A Multi-Valued Simplified Halpern–Shoham–Moszkowski Logic for Gradable Verifiability in Reasoning about Digital Circuits

In 1983, B. Moszkowski introduced a first interval-interpreted temporal logic system, the so-called Interval Temporal Logic (ITL), as a system suitable to express mutual relations inside intervals for reasonings about digital circuits. In 1991, Halpern and Shoham proposed a new temporal system (HS) to describe external relations between intervals. This paper is aimed at proposing a basis-type combination of HS and a simplified ITL end extends it towards a multi-valued system—also capable of rendering a gradable justification of agents in a similar contexts of reasoning about digital circuits. This newly introduced system is semantically interpreted in the so-called fibred semantics.

An Interval Temporal Logic for Time Series Specification and Data Integration

The analysis of temporal series—in particular, analysis of multisensor data—is a complex problem. It depends on the application domain, the way the data have to be used, and sensors available, among other factors. Various models, algorithms, and technologies have been designed for this goal. Temporal logics are used to describe temporal properties of systems. The properties may specify the occurrence and the order of events in time, recurring patterns, complex behaviors, and processes. In this paper, a new interval logic, called duration calculus for functions (DC4F), is proposed for the specification of temporal series corresponding to multisensor data. DC4F is a natural extension of the well-known duration calculus, an interval temporal logic for the specification of process duration. The adequacy of the proposed logic is analyzed in the case of multisensor data concerning volcanic eruption monitoring. It turns out that the relevant behavior concerns time intervals, not only accumulated history as it is described in other kinds of temporal logics. The examples analyzed demonstrate that a description language is required to specify time series of various kind relative to time intervals. The duration calculus cannot be successfully applied for this task. The proposed calculus allows one to specify temporal series and complex interval-dependent behaviors, and to evaluate the corresponding data within a unifying logical framework. It allows to formulate hypotheses concerning volcano eruption phenomena. However, the expressivity of DC4F comes at the cost of its decidability.

Ultimately-periodic Interval Model Checking for Temporal Dataset Evaluation

Temporal dataset evaluation is the problem of establishing to what extent a set of temporal data (histories) complies with a given temporal condition. Checking interval temporal logic formulas against a finite model has been recently proposed, and proved successful, as a tool to solve such a problem. In this paper, we address the problem of checking interval temporal logic specifications, supporting interval length constraints, against infinite, finitely representable models, and we show the applicability of the resulting procedure to the evaluation of incomplete temporal datasets viewed as finite prefixes of ultimately-periodic histories.