Knowledge Representation in a Proof Checker for Logic Programs 163 specification expressed in typed FOL into structured form which is required by our correctness method (Marakakis, 1997) , (Marakakis, 2005) . 2) The component "Theorem Proof Checker supports the proof task of the selected correctness theorem. The "KB Update" subsystem allows the user to update the KB of the system through a userfriendly interface. The knowledge base (KB) and its contents are also shown in Fig. 2 . The KB

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... the representation of specifications, theorems, axioms, lemmas, and programs complements. It also has the representation of FOL laws in order to facilitate their selection for application. These entities are represented in ground representation (Hill & Gallagher, 1998) . The main benefit of this representation is the distinct semantics of the object program variables from the meta-variables. It should be noted that the user would like to see theorems, axioms, lemmas and programs in a comprehensible form which is independent of their representation. However, the ground representation cannot be easily understood by users. Moreover, the editing of elements in ground representation is error-prone. Part of the interface of the system is the "Ground-Nonground Representation Transformer" component which transforms an expression in ground representation into a corresponding one in the standard formalism of FOL and vice-versa. The standard form of expressions helps users in the proof task and for the update of the KB. Fig. 2. Main components of the proof-checker. Knowledge representation Knowledge and representation are two distinct concepts. They play a central role in the development of intelligent systems. Knowledge is a description of the world, i.e. the problem domain. Representation is how knowledge is encoded. Reasoning is how to extract more information from what is explicitly represented. www.intechopen.com Advances in Knowledge Representation