Speaker
Simon Vonlanthen
RuhrUniversität Bochum
Talks at this conference:
Friday, 14:00, J336 
Modal extensions of the quantified argument calculus 
The quantified argument calculus (Quarc) is a novel logic which departs from mainstream firstorder logic by having quantifiers bind unary predicates instead of variables. Moreover, it also contains devices for modelling anaphoras, activepassivevoice distinctions and sentence versus predicatenegation. First presented in [1], it has since been the subject of multiple further research directions. In [2], a first foray into modal extensions of Quarc was presented. Quarcanalogues of the Barcan formulas were shown to be invalid and existence to be contingent across the board. \indent However, while a proof system was sketched, its completeness was not demonstrated. My talk presents the first strongly sound and complete proof systems for modal extensions of Quarc, based on work done in [4]. A family of unlabelled, Gentzenstyle natural deduction systems are presented, each being an analogue of the usual modal logics K, D, T, S4 and S5. Moreover, identity is incorporated and shown to be contingent by default. Lastly, while the base semantics are twovalued, the proof systems can also be proven to be strongly sound and complete with respect to strongKleene threevalued semantics, assuming STvalidity (cf. [3]). I argue that such semantics are crucial for capturing presuppositionfailure with respect to quantification, and finish my talk with an outlook on these threevalued semantics. Bibliography
