mega is a mixed-initiative system with the ultimate purpose of supporting theorem proving in mainstream mathematics and mathematics education. The current system consists of a proof planner and an integrated collection of tools for formulating problems, proving subproblems, and proof presentation.
We present a new data structure that enables to store three-dimensional proof objects in a proof development environment. The aim is to handle calculus level proofs as well as abstract proof plans together with information of their correspondences in a single structure. This enables not only different means of the proof development environment (e.g.,… (More)
The Ωmega proof development system  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)
The reasoning power of human-oriented plan-based reasoning systems is primarily derived from their domain-speciic problem solving knowledge. Such knowledge is, however, intrinsically incomplete. In order to model the human ability of adapting existing methods to new situations we present in this work a declarative approach for representing methods, which… (More)
Proof planning is a novel knowledge-based approach for proof construction, which supports the incorporation of mathematical knowledge and the common mathematical proof techniques of a particular mathematical eld. The diagonalization proof technique is a well-known method in theoretical computer science and in mathematics that originated with Can-tor, who… (More)
Most interactive proof development e n vironments are insuucient to handle the complexity of the information to be conveyed to the user and to support his orientation in large-scale proofs. In this paper we present a distributed client-server extension of the mega proof development system, focusing on the LU ILovely mega User Interface client. This… (More)
Current semi-automated theorem provers are often advertised as " mathematical assistant systems ". However, these tools behave too passively and in a stereotypic way to meet this ambitious goal because they lack the capability to adequately take into account requirements on proof search control and user demands for their own actions. Motivated by this… (More)
Extending the plan-based paradigm for automated theorem proving, we developed in previous work a declarative approach towards representing methods in a proof planning framework to support their mechanical modiication. This paper presents a detailed study of a class of particular methods, embodying variations of a mathematical technique called… (More)