An algebraic study of exactness in partial contexts
DMF DMF ?s are the natural algebraic tool for modelling reasoning with Krner?s partial predicates. We provide two representation theorems for DMF DMF ?s which give rise to two adjunctions, the first between DMF DMF and the category of sets and the second between DMF DMF and the category of distributive lattices with minimum. Then we propose a logic L{1} L { 1 } for dealing with exactness in partial contexts, which belongs neither to the Leibniz, nor to the Frege hierarchies, and carry on its study with techniques of abstract algebraic logic. Finally a fully adequate and algebraizable Gentzen system for L{1} L { 1 } is given.
partial predicates abstract algebraic logic algebraic logic dmf lattice kleene lattice fixed point