An Integrated First-Order Theory of Points and Intervals over Linear Orders (Part II)

There are two natural and well-studied approaches to temporal ontology and reasoning: point-based and interval-based. Usually, interval-based temporal reasoning deals with points as a particular case of duration-less intervals. A recent result by Balbiani, Goranko, and Sciavicco presented an explicit two-sorted point-interval temporal framework in which time instants (points) and time periods (intervals) are considered on a par, allowing the perspective to shift between these within the formal discourse. We consider here two-sorted first-order languages based on the same principle, and therefore including relations, as first studied by Reich, among others, between points, between intervals, and inter-sort. We give complete classifications of its sub-languages in terms of relative expressive power, thus determining how many, and which, are the intrinsically different extensions of two-sorted first-order logic with one or more such relations. This approach roots out the classical problem of whether or not points should be included in a interval-based semantics. In this Part II, we deal with the cases of all dense and the case of all unbounded linearly ordered sets.Comment: This is Part II of the paper `An Integrated First-Order Theory of Points and Intervals over Linear Orders' arXiv:1805.08425v2. Therefore the introduction, preliminaries and conclusions of the two papers are the same. This version implements a few minor corrections and an update to the affiliation of the second autho

A Logical Method for Policy Enforcement over Evolving Audit Logs

We present an iterative algorithm for enforcing policies represented in a first-order logic, which can, in particular, express all transmission-related clauses in the HIPAA Privacy Rule. The logic has three features that raise challenges for enforcement --- uninterpreted predicates (used to model subjective concepts in privacy policies), real-time temporal properties, and quantification over infinite domains (such as the set of messages containing personal information). The algorithm operates over audit logs that are inherently incomplete and evolve over time. In each iteration, the algorithm provably checks as much of the policy as possible over the current log and outputs a residual policy that can only be checked when the log is extended with additional information. We prove correctness and termination properties of the algorithm. While these results are developed in a general form, accounting for many different sources of incompleteness in audit logs, we also prove that for the special case of logs that maintain a complete record of all relevant actions, the algorithm effectively enforces all safety and co-safety properties. The algorithm can significantly help automate enforcement of policies derived from the HIPAA Privacy Rule.Comment: Carnegie Mellon University CyLab Technical Report. 51 page

A Theory of Sampling for Continuous-time Metric Temporal Logic

This paper revisits the classical notion of sampling in the setting of real-time temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over continuous-time models and over discrete-time models is studied. It is shown to what extent discrete-time sequences obtained by sampling continuous-time signals capture the semantics of MTL formulas over the two time domains. The main results apply to "flat" formulas that do not nest temporal operators and can be applied to the problem of reducing the verification problem for MTL over continuous-time models to the same problem over discrete-time, resulting in an automated partial practically-efficient discretization technique.Comment: Revised version, 43 pages

An Integrated First-Order Theory of Points and Intervals over Linear Orders (Part I)

There are two natural and well-studied approaches to temporal ontology and reasoning: point-based and interval-based. Usually, interval-based temporal reasoning deals with points as a particular case of duration-less intervals. A recent result by Balbiani, Goranko, and Sciavicco presented an explicit two-sorted point-interval temporal framework in which time instants (points) and time periods (intervals) are considered on a par, allowing the perspective to shift between these within the formal discourse. We consider here two-sorted first-order languages based on the same principle, and therefore including relations, as first studied by Reich, among others, between points, between intervals, and inter-sort. We give complete classifications of its sub-languages in terms of relative expressive power, thus determining how many, and which, are the intrinsically different extensions of two-sorted first-order logic with one or more such relations. This approach roots out the classical problem of whether or not points should be included in a interval-based semantics

Integrated Modeling and Verification of Real-Time Systems through Multiple Paradigms

Complex systems typically have many different parts and facets, with different characteristics. In a multi-paradigm approach to modeling, formalisms with different natures are used in combination to describe complementary parts and aspects of the system. This can have a beneficial impact on the modeling activity, as different paradigms an be better suited to describe different aspects of the system. While each paradigm provides a different view on the many facets of the system, it is of paramount importance that a coherent comprehensive model emerges from the combination of the various partial descriptions. In this paper we present a technique to model different aspects of the same system with different formalisms, while keeping the various models tightly integrated with one another. In addition, our approach leverages the flexibility provided by a bounded satisfiability checker to encode the verification problem of the integrated model in the propositional satisfiability (SAT) problem; this allows users to carry out formal verification activities both on the whole model and on parts thereof. The effectiveness of the approach is illustrated through the example of a monitoring system.Comment: 27 page

Completeness, robustness, and safety in real-time software requirements specification

This paper presents an approach to providing a rigorous basis for ascertaining whether or not a given set of software requirements is internally complete, i.e., closed with respect to questions and inferences that can be made on the basis of information included in the specification. Emphasis is placed on aspects of software requirements specifications that previously have not been adequately handled, including timing abstractions, safety, and robustness

Putting time into proof outlines

A logic for reasoning about timing of concurrent programs is presented. The logic is based on proof outlines and can handle maximal parallelism as well as resource-constrained execution environments. The correctness proof for a mutual exclusion protocol that uses execution timings in a subtle way illustrates the logic in action

Method for Detecting Anomalous States of a Control Object in Information Systems Based on the Analysis of Temporal Data and Knowledge

The problem of finding the anomalous states of the control object in the management information system under conditions of uncertainty caused by the incompleteness of knowledge about this object is considered. The method of classifying the current state of the control object in real time, allowing to identify the current anomalous state. The method uses temporal data and knowledge. Data is represented by sequences of events with timestamps. Knowledge is represented as weighted temporal rules and constraints. The method includes the following key phases: the formation of sequences of logical facts; selection of temporal rules and constraints; classification based on a comparison of rules and constraints. Logical facts are represented as predicates on event attributes and reflect the state of the control object. Logical rules define valid sequences of logical facts. Performing a classification by successive comparisons of constraints and weights of the rules makes it possible to more effectively identify the anomalous state since the comparison of the constraints reduces the subset of facts comparing to the current state. The method creates conditions for improving management efficiency in the context of incomplete information on the state of a complex object by using logical inference in knowledge bases for anomalous states of such control objects