In the present paper,we give a systematic study of the discrete correspondence the-ory and topological correspondence theory of modal meet-implication logic and moda1 meet-semilattice logic,in the semantics provided i...In the present paper,we give a systematic study of the discrete correspondence the-ory and topological correspondence theory of modal meet-implication logic and moda1 meet-semilattice logic,in the semantics provided in[21].The special features of the present paper include the following three points:the first one is that the semantic structure used is based on a semilattice rather than an ordinary partial order,the second one is that the propositional vari-ables are interpreted as filters rather than upsets,and the nominals,which are the“first-order counterparts of propositional variables,are interpreted as principal filters rather than principal upsets;the third one is that in topological correspondence theory,the collection of admissi-ble valuations is not closed under taking disjunction,which makes the proof of the topological Ackermann 1emma different from existing settings.展开更多
To deal with automated reasoning of linguistic truth-valued lattice-valued logic system, a lattice implication algebra with 14 elements, L14, was defined, and the J-resolution fields of constants, propositional variab...To deal with automated reasoning of linguistic truth-valued lattice-valued logic system, a lattice implication algebra with 14 elements, L14, was defined, and the J-resolution fields of constants, propositional variables and some generalized literals of L14P（X）, which is a lattice-valued propositional logic system with truth-values in L14, were discussed. There are 4 filters in L14. For any constant a not belonging to J, a and g （generalized literal of L14P（X）） form a J-resolution pair. For a propositional variable x, if x belongs to J and g does not belong to J, then x and g form a J-resolution pair.展开更多
基金supported by the Chinese Ministry of Education of Humanities and Social Science Project(23YJC72040003)the Key Project of Chinese Ministry of Education(22JJD720021)supported by the Natural Science Foundation of Shandong Province,China(project number:ZR2023QF021)。
文摘In the present paper,we give a systematic study of the discrete correspondence the-ory and topological correspondence theory of modal meet-implication logic and moda1 meet-semilattice logic,in the semantics provided in[21].The special features of the present paper include the following three points:the first one is that the semantic structure used is based on a semilattice rather than an ordinary partial order,the second one is that the propositional vari-ables are interpreted as filters rather than upsets,and the nominals,which are the“first-order counterparts of propositional variables,are interpreted as principal filters rather than principal upsets;the third one is that in topological correspondence theory,the collection of admissi-ble valuations is not closed under taking disjunction,which makes the proof of the topological Ackermann 1emma different from existing settings.
基金The Nationl Natural Science Foundation of China (No.60474022)
文摘To deal with automated reasoning of linguistic truth-valued lattice-valued logic system, a lattice implication algebra with 14 elements, L14, was defined, and the J-resolution fields of constants, propositional variables and some generalized literals of L14P（X）, which is a lattice-valued propositional logic system with truth-values in L14, were discussed. There are 4 filters in L14. For any constant a not belonging to J, a and g （generalized literal of L14P（X）） form a J-resolution pair. For a propositional variable x, if x belongs to J and g does not belong to J, then x and g form a J-resolution pair.
