Aristotelian syllogisms and generalized quantifiers

  title={Aristotelian syllogisms and generalized quantifiers},
  author={Dag Westerst{\aa}hl},
  journal={Studia Logica},
The paper elaborates two points: i) There is no principal opposition between predicate logic and adherence to subject-predicate form, ii) Aristotle's treatment of quantifiers fits well into a modern study of generalized quantifiers. 
Arithmetizations of Syllogistic à la Leibniz
  • V. Sotirov
  • Philosophy
    J. Appl. Non Class. Logics
  • 1999
Two models of the Aristotelian syllogistic in arithmetic of natural numbers are built as realizations of an old Leibniz idea, called Scholastic, where terms are replaced by integer terms in the interpretation.
The propositional and relational syllogistic
In this paper it is shown how syllogistic reasoning can be extended to account for propositional logic and relations.
Generalized Intermediate Syllogisms with More Premises
  • Petra Murinová
  • Computer Science
    2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
  • 2019
The main objective of this paper is to show how the theory of syllogistic reasoning can be applied for a derivation of new information which is not included in data.
This paper identifies several fragments based on whether negation is permitted on all nouns, including those in the subject of a sentence; and whether the subject noun phrase may contain a relative clause.
Bibliography on Aristotle's Theory of Categorical Syllogism
  • Philosophy
  • 2015
Angelelli, Ignacio. 1978. "Analytica priora, I, 38 and Reduplication." Notre Dame Journal of Formal Logic no. 19:295-296. "Although many commentators have summarized chapter 38 of Analytica Priora I
A Generalized Syllogistic Inference System based on Inclusion and Exclusion Relations
A simple inference system based on two primitive relations between terms, namely, inclusion and exclusion relations, is introduced and it is shown that this system can be embedded into a fragment of propositional minimal logic.
UvA-DARE ( Digital Academic Repository ) The propositional and relational syllogistic
In this paper it is shown how syllogistic reasoning can be extended to account for propositional logic and relations.
Is Modern Logic Non-Aristotelian?
In this paper we examine up to which point Modern logic can be qualified as non-Aristotelian. After clarifying the difference between logic as reasoning and logic as a theory of reasoning, we compare
Intersecting Adjectives in Syllogistic Logic
This paper explores simple systems of natural logic which make use of intersecting adjectives; these are adjectives whose interpretation does not vary with the noun they modify.
Syllogistic Logics with Verbs
  • L. Moss
  • Linguistics
    J. Log. Comput.
  • 2010
This article provides sound and complete logical systems for several fragments of English which go beyond syllogistic logic in that they use verbs as well as other limited syntactic material:


Quantifiers in Formal and Natural Languages
For a long time, the word ‘quantifier’ in linguistics and philosophy simply stood for the universal and existential quantifiers of standard predicate logic, but the dominance of predicate logic has obscured the fact that the quantifier expressions form a syntactic category, with characteristic interpretations, and with many more members than ∀ and ∃.
Generalized quantifiers and natural language
In 1957, the Polish logician Andrej Mostowski pointed out that there are many mathematically interesting quantifiers that are not definable in terms of the first-order ∀, ∃ and initiated study of
Aristotle's syllogistic
Questions About Quantifiers