•  33
    Arithmetizations of Syllogistic à la Leibniz
    Journal of Applied Non-Classical Logics 9 (2-3): 387-405. 1999.
    ABSTRACT Two models of the Aristotelian syllogistic in arithmetic of natural numbers are built as realizations of an old Leibniz idea. In the interpretation, called Scholastic, terms are replaced by integers greater than 1, and s.Ap is translated as “s is a divisor of p”, sIp as “g.c.d. > 1”. In the interpretation, called Leibnizian, terms are replaced by proper divisors of a special “Universe number” u < 1, and sAp is translated as “s is divisible by p”, sIp as ‘l.c.m. < u”. Both interpretation…Read more
  • GW LEIBNIZ Samtliche Schriften und Briefe
    History and Philosophy of Logic 22 (3): 163-168. 2001.
  •  44
    Non-classical operations hidden in classical logic
    Journal of Applied Non-Classical Logics 18 (2-3): 309-324. 2008.
    Objects of consideration are various non-classical connectives “hidden” in the classical logic in the form of G˛s with ˛ —a classical connective, and s—a propositional variable. One of them is negation, which is defined as G ⇒ s; another is necessity, which is defined as G ∧ s. The new operations are axiomatized and it is shown that they belong to the 4-valued logic of Lukasiewicz. A 2-point Kripke semantics is built leading directly to the 4-valued logical tables.