Using Probability to Reason about Soft Deadlines

Soft deadlines are significant in systems in which a bound on the response time is important, but the failure to meet the response time is not a disaster. Soft deadlines occur, for example, in telephony and switching networks. We investigate how to put probabilistic bounds on the time-complexity of a concurrent logic program by combining (on-line) profiling with an (off-line) probabilistic complexity analysis. The profiling collects information on the likelihood of case selection and the analysis uses this information to infer the probability of an agent terminating within k steps. Although the approach does not reason about synchronization, we believe that its simplicity and good (essentially quadratic) complexity mean that it is a promising first step in reasoning about soft deadlines

Learning and Designing Stochastic Processes from Logical Constraints

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics must be known exactly. As this is seldom the case, many methods have been devised over the last decade to infer (learn) such parameters from observations of the state of the system. In this paper, we depart from this approach by assuming that our observations are {\it qualitative} properties encoded as satisfaction of linear temporal logic formulae, as opposed to quantitative observations of the state of the system. An important feature of this approach is that it unifies naturally the system identification and the system design problems, where the properties, instead of observations, represent requirements to be satisfied. We develop a principled statistical estimation procedure based on maximising the likelihood of the system's parameters, using recent ideas from statistical machine learning. We demonstrate the efficacy and broad applicability of our method on a range of simple but non-trivial examples, including rumour spreading in social networks and hybrid models of gene regulation

Utilizing stochastic model checking to analyze genetic circuits

pre-printWhen designing and analyzing genetic circuits, researchers are often interested in the probability of the system reaching a given state within a certain amount of time. Usually, this involves simulating the system to produce some time series data and analyzing this data to discern the state probabilities. However, as the complexity of models of genetic circuits grow, it becomes more difficult for researchers to reason about the different states by looking only at time series simulation results of the models. To address this problem, this paper employs the use of stochastic model checking, a method for determining the likelihood that certain events occur in a system, with continuous stochastic logic (CSL) properties to obtain similar results. This goal is accomplished by the introduction of a methodology for converting a genetic circuit model (GCM) into a continuous-time Markov chain (CTMC). This CTMC is analyzed using transient Markov chain analysis to determine the likelihood that the circuit satisfies a given CSL property in a finite amount of time. This paper illustrates a use of this methodology to determine the likelihood of failure in a genetic toggle switch and compares these results to stochastic simulation-based analysis of this same circuit. Our results show that this method results in a substantial speedup as compared with conventional simulation-based approaches

A probabilistic analysis of argument cogency

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align

A logic for reasoning about upper probabilities

We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is NP-complete, no harder than satisfiability for propositional logic.Comment: A preliminary version of this paper appeared in Proc. of the 17th Conference on Uncertainty in AI, 200

Leibniz and Probability in the Moral Domain

Leibniz’s account of probability has come into better focus over the past decades. However, less attention has been paid to a certain domain of application of that account, that is, the application of it to the moral or ethical domain—the sphere of action, choice and practice. This is significant, as Leibniz had some things to say about applying probability theory to the moral domain, and thought the matter quite relevant. Leibniz’s work in this area is conducted at a high level of abstraction. It establishes a proof of concept, rather than concrete guidelines for how to apply calculations to specific cases. Still, this highly abstract material does allow us to begin to construct a framework for thinking about Leibniz’s approach to the ethical side of probability

The Problem of Measure Sensitivity Redux

Fitelson (1999) demonstrates that the validity of various arguments within Bayesian confirmation theory depends on which confirmation measure is adopted. The present paper adds to the results set out in Fitelson (1999), expanding on them in two principal respects. First, it considers more confirmation measures. Second, it shows that there are important arguments within Bayesian confirmation theory and that there is no confirmation measure that renders them all valid. Finally, the paper reviews the ramifications that this "strengthened problem of measure sensitivity" has for Bayesian confirmation theory and discusses whether it points at pluralism about notions of confirmation