A Logic of Probability with Decidable Model Checking

Beauquier, Danièle; Rabinovich, Alexander; Slissenko, Anatol

doi:10.1093/logcom/exl004

Cited by 15 publications

(28 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Apart from the line of work on logics like PCTL, there have a couple of proposals on exogenous logics that reason about probability distributions [13], [14]. Beauquier et.…”

Section: Related Workmentioning

confidence: 99%

“…al. [13] consider a predicate logic of probability that does allow comparing the probability of being in different states at the same time. However, this logic of probability is also incomparable to the properties we consider here.…”

Section: Related Workmentioning

confidence: 99%

“…al. [13]. We recall that the logic of probability and PCTL * were shown to have different expressiveness in [13].…”

Section: Related Workmentioning

confidence: 99%

“…Consider [13], that the property ψ 1 = ∃t. Prob ≥1 (Q(t)) in logic of probability is not expressible in PCTL * .…”

Section: Related Workmentioning

confidence: 99%

See 3 more Smart Citations

Reasoning about MDPs as Transformers of Probability Distributions

Korthikanti

Viswanathan

Agha

et al. 2010

2010 Seventh International Conference on the Quantitative Evaluation of Systems

View full text Add to dashboard Cite

Abstract-We consider Markov Decision Processes (MDPs) as transformers on probability distributions, where with respect to a scheduler that resolves nondeterminism, the MDP can be seen as exhibiting a behavior that is a sequence of probability distributions. Defining propositions using linear inequalities, one can reason about executions over the space of probability distributions. In this framework, one can analyze properties that cannot be expressed in logics like PCTL * , such as expressing bounds on transient rewards and expected values of random variables, and comparing the probability of being in one set of states at a given time with that of being in another set of states. We show that model checking MDPs with this semantics against ω-regular properties is in general undecidable. We then identify special classes of propositions and schedulers with respect to which the model checking problem becomes decidable. We demonstrate the potential usefulness of our results through an example.

show abstract

“…Apart from the line of work on logics like PCTL, there have a couple of proposals on exogenous logics that reason about probability distributions [13], [14]. Beauquier et.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Reasoning about MDPs as Transformers of Probability Distributions

Korthikanti

Viswanathan

Agha

et al. 2010

2010 Seventh International Conference on the Quantitative Evaluation of Systems

View full text Add to dashboard Cite

show abstract

“…In this logic, the agent knowledge and probability operators are indexed by a temporal variable. This logic generalizes the logic of [3]. Our logics allow polynomial comparisons of probability terms, as well as comparisons of agent probability terms referring to multiple time points.…”

Section: Introductionmentioning

confidence: 99%

Undecidable Cases of Model Checking Probabilistic Temporal-Epistemic Logic (Extended Abstract)

Meyden

Patra

2016

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

We investigate the decidability of model-checking logics of time, knowledge and probability, with respect to two epistemic semantics: the clock and synchronous perfect recall semantics in partially observed discrete-time Markov chains. Decidability results are known for certain restricted logics with respect to these semantics, subject to a variety of restrictions that are either unexplained or involve a longstanding unsolved mathematical problem. We show that mild generalizations of the known decidable cases suffice to render the model checking problem definitively undecidable. In particular, for a synchronous perfect recall, a generalization from temporal operators with finite reach to operators with infinite reach renders model checking undecidable. The case of the clock semantics is closely related to a monadic second order logic of time and probability that is known to be decidable, except on a set of measure zero. We show that two distinct extensions of this logic make model checking undecidable. One of these involves polynomial combinations of probability terms, the other involves monadic second order quantification into the scope of probability operators. These results explain some of the restrictions in previous work.

show abstract

MDPs as Distribution Transformers: Affine Invariant Synthesis for Safety Objectives

Chatterjee

Meggendorfer

et al. 2023

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Markov decision processes can be viewed as transformers of probability distributions. While this view is useful from a practical standpoint to reason about trajectories of distributions, basic reachability and safety problems are known to be computationally intractable (i.e., Skolem-hard) to solve in such models. Further, we show that even for simple examples of MDPs, strategies for safety objectives over distributions can require infinite memory and randomization.In light of this, we present a novel overapproximation approach to synthesize strategies in an MDP, such that a safety objective over the distributions is met. More precisely, we develop a new framework for template-based synthesis of certificates as affine distributional and inductive invariants for safety objectives in MDPs. We provide two algorithms within this framework. One can only synthesize memoryless strategies, but has relative completeness guarantees, while the other can synthesize general strategies. The runtime complexity of both algorithms is in PSPACE. We implement these algorithms and show that they can solve several non-trivial examples.

show abstract

A Logic of Probability with Decidable Model Checking

Cited by 15 publications

References 12 publications

Reasoning about MDPs as Transformers of Probability Distributions

Reasoning about MDPs as Transformers of Probability Distributions

Undecidable Cases of Model Checking Probabilistic Temporal-Epistemic Logic (Extended Abstract)

MDPs as Distribution Transformers: Affine Invariant Synthesis for Safety Objectives

Contact Info

Product

Resources

About