Little Tricky Logic: Misconceptions in the Understanding of LTL

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2023-11-21 06:00:04

AbstractContext Linear Temporal Logic (LTL) has been used widely in verification. Its importance and popularity have only grown with the revival of temporal logic synthesis, and with new uses of LTL in robotics and planning activities. All these uses demand that the user have a clear understanding of what an LTL specification means.

Inquiry Despite the growing use of LTL, no studies have investigated the misconceptions users actually have in understanding LTL formulas. This paper addresses the gap with a first study of LTL misconceptions.

Approach We study researchers’ and learners’ understanding of LTL in four rounds (three written surveys, one talk-aloud) spread across a two-year timeframe. Concretely, we decompose ‘‘understanding LTL’’ into three questions. A person reading a spec needs to understand what it is saying, so we study the mapping from LTL to English. A person writing a spec needs to go in the other direction, so we study English to LTL. However, misconceptions could arise from two sources: a misunderstanding of LTL’s syntax or of its underlying semantics. Therefore, we also study the relationship between formulas and specific traces.

Knowledge We find several misconceptions that have consequences for learners, tool builders, and designers of new property languages. These findings are already resulting in changes to the Alloy modeling language. We also find that the English to LTL direction was the most common source of errors; unfortunately, this is the critical ‘‘authoring’’ direction in which a subtle mistake can lead to a faulty system. We contribute study instruments that are useful for training learners (whether academic or industrial) who are getting acquainted with LTL, and we provide a code book to assist in the analysis of responses to similar-style questions.

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