modal
logic, which allow us to transfer known upper and lower bounds. We also use
these translations to introduce a terminating tableau system for the logics we
study, based on Kozen's tableau for the -calculus, and the one of Fitting
and Massacci for modal logic. Finally, we show how to encode the tableaux we
introduced into -calculus formulas. This encoding provides upper bounds
for the satisfiability checking of the few logics we previously did not have
algorithms for.Comment: 43 pages. arXiv admin note: substantial text overlap with
arXiv:2209.1037
Adventures in monitorability: From branching time to linear time and back again.
This paper establishes a comprehensive theory of runtime monitorability for Hennessy-Milner logic with recursion, a very expressive variant of the modal µ-calculus. It investigates the monitorability of that logic with a linear-time semantics and then compares the obtained results with ones that were previously presented in the literature for a branching-time setting. Our work establishes an expressiveness hierarchy of monitorable fragments of Hennessy-Milner logic with recursion in a linear-time setting and exactly identifies what kinds of guarantees can be given using runtime monitors for each fragment in the hierarchy. Each fragment is shown to be complete, in the sense that it can express all properties that can be monitored under the corresponding guarantees. The study is carried out using a principled approach to monitoring that connects the semantics of the logic and the operational semantics of monitors. The proposed framework supports the automatic, compositional synthesis of correct monitors from monitorable properties