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The timed position of documents retrieved by learning to rank models can be seen as signals. Signals carry useful information such as drop or rise of documents over time or user behaviors. In this work, we propose to use the logic formalism called Signal Temporal Logic (STL) to characterize document behaviors in ranking accordingly to the specified formulas. Our analysis shows that interesting document behaviors can be easily formalized and detected thanks to STL formulas. We validate our idea on a dataset of 100K product signals. Through the presented framework, we uncover interesting patterns, such as cold start, warm start, spikes, and inspect how they affect our learning to ranks models.
We propose a measure and a metric on the sets of infinite traces generated by a set of atomic propositions. To compute these quantities, we first map properties to subsets of the real numbers and then take the Lebesgue measure of the resulting sets.
Linear temporal logic was introduced in order to reason about reactive systems. It is often considered with respect to infinite words, to specify the behaviour of long-running systems. One can consider more general models for linear time, using words
The deployment of autonomous systems in uncertain and dynamic environments has raised fundamental questions. Addressing these is pivotal to build fully autonomous systems and requires a systematic integration of planning and control. We first propose
In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical theorem stating that every formula of Past LTL (the extension of LTL with past operators) is equivalent to a formula of the form $bigwedge_{i=1}^n mathbf{G}mathbf{F} varphi_i vee mathb
One of the advantages of adopting a Model Based Development (MBD) process is that it enables testing and verification at early stages of development. However, it is often desirable to not only verify/falsify certain formal system specifications, but