{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T09:22:31Z","timestamp":1725441751240},"reference-count":0,"publisher":"EasyChair","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>(This is joint work with Nick Bezhanishvili).<\/jats:p><jats:p>In the first part of our contribution, we review and compare existing constructions of finitely generated free algebras in modal logic focusing on step-by-step methods. We discuss the notions of step algebras and step frames arising from recent investigations, as well as the role played by finite duality.<\/jats:p><jats:p>In the second part of the contribution, we exploit the potential of step frames for investigating proof-theoretic aspects. This includes developing a method which detects when a specific rule-based calculus Ax axiomatizing a given logic L has the so-called bounded proof property. This property is a kind of an analytic subformula property limiting the proof search space. We prove that every finite conservative  step frame for Ax is a p-morphic image of a finite Kripke frame for L iff Ax has the bounded proof property and L has  the finite model property. This result, combined with a  `step version' of the classical correspondence theory turns out to be quite powerful in applications.<\/jats:p>","DOI":"10.29007\/md5x","type":"proceedings-article","created":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T22:59:06Z","timestamp":1516748346000},"page":"5-3","source":"Crossref","is-referenced-by-count":0,"title":["From free algebras to proof bounds"],"prefix":"10.29007","volume":"25","author":[{"given":"Silvio","family":"Ghilardi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"11545","event":{"name":"TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic"},"container-title":["EPiC Series in Computing"],"original-title":[],"deposited":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T23:01:15Z","timestamp":1516748475000},"score":1,"resource":{"primary":{"URL":"https:\/\/easychair.org\/publications\/paper\/cDvQ"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"references-count":0,"URL":"https:\/\/doi.org\/10.29007\/md5x","relation":{},"ISSN":["2398-7340"],"issn-type":[{"type":"print","value":"2398-7340"}],"subject":[]}}