Logic and Logical Philosophy Volume ... (2011), ..- .. Janusz Kaczmarek Two Ontological Structures: Concepts Structure and Lattice of Elementary Situations Abstract. In 1982, Wolniewicz proposed a formal ontology of situations based on the lattice of elementary situations (cf. [5], [6]). In 2008, I constructed some formal ontological structures, i.e. Porphyrian Tree Structure (PTS), Concepts Structure (CS) and Structure of Individuals (U) that formally represent ontologically fundamental categories like: species and genera (PTS), concepts (CS) and individual beings (U) (cf. [2], [3]). From ontological perspective, situations and concepts belong to different categories. But, unexpectedly, as I shall show, some variants of CS and Wolniewicz’ lattice are similar. The main theorem states that some subset of modified concepts structure (called CS+) based on CS fulfils the axioms of Wolniewicz’ lattice. Finally, some philosophical conclusions and formal facts will be proposed. Keywords: formal (formalized) ontology, ontology of situations, concepts structure, lattice 1. Preliminaries Following [2] and [3], let us remind some indispensable definitions. Definition 1. Let Q be a set of cardinality 0 .Then CS = {c: c {0,1} Q’ , for Q’ Q & card(Q’) < 0 }. If Q’ = , c denotes the function c on and is called the root of CS. An element c CS is called a formal concept (shortly: concept). An example: If we consider the qualities (their school definitions): of being a number (q 1 ), being a natural (q 2 ), being divided by 2 (q 3 ), then the concepts of (a): even number and of (b): odd number, can be defined by functions from Q’ = {q 1 , q 2 , q 3 } into {0, 1} in the following way: even number odd number q 1 1 q 1 1 q 2 1 q 2 1 q 3 1 q 3 0 Definition 2. A set CS with a relation CS described by the condition: ( CS ) c CS c’ iff c c’, in short, <CS, CS >, will be called a concepts system. Fact 1. <CS, CS > is a partially ordered set. Proof. Reflexivity, antisymmetry and transitivity are evident. ■