Karsten Konrad

Omega: Towards a Mathematical Assistant

Ωmega is a mixed-initiative system with the ultimate purpose of supporting theorem proving in main-stream 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.

LΩUI: Lovely ΩMEGA User Interface

Abstract. The capabilities of a automated theorem provers interface are essential for the effective use of (interactive) proof systems. LΩUI is the multi-modal interface that combines several features: a graphical display of information in a proof graph, a selective term browser with hypertext facilities, proof and proof plan presentation in natural language, and an editor for adding and maintaining the knowledge base. LΩUI is realized in an agent-based client-server architecture and implemented in the concurrent constraint programming language Oz.

LOUI: Lovely OMEGA User Interface

Abstract. The capabilities of a automated theorem provers interface are essential for the effective use of (interactive) proof systems. LΩUI is the multi-modal interface that combines several features: a graphical display of information in a proof graph, a selective term browser with hypertext facilities, proof and proof plan presentation in natural language, and an editor for adding and maintaining the knowledge base. LΩUI is realized in an agent-based client-server architecture and implemented in the concurrent constraint programming language Oz.

System Description: Kimba, A Model Generator for Many-Valued First-Order Logics

Kimba is the first model generation program which implements a semi-decision procedure for nite satisability of rst-order logics with nitely many truth values. The procedure enumerates the nite models of its input and can be used to compute efficiently domain minimal models whose positive part is minimal in size. Kimba has been implemented in the constraint logic programming language Oz [6] and is based on a tableaux calculus that translates deduction problems into Constraint Satisfaction Problems (CSPs). The constraint propagators needed to solve these problems are realized as concurrent procedures that can make use of Oz’s built-in capabilities for solving CSPs.

HOT: A Concurrent Automated Theorem Prover Based on Higher-Order Tableaux

Hot is an automated higher-order theorem prover based on HTE, an extensional higher-order tableaux calculus. The first part of this paper introduces an improved variant of the calculus which closely corresponds to the proof procedure implemented in Hot. The second part discusses Hots design that can be characterized as a concurrent blackboard architecture. We show the usefulness of the implementation by including benchmark results for over one hundred solved problems from logic and set theory.

L Ω UI : L ovely ΩMEGA U ser I nterface

Abstract. The capabilities of a automated theorem provers interface are essential for the effective use of (interactive) proof systems. LΩUI is the multi-modal interface that combines several features: a graphical display of information in a proof graph, a selective term browser with hypertext facilities, proof and proof plan presentation in natural language, and an editor for adding and maintaining the knowledge base. LΩUI is realized in an agent-based client-server architecture and implemented in the concurrent constraint programming language Oz.