Niki Pfeifer Contemporary syllogistics.pdf

Niki Pfeifer Contemporary syllogistics Comparative and quantitative syllogisms Abstract: Traditionally, syllogisms are arguments with two premises and one conclu- sion which are constructed by propositions of the form “All… are…” and “At least one… is…” and their respective negated versions. Unfortunately, the practical use of traditional syllogisms is quite restricted. On the one hand, the “All…” propositions are too strict, since a single counterexample suffices for falsification. On the other hand, the “At least one …” propositions are too weak, since a single example suffices for verification. The present contribution studies algebraic interpretations of syllogisms with comparative quantifiers (e.g., “Most… are…”) and quantitative quantifiers (e.g., “n/m… are…”, “all, except n… are…”). This modern version of syllogistics is intended to be a more adequate framework for argumentation theory than traditional syllogistics. Keywords: Syllogisms, comparative and quantitative quantifiers, exceptions, rational argumentation. Author: Pfeifer, Niki; Universit?t Salzburg, Fachbereich Psychologie, Hellbrunner- strasse 34, A-5020 Salzburg, niki.pfeifer@sbg.ac.at. 1. Introduction The oldest and most famous reasoning system is Aristotelian syllogistics. During the last 50 years many new approaches to old logical problems were developed in philosophy, artificial intelligence, and linguistics. These generalizations or extensions of traditional syllogistics are of spe- cial interest to argumentation theory as they try to do more justice to practical reasoning than classical syllogistics did. The present paper focuses on two not very well known recent devel- opments in syllogistic inference, namely syllogisms containing compara- tive and quantitative quantifiers. The classical universal (“All …”) and the existential quantifiers (“At least one …”)1 in syllogisms are either too strict or too weak, respectively. On the one hand, the universal quantifier i