Popper's Notion of Duality and His Theory of Negations

Popper’s Theory of Deductive Logic

“…Detailed investigations of Popper's theory are given in the articles of Lejewski (1974) in the Schilpp volume on Popper (cf. Schilpp, 1974)16;Schroeder-Heister (1984, 2006 and Binder andPiecha (2017, 2021), which were already mentioned above; Bar-Am (2009), which discusses a distinction between the notions of sound inference and proof; and Moriconi (2019), which provides a detailed overview and elucidates in particular Popper's treatment of negation and implication by making use of a sequent calculus setting. There are some unpublished theses dealing with Popper's logic, of which we know Cohen (1953b), Brooke-Wavell (1958) and Dunn (1963).…”

“…We heavily rely on our previous work on Popper's logic which resulted in four articles (Schroeder-Heister, 1984, 2006Binder andPiecha, 2017, 2021), but deviate in several respects from the interpretation given there. The reader may well skip this chapter and study Popper's contributions directly, the most general and readable being "Logic without Assumptions" (Popper, 1947b), followed by "New Foundations for Logic" (Popper, 1947c).…”

Logicality, Double-Line Rules, and Modalities

“…For each operator of the language L we have a left and a right segregated rule, which are given in Table 2. 4 Finally, we have the structural rules which govern the behaviour that the 3 In [28] this property is called visibility. 4 In [22] only ¬, ∧, and ◻ are considered.…”

“…4 Finally, we have the structural rules which govern the behaviour that the 3 In [28] this property is called visibility. 4 In [22] only ¬, ∧, and ◻ are considered. The rules for the other operators are derivable from their definitions.…”