A syllogistic system for propositions with intermediate quantifiers
Pasquale Iero, Allan Third, Paul Piwek
TL;DR
This paper introduces an extended syllogistic formalism that incorporates intermediate quantifiers, negation, and Monotonicity Calculus to enhance logical deduction capabilities.
Contribution
It extends Peterson's intermediate quantifier syllogistic system by integrating negation and Monotonicity Calculus, providing a more expressive logical framework.
Findings
Formalism subsumes Peterson's system
Includes contradictory and contrary relationships
Enables deduction of negated propositions
Abstract
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.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Logic, programming, and type systems · Advanced Algebra and Logic