We introduce a family of logics and associated programming languages for representing and reasoning about time. The family is conceptually simple while allowing for different models of time. Formulas can be labeled with temporal information using annotations. In this way we avoid the proliferation of variables and quantifiers as encountered in first order approaches. Unlike temporal logic, both...

We present regular linear temporal logic (RLTL), a logic that generalizes linear temporal logic with the ability to use regular expressions arbitrarily as sub-expressions. Every LTL operator can be defined as a context in regular linear temporal logic. This implies that there is a (linear) translation from LTL to RLTL. Unlike LTL, regular linear temporal logic can define all ω-regular languages...

This paper presents a structured, annotated bibliography of extensions of logic programming based on temporal and modal logics. Temporal and modal logic programming is a new area of research, which gained momentum in the late 1980'ies. The paper discusses temporal and modal logic programming under three headings: (1) interval logic programming , (2) temporal logic programming, and (3) modal log...

This paper studies the relation between two recent extensions of propositional Equilibrium Logic, a well-known logical characterisation of Answer Set Programming. In particular, we show how Temporal Equilibrium Logic, which introduces modal operators as those typically handled in Linear-Time Temporal Logic (LTL), can be encoded into Infinitary Equilibrium Logic, a recent formalisation that allo...

We add to the standard temporal logic with the modalities ”Until” and ”Since”, a sequence of “counting modalities”: For each n the modality Cn(X), which says that X will be true at least at n points in the next unit of time, and its past counterpart ←− C n, which says that X has happened at least n times in the last unit of time. We prove that this temporal logic is as expressive as can be hope...

The struggle to delineate the relationship between theology and logic flourished in the thirteenth century and culminated in two condemnations in early 1277, one in Paris and the other in Oxford. To see how much and what kind of affect ecclessiastical actions such as condemnations and prohibitions to teach had on the development of logic in the Middle Ages, we investigate the events leading up ...

In contrast to qualitative linear temporal logics, which can be used to state that some property will eventually be satisfied, metric temporal logics allow to formulate constraints on how long it may take until the property is satisfied. While most of the work on combining Description Logics (DLs) with temporal logics has concentrated on qualitative temporal logics, there has recently been a gr...

By explicitly identifying the temporal aspect of a default rule as it is used in a reasoning process, it is argued that a natural semantic theory of Reiter's default logic is a temporal one. To be able to accommodate the lack of complete knowledge at any point in time, the temporal models should be partial models. A temporal partial logic is introduced, and it is shown that this logic can provi...

We review some results on global and local temporal logic on Mazurkiewicz traces. Our main contribution is to show how to derive the expressive completeness of global temporal logic with respect to first order logic [9] from the similar result on local temporal logic [11].

We provide semantics for the powerful scenario-based language of live sequence charts (LSCs). We show how the semantics of live sequence charts can be captured using temporal logic. This is done by studying various subsets of the LSC language and providing an explicit translation into temporal logic. We show how a kernel subset of the LSC language (which omits variables, for example) can be emb...