15 research outputs found
Semi De Morgan Logic Properly Displayed
In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi
Semi De Morgan Logic Properly Displayed
In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi
Slanted canonicity of analytic inductive inequalities
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 G\"odel-McKinsey-Tarski translations.Comment: arXiv admin note: text overlap with arXiv:1603.08515,
arXiv:1603.0834