Equational logic as a tool

Abstract

Software tools and methods that approach being formal are not readily used by programmers, software engineers, and even most computer scientists. (There are avid users of mechanical verifiers and proof checkers, but they are a small the minority.) One reason for this is that the foundation of many formalisms —propositional and predicate logic— has been viewed and taught more as an object of study than as a useful tool.We believe that formal logic can a useful mental tool. In fact, logic is the glue that binds together methods of reasoning, in all domains. Further, logic can be taught in a way that imparts appreciation for logic and rigorous proof, as well as some skill in formal manipulation. This is most easily done using an equational logic —a logic based on substitution of equals for equals and the kinds of manipulations people in scientific disciplines already perform. We outline this logic, explain its pedagogical advantages, and discuss teaching it.KeywordsInference RuleDiscrete MathPredicate LogicNatural DeductionPigeonhole PrincipleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.