Inference rules and decision rules

Abstract

Basic rules of inference used in classical logic are Modus Ponens (MP) and Modus Tollens (MT). These two reasoning patterns start from some general knowledge about reality, expressed by true implication, " if φ then ψ". Then basing on true premise φ we arrive at true conclusion ψ (MP), or from negation of true conclusion ψ we get negation of true premise φ (MT). In reasoning from data (data mining) we also use rules " if φ then ψ", called decision rules, to express our knowledge about reality, but in this case the meaning of the expression is different. It does not express general knowledge but refers to partial facts. Therefore decision rules are not true or false but probable (possible) only. In this paper we compare inference rules and decision rules in the context of decision networks, proposed by the author as a new approach to analyze reasoning patterns in data.