Considerations on the Complexity of Visual Reasoning with Sentences and Diagrams

Abstract

Deduction by a computer studied so far has been centered around symbolic reasoning with formulas. Recently, attention has been directed to reasoning with diagrams as well, in order to augment the deficiency of reasoning with symbols only. In this paper, we consider the deductive reasoning method with diagrams (Venn diagram) and its proof complexity. For this, we examined the three aspects of differences between symbolic reasoning and diagrammatic reasoning: proof complexity and proof similarity, by proving the validity of a variety of Aristotelian syllogisms both symbolically and diagrammatically. The results we have found include that the proof steps by Venn diagram are much shorter than those by natural deduction, and there are eight different diagrammatic proofs and only two different diagrammatic proof patterns for fifteen valid Aristotelian syllogisms.