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Using such supports, we formulate proof rules that facilitate frame reasoning elegantly when the underlying model undergoes change. We show that the logic is expressive by capturing several data-structures and also exhibit a translation from a <jats:italic>precise<\/jats:italic> fragment of separation logic to frame logic. Finally, we design a program logic based on frame logic for reasoning with programs that dynamically update heaps that facilitates local specifications and frame reasoning. This program logic consists of both localized proof rules as well as rules that derive the weakest tightest preconditions in FL.<\/jats:p>","DOI":"10.1007\/978-3-030-44914-8_19","type":"book-chapter","created":{"date-parts":[[2020,4,17]],"date-time":"2020-04-17T10:02:53Z","timestamp":1587117773000},"page":"515-543","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A First-Order Logic with Frames"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6311-1467","authenticated-orcid":false,"given":"Adithya","family":"Murali","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lucas","family":"Pe\u00f1a","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christof","family":"L\u00f6ding","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9782-721X","authenticated-orcid":false,"given":"P.","family":"Madhusudan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,4,18]]},"reference":[{"key":"19_CR1","doi-asserted-by":"crossref","unstructured":"Banerjee, A., Naumann, D.: Local reasoning for global invariants, Part II: Dynamic boundaries. 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