Abstract
A universally free logic is a system of quantification theory, with or without identity, whose theses remain logically true if (a) the domain of quantification is empty and (b) some of the singular terms present in the language do not denote existing objects. In the West, (inclusive) logics satisfying (a) and (free) ones satisfying (b) were developed starting in the 1950s. But Stanisław Jaśkowski preceded all this work by some twenty years: his paper “On the Rules of Supposition in Formal Logic” of 1934 can be regarded as containing, at least implicitly, the first universally free logic. The system proposed there is an inclusive logic as it is, and a straightforward extension of it is also free.
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Bencivenga, E. Jaśkowski’s Universally Free Logic. Stud Logica 102, 1095–1102 (2014). https://doi.org/10.1007/s11225-014-9561-4
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DOI: https://doi.org/10.1007/s11225-014-9561-4