abstract
in this paper, we deal with a calculus system slcd (syllogistic logic with
carroll diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental aristotelian categorical propositions and show that they are closed under the syllogistic criterion of inference
which is the deletion of middle term. therefore, it is implemented to let the
formalism comprise synchronically bilateral and trilateral diagrammatical appearance and a naive algorithmic nature. and also, there is no need specific
knowledge or exclusive ability to understand as well as to use it. consequently,
we give an effective algorithm used to determine whether a syllogistic reasoning
valid or not by using slcd.
keywords: categorical syllogism, validity, algorithm
2010 msc: 68q60, 03b70, 68t27