Talk: Edi Pavlovic (Helsinki)
Generalized free logic and the Quantified argument calculus
This talk presents a sequent calculus account of free logics, of both positive and negative variety, as well as a general system of semantics for them. This semantics allows us to systematize the relationship between variety of logics, including positive and negative free logic, classical logic, empty logic and inclusive logics. It is then noted that this framework bears a close resemblance to the Quantified argument calculus (Quarc).
Quarc is a novel and peculiar system of quantified logic, particularly in its treatment of non-emptiness of unary predicates, as in Quarc unary predicates are never empty, (and singular terms denote). Moreover, and as a consequence of this, the universally quantified formulas entail their corresponding particular ones, similar to existential import. But at the same time, Quarc eschews talk of existence entirely by having a particular quantifier instead of an existential one.
Using the general framework and the sequent calculus, the relationship between quantification and existence in Quarc is explored.