The R.I. Economic Development Corp. has given four state businesses $1.75 million in new expansion capital loans from its Small Business Loan Fund. Linear Title & Closing Ltd. - a Middletown title agency, abstracting company and settlement solution provider - received a $250,000 loan. LogicBay Inc. of Newport, which moved here from Cleveland in 2005, received a $250,000 loan. CleanBrands LLC received a $500,000 loan. The fourth recipient is InQuest Technologies Inc., which in September will be moving its headquarters to Providence from Southborough, Mass. (InQuest received a $750,000 loan to help fund its expansion as it increases its workforce from about 20 to 50.