[ Fred Johnson (2004), “Aristotle’s modal syllogisms”, in D. Gabbay and J. Woods (eds.)(2004), Handbook of the History of Logic Volume 1: Greek, Indian and Arabic Logic (Elsevier), pp. 247-307. ]
1. Łukasiewicz’s Assertoric System, ŁA
1.1 Rejection in ŁA
2 Łukasiewicz’s Modal System, ŁM
3 Modern Modal Predicate Logic
4 McCall’s L-X-M System
4.1 Rejections in L-X-M
5 Semantics for L-X-M
5.1 Thomason models
5.2 Variants of the L-X-M system
6 The Chain Condition, Relevance Logic and the AP system
7 Contingent Syllogisms
7.1 Overlooked acceptances in the Q-L-X-M system
8 QLXM’
8.1 Semantics for QLXM’
8.2 Q-valid moods needed for completeness
9 The Aristotelicity of QLXM’
10 Tally of the Two-Premised Q-Valid Syllogisms
11 Extensions
1. Łukasiewicz’s Assertoric System, ŁA
1.1 Rejection in ŁA
2 Łukasiewicz’s Modal System, ŁM
3 Modern Modal Predicate Logic
4 McCall’s L-X-M System
4.1 Rejections in L-X-M
5 Semantics for L-X-M
5.1 Thomason models
5.2 Variants of the L-X-M system
6 The Chain Condition, Relevance Logic and the AP system
7 Contingent Syllogisms
7.1 Overlooked acceptances in the Q-L-X-M system
8 QLXM’
8.1 Semantics for QLXM’
8.2 Q-valid moods needed for completeness
9 The Aristotelicity of QLXM’
10 Tally of the Two-Premised Q-Valid Syllogisms
11 Extensions
(2021.04.02.)
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