In this paper, we focus our attention on the interval temporal logic of the Allen’s relations “meets”, “begins”, and “begun by” (ABB for short), interpreted over natural numbers. We first introduce the logic and we show that it is expressive enough to model distinctive interval properties, such as accomplishment conditions, to capture basic modalities of point-based temporal logic, such as the ...

This paper presents simulation-based relations for probabilistic game structures. The first relation is called probabilistic alternating simulation, and the second called probabilistic alternating forward simulation, following the naming convention of Segala and Lynch. We study these relations with respect to the preservation of properties specified in probabilistic alternating-time temporal lo...

In this paper, we focus our attention on the interval temporal logic of the Allen’s relations “meets”, “begins”, and “begun by” (ABB for short), interpreted over natural numbers. We first introduce the logic and we show that it is expressive enough to model distinctive interval properties, such as accomplishment conditions, to capture basic modalities of point-based temporal logic, such as the ...

The complexity of LTrL, a global linear time temporal logic over traces is investigated. The logic is global because the truth of a formula is evaluated in a global state, also called connguration. The logic is shown to be non-elementary with the main reason for this complexity being the nesting of until operators in formulas. The fragment of the logic without the until operator is shown to be ...

Propositional temporal logic is now well established, both in its theory and its utility for practical applications in computing. In contrast, predicate, or first-order, temporal logic has been less studied. Unpublished results of Lindström and Scott in the 1960s showed that even weak fragments of first-order temporal logic are highly undecidable, and these and later similar results (see, e.g.,...

Temporal logic based on the two modalities “Since” and “Until” (TL) is the most popular logic for the specification of reactive systems. It is often called the linear time temporal logic. However, metric properties of real time cannot be expressed in this logic. The simplest modalities with metric properties are “X will happen within units of time”. The extension of TL by all these modalities w...

Temporal logics of knowledge are useful in order to specify complex systems in which agents are both dynamic and have information about their surroundings. We present a resolution method for propositional temporal logic combined with multi-modal S5 and illustrate its use on examples. This paper corrects a previous proposal for resolution in multi-modal temporal logics of knowledge.

Interval temporal logics provide a natural framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities. The most influential propositional interval-based logic is probably Halpern and Shoham’s Modal Logic of Time Intervals, a.k.a. HS. While most studies focused on the computational properties of the sy...