An IS-A taxonomy and a PART-OF relation are fundamental to knowledge representation. In many logic languages, computational objects have classes (or types) in an IS-A taxonomy and are composed of their components (substructures). This paper proposes a new language for representation and calculation of logical objects which have classes and substructures. In high-level knowledge representation systems based on conventional logic, computational objects are often very complicated. In order to define their meanings, we need many concepts such as higher-order predicates (e. g. "map"), predicates (e. g. inc), functions (e. g. cons), constants (e. g. 3), variables (e. g. B), classes (or types) (e. g. human) and instances (e. g. adam). This complexity makes it difficult to improve the expressive and computational power of conventional knowledge representation systems. One of the difficulties is to formalize higher-order predicates in typed logic languages, i.e., having predicate variables as arguments in atoms may produce type mismatches. To overcome this difficulty, we reconsider the basic concepts and simplify the language by integrating some basic concepts. Thus, conventional basic concepts (constants, classes, instances, predicates, higher order predicates and functions) are integrated into a single concept. Some other features of the proposed language are: (1) A class is not a simple constant but a sequence of constants, which allows us to represent complex class structures more easily. (2) Constraints of substructures of objects in a crass can be defined by specification of the classes of substructures of the objects. (3) Class objects are introduced to handle classes as logical objects, which solves the problem of higher-order predicates. (4) The computation for the language is defined based on the extended unification of above-mentioned objects. The proposed language is a simpler and more powerful computation system than conventional typed languages based on logic.