Metric Temporal Logic (MTL) is a widely-studied real-time extension of Linear Temporal Logic. In this paper we consider a fragment of MTL, called Safety MTL, capable of expressing properties such as invariance and time-bounded response. Our main result is that the satisfiability problem for Safety MTL is decidable. This is the first positive decidability result for MTL over timed ω-words that d...

A seminal result of Kamp is that over the reals Linear Temporal Logic (LTL) has the same expressive power as first-order logic with binary order relation < and monadic predicates. A key question is whether there exists an analogue of Kamp’s theorem for Metric Temporal Logic (MTL) – a generalization of LTL in which the Until and Since modalities are annotated with intervals that express metric c...

In ontology-based systems that process data stemming from different sources and that is received over time, as in context-aware systems, reasoning needs to cope with the temporal dimension and should be resilient against inconsistencies in the data. Motivated by such settings, this paper addresses the problem of handling inconsistent data in a temporal version of ontology-based query answering....

We prove that model-checking and satisfiability problems for propositional Linear-time Temporal Logic with a single variable are PSPACE-complete.

The specification of a database system consists of the description of its static information structure as well as of its dynamic behaviour. Whereas in classic conceptual database design the main interest was on the static part, specification of database dynamics became an important topic in the last few years. The specification of dynamic database behaviour has to describe the correct evolution...

We show how the ntcc calculus, a model of temporal concurrent constraint programming with the capability of modeling asynchronous and non-deterministic timed behavior, can be used for modeling real musical processes. We use the nondeterminism facility of ntcc to build weaker representations of musical processes that greatly simplifies the formal expression and analysis of its properties. We arg...

Recent logic calculi open new possibilities for logic programming. Apparently the most important of them is a linear logic which makes possible to solve problems by resources treatment. The linear logic has already been used for several proposals of logic programming language. But authors of these languages mostly focused on the proposal of language and somewhat turned aside its efficient imple...

In this paper we consider two logics: temporal logic of common knowledge and temporal logic of common belief. These logics involve the discrete time linear temporal logic operators “next” and “until”. In addition the first logic contains an indexed set of unary modal operators “agent i knows”, the second one contains an indexed set of unary modal operators “agent i believes”. Also the first log...

Given modal logics 1, 2, their lexicographic product 1 ⇤ 2 is a new logic whose frames are the Cartesian products of a 1-frame and a 2-frame, but with the new accessibility relations reminiscent of a lexicographic ordering. This article considers the lexicographic products of several modal logics with linear temporal logic (LTL) based on “next” and “always in the future”. We provide axiomatizat...

Model checking as an approach to the automatic veri cation of nite state systems has focussed predominantly on system speci cations expressed in temporal logic. In the distributed systems community, logics of knowledge (epistemic logics) have been advocated for expressing desirable properties of protocols and systems. A range of logics combining temporal and epistemic components have been devel...