Bernd I. Dahn

Integrating Logical Functions with ILF

This is a description of the system ILF developed at the Humboldt University at Berlin ILF is a system that integrates automated theorem provers proof tactics for interactive deductive systems and models within a graphical user interface The structure and commands of ILF are presented A special part is devoted to the TreeViewer a part of ILF used for visualising directed acyclic graphs which can be used as a separate programme We describe the possibilities to extend ILF by integrating more interactive and automated deductive systems The last part describes the ProofPad a sample con guration for editing proofs in the eld of lattice ordered groups This work was supported by the Deutsche Forschungsgemeinschaft within the project Deduktion und verbandsgeordnete Gruppen for further information contact e mail gehne mathematik hu berlin de

Natural Language Presentation and Combination of Automatically Generated Proofs

The paper describes a generic tool that generates automatically natural language presentations of proofs from various automated and interactive deductive systems. Proofs from different sources are translated into a unified format and equipped with a block structure. These proofs can be easily combined. Several proof transformation procedures, based only on the analysis of structural aspects of the proofs, are available. The tool is part of the ILF system and of the ILF mail server.

Integration of Automated and Interactive Theorem Proving in ILP

Ilf is a convenient interface between the non-expert user of ATPs and most of the available high performance ATPs. The typed first order input language and the transformation algorithms for coding types into clausal logic, which are integrated into Ilf, make ATPs almost transparent to the user. One only has to learn one language to use many provers. The natural language proof presentation unit closes the gap between the (illegible) machine output of ATPs and the desire of the user to understand machine generated proofs. It is planned to upgrade all integrated ATPs as well as to integrate new high performance provers.

Constructions of classical models by means of Kripke models (survey)

It is demonstrated how Kripke models for intuitionistic predicate logic can be applied in order to prove classical theorems. As examples proofs of the independence of the axiom of constructibility, of the omitting types theorem and of Shelahs ultrapower theorem are sketched.

Boolean valued models and incomplete specifications

Abstract For each consistent universal first order theory T a Boolean valued model of T is constructed that satisfies an existential sentence if and only if it is provable from T . The resolution calculus is extended so that proofs from T yield representations of objects incompletely specified by T in a Boolean valued model.

On models with variable universe

In this paper some parts of the model theory for logics based on generalised Kripke semantics are developed. Löwenheim-Skolem theorems and some applications of ultraproduct constructions for generalised Kripke models with variable universe are investigated using similar theorems of the model theory for classical logic. The results are generalizations of the theorems of [4].

Universally generic finitely generated ordered Abelian groups

It is shown that a finitely generated ordered Abelian group is generic if and only if it is superdiscrete, i.e., each homomorphic image is discretely ordered. The forcing concept uses universal sentences as forcing conditions.

Partial isomorphisms and intuitionistic logic

A game for testing the equivalence of Kripke models with respect to finitary and infinitary intuitionistic predicate logic is introduced and applied to discuss a concept of categoricity for intuitionistic theories.

Admissible sets and structures

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