Abstract
The paper solves how to reform Aristotelian syllogisms (ASs) to make it compatible with classic logic, and further formally deduct them in logic programming languages. It asserts that there exist two challenging problems in Aristotelian categorical propositions (ACPs) among ASs. One is inconsistently to regard the particular quantifier as the existential quantifier meanwhile as the partial, another one is lacking a quantifier binding the second term. To overcome the two problems, new forms of categorical propositions (called expanded categorical propositions, ECPs) are introduced without semantic confusion in interpretations of the particular quantifier, and with the remedied second quantifier. Naturally, made up of ECPs, the forms of quantifier-expanded syllogisms (QESs) are constructed. To deduct QESs, a formal system, also a Turing machine, is designed to decide and symbolically generate valid conclusions. Thus, a semantics-consistent and form-intact system of QESs, with deductive rules based on mathematically computing models has been established.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Westerstah, D.: Aristotelian syllogisms and generalized quantifiers. Studia Logica XLVII I(4), 577–585 (1989)
Cooke, H.P., Tredennick, H.: Aristotle: Prior Analytics, Categories, On Interpretation, Prior Analysis. Loeb Classical Library, Later printing Edition. Harvard University Press. Cambridge (1938)
Preece, W.E., Goetz, P.W.: “Syllogistic”. The new Encyclopaedia Britannica, vol. 32, 15th edn. Encyclopaedia Britannica Inc., London (2009)
Kneale, W., Kneale, M.: The Development of Logic, 1st edn. Oxford at the Clarendon Press, Oxford (1962)
Euler, L.: Lettres à une Princesse d′Allemagne, l′ Academie Imperiale des Science. St. Petersberg (1768)
Gergonne, J.D.: Essai de dialectique rationelle. Annales des mathématiques qures et appliqués 7, 189–228 (1816–1817)
Stenning, K., Van Lambalgen, M.: Human Reasoning and Cognitive Science, 1st edn. The MIT Press, Cambridge MA (2008)
Harrison, J.: Handbook of Practical Logic and Automated Reasoning/Syllogism, 1st edn. Cambridge University Press, Cambridge (2009)
Zhang, Y.: Improvements of categorical propositions on consistency and computability. J. Multiple-Valued Logic Soft Comput. 33(4–5), 397–413 (2019)
Zhang, Y.: Expanded Syllogisms and Automated Reasoning, 1st edn. Science and Technology Documentary Publishing House, Beijing (2009)
Turing, A.: On computable numbers, with an application to the entscheidungs problem. In: Proceedings of the London Mathematical Society, vol. 42,pp. 230–231, 263–265 (1936–1937)
Chomsky, N.: Syntactic Structures, 2nd edn. De Gruyter, Berlin (1975)
Acknowledgement
Some results in the paper are cited from the author’s doctoral thesis and post-doctoral academic report; the author is full of gratitude to the respective tuition of Prof. Dachun Liu and Prof. Shushan Cai.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix
Appendix
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Zhang, Y. (2022). Formalized Deduction of Semantics-Consistent and Quantifier-Dyadic Syllogisms. In: Kahraman, C., Tolga, A.C., Cevik Onar, S., Cebi, S., Oztaysi, B., Sari, I.U. (eds) Intelligent and Fuzzy Systems. INFUS 2022. Lecture Notes in Networks and Systems, vol 505. Springer, Cham. https://doi.org/10.1007/978-3-031-09176-6_67
Download citation
DOI: https://doi.org/10.1007/978-3-031-09176-6_67
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-09175-9
Online ISBN: 978-3-031-09176-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)