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 relatio...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.展开更多
The development of the object-oriented paradigm has suffered from the lackof any generally accepted formal foundations for its semantic definition. Toaddress this issue, we propose the development of the logic-based s...The development of the object-oriented paradigm has suffered from the lackof any generally accepted formal foundations for its semantic definition. Toaddress this issue, we propose the development of the logic-based semantics ofthe object-oriented paradigm. By combining the logic- with the object-orientedparadigm of computing first, this paper discusses formally the semantics of aquite purely object-oriented logic paradigm in terms of proof theory modeltheory and Aspoint theory from the viewpoint of logic. The operational anddeclarative semantics is given. And then the correspondence between soundnessand completeness has been discussed formally.展开更多
文摘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.
文摘The development of the object-oriented paradigm has suffered from the lackof any generally accepted formal foundations for its semantic definition. Toaddress this issue, we propose the development of the logic-based semantics ofthe object-oriented paradigm. By combining the logic- with the object-orientedparadigm of computing first, this paper discusses formally the semantics of aquite purely object-oriented logic paradigm in terms of proof theory modeltheory and Aspoint theory from the viewpoint of logic. The operational anddeclarative semantics is given. And then the correspondence between soundnessand completeness has been discussed formally.
