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

Definability and canonicity for Boolean logic with a binary relation

International audienceThis paper studies the concepts of definability and canonicity in Boolean logic with a binary relation. Firstly, it provides formulas defining first-order or second-order conditions on frames. Secondly, it proves that all formulas corresponding to compatible first-order conditions on frames are canonical

Sahlqvist theorems for precontact logics

Precontact logics are propositional modal logics that have been recently considered in order to obtain decidable fragments of the region-based theories of space introduced by De Laguna and Whitehead. We give the definition of Sahlqvist formulas to this region-based setting and we prove correspondence and canonicity results. Together, these results give rise to a completeness result for precontact logics that are axiomatized by Sahlqvist axioms

Sahlqvist Theorems for Precontact Logics

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