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The Ωmega proof development system [2] is the core of several related and well integrated research projects of the Ωmega research group. Ωmega is a mathematical assistant tool that supports proof development in mathematical domains at a user-friendly level of abstraction. It is a modular system with a central data structure and several complementary… (More)

There are two approaches to lattices used in the Mizar Mathematical Library: on the one hand, these structures are based on the set with two binary operations (with an equational characterization as in [17]). On the other hand, we may look at them as at relational structures (posets – see [12]). As the main result of this article we can state that the Mizar… (More)

Knowledge bases that represent some domain expertise for use in a formal system typically serve one of two major purposes: (1) inferencing in some problem-solving context, or (2) interfacing the system by natural language. Interfacing may be for accessing the system's functionality or for presenting its results. Techniques for addressing the natural… (More)

- Markus Moschner
- 2007

Orthoposets are defined. The approach is the standard one via order relation similar to common text books on algebra like [8]. The terminology and notation used in this paper are introduced in the following In this paper S, X denote non empty sets and R denotes a binary relation on X. We consider orthorelational structures, extensions of relational… (More)

- Markus Moschner
- 2004

Orthoposets are defined. The approach is the standard one via order relation similar to common text books on algebra like [9]. In this paper S, X denote non empty sets and R denotes a binary relation on X. We introduce orthorelational structures which are extensions of relational structure and Com-plStr and are systems a carrier, an internal relation, a… (More)

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