Agents and Lattice-valued Logic

In fuzzy set theory, instead of the underlying membership set being a two -valued set it is a multi-valued set that generally has the structure of a lattice L with a minimal element O and the maximal element I. Furthermore if ∧, ∨, → and ┐ are defined in the set L, then we can use these operations to define, as in the ordinary set theory, operations on fuzzy subsets. In this paper we give a model of the Lattice-Valued Logic with set of agents.Any agents know the logic value of a sentence p. The logic value is compatible with all of the accessible conceptual models or worlds of p inside the agent. Agent can be rational or irrational in the use of the logic operation.Every agent of n agents can have the same set of conceptual models for p and know the same logic for p in this case the agents form a consistent group of agents.When agents have different conceptual models for p,different subgroup of agents know different logic value for p. In this case the n agents are inconsistent in the expression of the logic value for p. The valuation structure of set of agents can be used as a semantic model for the Lattice-valued Logic and fuzzy logic.