The Deductibility of the Aristotelian Modal Syllogism ⼞IAI-4 from the Perspective of Natural Language Information Processing

Volume 8, Issue 2, April 2024     |     PP. 74-83      |     PDF (247 K)    |     Pub. Date: April 1, 2024
DOI: 10.54647/isss120344    29 Downloads     34692 Views  

Author(s)

Siyi Yu, School of Philosophy, Anhui University, Hefei, China
Xiaojun Zhang, School of Philosophy, Anhui University, Hefei, China

Abstract
Aristotelian modal syllogisms characterize the semantic and reasoning properties of Aristotelian quantifiers and modalities. In order to give a consistent explanation for Aristotelian modal syllogisms, this paper reveals the reduction between modal syllogisms on the basis of generalized quantifier theory, set theory, first-order logic, and modern modal logic. To be more specific, this paper firstly proves the validity of the modal syllogism ⼞IAI-4 based on the truth value definitions of modal categorical propositions, and secondly deduces the other 32 valid modal syllogisms from this syllogism based on related definitions, facts and inference rules. That is to say that there is reducibility among modal syllogisms with different figures and forms. This formal study not only conforms with the needs for formal transformation of all kinds of information in the era of artificial intelligence, but also provides other types of syllogisms with unified mathematical paradigm.

Keywords
Aristotelian modal syllogisms; Aristotelian quantifiers; possible worlds; symmetry

Cite this paper
Siyi Yu, Xiaojun Zhang, The Deductibility of the Aristotelian Modal Syllogism ⼞IAI-4 from the Perspective of Natural Language Information Processing , SCIREA Journal of Information Science and Systems Science. Volume 8, Issue 2, April 2024 | PP. 74-83. 10.54647/isss120344

References

[ 1 ] Łukasiewicz, J. (1957). Aristotle’s Syllogistic: From the Standpoint of Modern Formal Logic (2nd ed.). Clarendon Press.
[ 2 ] Patzig, G. (1969). Aristotle’s Theory of the Syllogism. D. Reidel.
[ 3 ] Chagrov, A., and Zakharyaschev, M. (1997). Modal Logical. Clarendon Press.
[ 4 ] Peters, S., and Westerståhl, D. (2006). Quantifiers in Language and Logic. Clarendon Press.
[ 5 ] Xiaojun Zhang, and Mengyao Huang. (2020). Assertion or Rejection of Łukasiewicz’s Assertoric Syllogism System ŁA. Journal of Chongqing University of Science and Technology (Social Sciences Edition), 2, 10-18. (In Chinese)
[ 6 ] Xiaojun Zhang. (2020). Reducible Relations between/among Aristotelian Modal Syllogisms. SCIREA Journal of Computer, 5, 1-33.
[ 7 ] Xiaojun Zhang, Baoxiang Wu, (2021), Research on Chinese Textual Reasoning, Beijing:People’s Publishing House. (in Chinese)
[ 8 ] Protin, C. L. (2022). A Logic for Aristotle’s Modal Syllogistic. History and Philosophy of Logic.
[ 9 ] Long Wei. (2023). Formal System of Categorical Syllogistic Logic Based on the Syllogism AEE-4. Open Journal of Philosophy, 13, 97-103.
[ 10 ] Hui, Li. (2023). Reduction between Categorical Syllogisms Based on the Syllogism EIO-2. Applied Science and Innovative Research, 7, 30-37.
[ 11 ] Cheng Zhang and Xiaojun Zhang (2023). Reduction between Aristotelian Modal Syllogisms Based on the Syllogism ◇I⼞A◇I-3. Open Journal of Philosophy, 2023, 13, 145-154.