Unified correspondence and proof theory for strict implication

Minghui Ma, Zhiguang Zhao
2016 Journal of Logic and Computation  
The unified correspondence theory for distributive lattice expansion logics (DLE-logics) is specialized to strict implication logics. As a consequence of a general semantic consevativity result, a wide range of strict implication logics can be conservatively extended to Lambek Calculi over the bounded distributive full non-associative Lambek calculus (BDFNL). Many strict implication sequents can be transformed into analytic rules employing one of the main tools of unified correspondence theory,
more » ... namely (a suitably modified version of) the Ackermann lemma based algorithm ALBA. Gentzen-style cut-free sequent calculi for BDFNL and its extensions with analytic rules which are transformed from strict implication sequents, are developed.
doi:10.1093/logcom/exw012 fatcat:b46elixh4nelfjxt6whkicpjdq