2020/03/27 by De Rudder, Laurent, Palmigiano, Alessandra
#03B45 #03B47 #03B60 #03G10 #06D10 #06D50 #06E15 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2003.12355
We prove an algebraic canonicity theorem for normal LE-logics of arbitrary signature, in a generalized setting in which the non-lattice connectives are interpreted as operations mapping tuples of elements of the given lattice to closed or open elements of its canonical extension. Interestingly, the syntactic shape of LE-inequalities which guarantees their canonicity in this generalized setting turns out to coincide with the syntactic shape of analytic inductive inequalities, which guarantees LE-inequalities to be equivalently captured by analytic structural rules of a proper display calculus. We show that this canonicity result connects and strengthens a number of recent canonicity results in two different areas: subordination algebras, and transfer results via Gödel-McKinsey-Tarski translations.