By L. we denote the set of all propositional fornmlas. Let C be the set of all clauses. Define C_n=C(Lη:η∈C}.In Sec. 2 of this paper. we prove that for normal modal logics S, the notions of (S. C_)-expansions and S...By L. we denote the set of all propositional fornmlas. Let C be the set of all clauses. Define C_n=C(Lη:η∈C}.In Sec. 2 of this paper. we prove that for normal modal logics S, the notions of (S. C_)-expansions and S-expansions coincide. In Sec. 3. we prove that if I consists of default clauses then the notions of S-expansions for I and (S.C)-expansions for I coincide. To this end. we first show. in Sec 3.that the notion of S-expansions for I is the same as that of (S.L)-expansions for I.展开更多
It is well known that there exists a tight connection between nonmonotonic reasoning and conditional implication. Many researchers have investigated it from various angles. Among th em, C.Boutilier and P.Lamarre hav...It is well known that there exists a tight connection between nonmonotonic reasoning and conditional implication. Many researchers have investigated it from various angles. Among th em, C.Boutilier and P.Lamarre have shown that some conditional implication may b e regarded as the homology of different nonmonotonic consequence relations. In t his paper, based on the plausibility space introduced by Friedman and Halpern, w e characterize the condition logic in which conditional implication is nonmonoto nic, and this result characterizes the conditional implication which may be rega rded as the corresponding object in Meta language for nonmonotonic inference rel ations.展开更多
In this paper, the sematics of a paraconsistent logic and its nonmonotonic extension by minimal inconsistency are presented first. And then signed tableaux for paraconsistelit logic and minimal tableaux for logic of...In this paper, the sematics of a paraconsistent logic and its nonmonotonic extension by minimal inconsistency are presented first. And then signed tableaux for paraconsistelit logic and minimal tableaux for logic of minimal inconsistency is proposetl. Finally the reduction of logic of paraconsistency and minimal inconsistency on ordinary semantics which provides new approach to proof procedure and implementation of paraconsistency and minimal inconsistency are provided.展开更多
As an important variant of Relier's default logic, Poole (1988) developed a nonmonotonic reasoning framework in the classical first-order language. Brewka and Nebel extended Poole's approach in order to enabl...As an important variant of Relier's default logic, Poole (1988) developed a nonmonotonic reasoning framework in the classical first-order language. Brewka and Nebel extended Poole's approach in order to enable a representation of priorities between defaults. In this paper a general framework for default reasoning is presented, which can be viewed as a generalization of the three approaches above. It is proved that the syntax-independent default reasoning in this framework is identical to the general belief revision operation introduced by Zhang et al. (1997). This result provides a solution to the problem whether there is a correspondence between belief revision and default logic for the infinite case. As a by-product, an answer to the question, raised by Mankinson and Gardenfors (1991), is also given about whether there is a counterpart contraction in nonmonotonic logic.展开更多
文摘By L. we denote the set of all propositional fornmlas. Let C be the set of all clauses. Define C_n=C(Lη:η∈C}.In Sec. 2 of this paper. we prove that for normal modal logics S, the notions of (S. C_)-expansions and S-expansions coincide. In Sec. 3. we prove that if I consists of default clauses then the notions of S-expansions for I and (S.C)-expansions for I coincide. To this end. we first show. in Sec 3.that the notion of S-expansions for I is the same as that of (S.L)-expansions for I.
文摘It is well known that there exists a tight connection between nonmonotonic reasoning and conditional implication. Many researchers have investigated it from various angles. Among th em, C.Boutilier and P.Lamarre have shown that some conditional implication may b e regarded as the homology of different nonmonotonic consequence relations. In t his paper, based on the plausibility space introduced by Friedman and Halpern, w e characterize the condition logic in which conditional implication is nonmonoto nic, and this result characterizes the conditional implication which may be rega rded as the corresponding object in Meta language for nonmonotonic inference rel ations.
文摘In this paper, the sematics of a paraconsistent logic and its nonmonotonic extension by minimal inconsistency are presented first. And then signed tableaux for paraconsistelit logic and minimal tableaux for logic of minimal inconsistency is proposetl. Finally the reduction of logic of paraconsistency and minimal inconsistency on ordinary semantics which provides new approach to proof procedure and implementation of paraconsistency and minimal inconsistency are provided.
基金This work was supported by the National Natural Science Foundation of China (No.69785004) and the Science and Technology Fundin
文摘As an important variant of Relier's default logic, Poole (1988) developed a nonmonotonic reasoning framework in the classical first-order language. Brewka and Nebel extended Poole's approach in order to enable a representation of priorities between defaults. In this paper a general framework for default reasoning is presented, which can be viewed as a generalization of the three approaches above. It is proved that the syntax-independent default reasoning in this framework is identical to the general belief revision operation introduced by Zhang et al. (1997). This result provides a solution to the problem whether there is a correspondence between belief revision and default logic for the infinite case. As a by-product, an answer to the question, raised by Mankinson and Gardenfors (1991), is also given about whether there is a counterpart contraction in nonmonotonic logic.
