Polymer lattice density functional theory (PLDFT) is used to investigate the cononsolvency (CNS) phenomena related to polymer adsorption in a slit pore. Specifically, the two simplest types of CNS are examined: CNS1 with solvent-cosolvent binding as the dominant factor and CNS2 with polymer-cosolvent binding as the dominant factor. The simplified models for CNS1/CNS2 well capture the symmetrical/asymmetrical reentrant swelling transition of polymers positively/negatively adsorbed on the solid surface as confirmed by the calculation of PLDFT. To more deeply understand the mechanism of CNS in polymer adsorption, the essential difference and connection between the two types of CNS are analyzed by PLDFT via the quantities as the surface/middle swelling ratio defined for the aggregated layer of polymers in the slit. Further investigation of the effects of binding strength on the collapsing state of the polymer membrane shows the existence of the critical binding energy to trigger drastic collapse through the cosolvent for CNS1 or CNS2. The effects from polymer concentration on two types of CNS are also discussed, showing two important results for CNS2 in agreement with reported experiments. For application, this work indicated the possibility of employing CNS (CNS1) in adsorbed polymers for a tunable surface, as an alternative to polymer brushes.