Abstract:
In this research, we have studied some formulas from Hyting’s system in calculating some semantics of intuitionistic logic, as it was relied on the axioms of Hyting’s system and the use of the three rules of derivation by conjunction, substitution and situation, and benefiting from the existing theorems in Hyting’s system to find new formulas derived from previous formulas and have come up with some forms of complementary formulas in the intuitionistic logic and most importantly:

K ,K⊃L ,K⊃( L⊃M) ⊢L∨M
L⊃M ,K⊃L ,K⊃M ⊢(L∨K)⊃(L∧M)
L⊃K ,M⊃K ,L∧M ⊢K∧L

The method of thruth trees was also used to prove a formula from the Hyting’s system.
Key words: Intuitionistic logic, Hyting’s system, derivation rules, truth trees, the problem of completion