In this paper, an α-resolution method for a set of lattice-valued Horn generalized clauses is established in lattice-valued propositional logic systemL P(X) based on lattice implication algebra. Firstly, the notions of lattice-valued Horn generalized clause, normal lattice-valued Horn generalized clause and unit latticevalued Horn generalized clause are given in L P(X). Then, the α-resolution o...

In order to process the linguistic-valued information with uncertainty in the financial decisionmaking, the present work uses a lattice-valued logical algebra lattice implication algebra to deal with both comparable and incomparable linguistic truth-values. A new personal financial decision auxiliary modeling framework based on the lattice-ordered linguistic truth-valued logic is proposed. The ...

Inconsistencies frequently occur in news about the real-world. Some of these inconsistencies may be more significant than others, and some news may contain more inconsistencies than others. This creates problems of deciding whether to act on these inconsistencies, and if so how. Possible actions on an inconsistency in a news report include ignore the inconsistency, resolve the inconsistency, an...

In [10] Osorio et al. introduced a paraconsistent three-valued logic, the logic CG3 which was named after the logic G ′ 3 due to the close relation between them. Authors defined CG3 via the three-valued matrix that defines G3 but changing the set of designated truth values. In this article we present a brief study of the Kripke-type semantics for some logics related with CG3 before constructing...

In this work we present additional results related to the property of strong equivalence of logic programs. This property asserts that two programs share the same set of stable models, even under the addition of new rules. As shown in a recent work by Lifschitz, Pearce and Valverde, strong equivalence can be simply reduced to equivalence in the logic of Here-and-There (HT). In this paper we pro...

A b s t r a c t. The paper deals with functional properties of three-valued logics. We consider the family of regular three-valued Kleene's logics (strong, weak, intermediate) and it's extensions by adding an implicative connectives (" natural " implications). The main result of our paper is the lattice that describes the relations between implicative extensions of regular logics. In this paper...

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.