The Rhode Island Economic Development Corporation has approved four requests for tax credits designed to help start-ups attract investment. The four companies — Lighthouse Security Group, Ocean State Solutions, Providence Health Solutions and Public Display — had received preliminary approval at an EDC board meeting in November. They were among six companies to receive an Innovation Tax Credit good for up to $100,000 off the individual state income-tax bill of any investor. Lighthouse received $50,000 in tax credits; Ocean State got $5,000, Providence Health collected $75,000, and Public Display received $100,000, according to Andrew S. Cutler, an EDC spokesman. The program reimburses investors for 50 percent of their investments, so that means these four companies raised double those amounts, Cutler said.