Interval-based temporal logics are natural frameworks for modeling a number of problems from various areas of computer science such as artificial intelligence, natural language processing, temporal databases and formal specification. Quite a few interval-based temporal logics became popular in recent years, such as Venema?s CDT logic, Halpern and Shoham?s HS logic, Moszkowski?s ITL and its propositional version, and Goranko, Montanari, and Sciavicco?s PNL. In this work we introduce a new propositional interval-based temporal logic called CW, which can be considered an extension of the propositional fragment of Moszkowski?s ITL evaluated over different (parallel) lines, and which is particularly adapt for expressing natural language sentences. We study the logic CW and develop a (non-terminating) sound and complete deduction system based on tableaux for it.