Canonical signed calculi with multi-ary quantifiers

Canonical Gentzen-type calculi are a natural class of systems, which in addition to the standard axioms and structural rules have only logical rules introducing exactly one connective. There is a strong connection in such systems between a syntactic constructive criterion of coherence, the existence of a two-valued non-deterministic semantics for them and strong cut-elimination. In this paper we extend the theory of canonical systems to signed calculi with multi-ary quantifiers. We show that the extended criterion of coherence fully characterizes strong analytic cut-elimination in such calculi, and use finite non-deterministic matrices to provide modular semantics for every coherent canonical signed calculus.