{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T14:01:50Z","timestamp":1725544910276},"reference-count":0,"publisher":"EasyChair","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We show how to implement an effective decision procedure to check if a propositional Basic Logic formula is a tautology. For a formula with $n$ variables, the procedure consists of a translation, depending on $n$, from Basic Logic to the language of Satisfiability Modulo Theories SMT-LIB2 using the theory of quantifier free linear real arithmetic. Many efficient SMT-solvers exist to decide formulas in the SMT-LIB2 language. We also study finitely generated varieties of Basic Logic (BL-)algebras and give a description of the lattice of these varieties. Extensions to finitely generated varieties of Generalized BL-algebras are discussed, and a simple connection between finite GBL-algebras and finite closure algebras is noted.<\/jats:p>","DOI":"10.29007\/nptc","type":"proceedings-article","created":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T17:59:06Z","timestamp":1516730346000},"page":"113-105","source":"Crossref","is-referenced-by-count":0,"title":["Basic Logic, SMT solvers and finitely generated varieties of GBL-algebras"],"prefix":"10.29007","volume":"25","author":[{"given":"Peter","family":"Jipsen","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":"2018-01-23T18:01:18Z","timestamp":1516730478000},"score":1,"resource":{"primary":{"URL":"https:\/\/easychair.org\/publications\/paper\/dxv"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"references-count":0,"URL":"https:\/\/doi.org\/10.29007\/nptc","relation":{},"ISSN":["2398-7340"],"issn-type":[{"type":"print","value":"2398-7340"}],"subject":[]}}