摘要
The deduction relation in logics is the relation between two formulas, which can be characterized by proof theoretic inference rules. Following the inference rules in Gentzen proof theory, a class of deduction relations called Horn style deduction relations is defined. By theorems in model theory, it is proved that this relation cannot extend the deductive power of classical deduction relation. Therefore, we reach a conclusion that when generalizing classical logic with the purpose of getting nonmonotonic deduction relation, negative assertions in the definition should be used.
The deduction relation in logics is the relation between two formulas, which can be characterized by proof theoretic inference rules. Following the inference rules in Gentzen proof theory, a class of deduction relations called Horn style deduction relations is defined. By theorems in model theory, it is proved that this relation cannot extend the deductive power of classical deduction relation. Therefore, we reach a conclusion that when generalizing classical logic with the purpose of getting nonmonotonic deduction relation, negative assertions in the definition should be used.
基金
ProjectsupportedbytheNationalNaturalScienceFoundationofChina (GrantNo .6 94330 30 )
