A syllogistic system for propositions with intermediate quantifiers
This work addresses a niche problem in formal logic for researchers in logic and AI, but it appears incremental as it builds directly on prior systems without broad application claims.
The paper tackles the problem of formalizing syllogistic reasoning with intermediate quantifiers by extending existing systems like Peterson's and van Eijck's work, resulting in a concise formalism that incorporates contradictory and contrary relationships for deduction with negation.
This paper describes a formalism that subsumes Peterson's intermediate quantifier syllogistic system, and extends the ideas by van Eijck on Aristotle's logic. Syllogisms are expressed in a concise form making use of and extending the Monotonicity Calculus. Contradictory and contrary relationships are added so that deduction can derive propositions expressing a form of negation.