Modal paraconsistent tableau systems of logic

The aim of this paper is to show how to simply define paraconsistent tableaus by liberalization of construction of complete tableaus. The presented notions allow us to list all tableau inconsistencies that appear in a complete tableau. Then we can easily choose these inconsistencies that are effects of interactions between premises and a conclusion, simultaneously excluding other inconsistencies. A general technique we describe is presented here for the case of modal logic, as one of the most interesting, and with many applications in communication theory and data mining. In case we have an inconsistent set of information and apply a logic that includes classically accepted patterns of reasoning, we may correctly conclude any arbitrary proposition. To avoid this we propose paraconsistent tableau proofs that list all relevant premises which guarantee truth of conclusion under consideration, but at the same time are consistent. Key–Words: blind rule, modal logic, paraconsistent tableaus, t-inconsistency, tableau rules, tableaus Typing manuscripts, LATEX