Allen Linear (Interval) Temporal Logic - Translation to LTL and Monitor Synthesis

The relationship between two well established formalisms for temporal reasoning is first investigated, namely between Allen's interval algebra (or Allen's temporal logic, abbreviated ATL) and linear temporal logic (LTL). A discrete variant of ATL is defined, called Allen linear temporal logic (ALTL), whose models are -sequences of timepoints, like in LTL. It is shown that any ALTL formula can be linearly translated into an equivalent LTL formula, thus enabling the use of LTL techniques and tools when requirements are expressed in ALTL. Then the monitoring problem for ALTL is discussed, showing that it is NP-complete despite the fact that the similar problem for LTL is EXPSPACE-complete. An effective monitoring algorithm for ALTL is given, which has been implemented and experimented with in the context of planning applications.

• Type: Conference
• Year: 2006
• Where: CAV
• Authors: Grigore Rosu, Saddek Bensalem
• Keywords: Allen's Temporal Logic, CAV 2006, Hardware, Linear Temporal Logic, Temporal Logic