Based on the general form of -resolution principle for a lattice-valued logic with truth-values defined in a latticevalued logical algebra structure lattice implication algebra, the further extended -resolution method in this lattice-valued logic is discussed in the present paper in order to increase the efficiency of the resolution method. Firstly, -quasi-lock semantic resolution method in lat...

As a continuation of our research work on resolutionbased automated reasoning approaches for latticevalued logic systems with truth-values in a latticevalued logical algebraic structure – lattice implication algebra (LIA), in the present paper, we prove thatα resolution for lattice-valued first-order logic ( ) LF X based on LIA can be equivalently transformed into that for lattice-valued propos...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

For the processing of decision making with uncertainty information, this paper establishes a decision model based on lattice-valued logic and researches the algorithm for extracting the maximum decision rules. Firstly, we further research the lattice-valued fuzzy concept lattice by combining the lattice implication algebra and classical concept lattice; secondly, we define the lattice-valued de...