We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric structures. To represent both aspect of uncertainty, we choose an expected distance function as a measure of uncertainty. A formal logical system is constructed for the reasoning about expected distance. Soundness and completeness are shown f...

We consider variants of Metric Temporal Logic (MTL) with the past operators S and SI . We show that these operators can be “eliminated” in the sense that for any formula in these logics containing the S and SI modalities, we can give a formula over an extended set of propositions which does not contain these past operators, and which is equivalent to the original formula modulo a projection ont...

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...

Answer Set Programming has separately been extended with constraints, to the streaming domain, and capabilities reason over quantities associated answer sets. We propose introduction analysis of a general framework that incorporates all three directions extension by exploiting strengths Here-and-There Logic Weighted Logic.

We introduce new classes of weighted automata on words. Equipped with pebbles, they go beyond the class of recognizable formal power series: they capture weighted first-order logic enriched with a quantitative version of transitive closure. In contrast to previous work, this calculus allows for unrestricted use of existential and universal quantifications over positions of the input word. We ac...

This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex time-sensitive tasks in presence an adversary. The task is specified as a formula metric interval temporal logic (MITL). CPSs operate adversarial environments have typically been abstracted stochastic games (SGs); however, because traditional SG models do not incorporate noti...