Dr. Hans Jürgen Ohlbach

## Miscellaneous Selected Publications

Book review: Maria Manzano: Extensions of First Order Logic
Hans Jürgen Ohlbach

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Computer Support for the Development and Investigation of Logics
Hans Jürgen Ohlbach

Abstract:
The development and investigation of application--oriented logics comprises many aspects and problems. For a few of them some computer support is possible which frees the investigator from sometimes quite complex computations. This paper gives an overview about some developments in this area. In particular, we consider the correspondences between axiomatic and semantic specifications of a logic and the problem of finding one from the other by means of automated theorem provers and quantifier elimination algorithms. Other topics adressed in this paper are reasoning in Hilbert systems, the investigation of the expressiveness of a logic and the axiomatizability of semantic conditions. For the technical details of the methods and the proofs I refer to the original papers.

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Towards Automating Duality
Chris Brink, Dov Gabbay and Hans Jürgen Ohlbach

Abstract:
Dualities between different theories occur frequently in mathematics and logic --- between syntax and semantics of a logic, between structures and power structures, between relations and relational algebras, to name just a few. In this paper we show for the case of structures and power structures how corresponding properties of the two related structures can be computed fully automatically by means of quantifier elimination algorithms and predicate logic theorem provers. We illustrate the method with a large number of examples and we give enough technical hints to enable the reader who has access to the Otter theorem prover to experiment herself.

Hans Jürgen Ohlbach and Andreas Herzig

Abstract:
The parameters of the parametrized modal operators [p] and >p\rangle< usually represent agents (in the epistemic interpretation) or actions (in the dynamic logic interpretation) or the like. In this paper the application of the idea of parametrized modal operators is extended in two ways: First of all a modified neighbourhood semantics is defined which permits among others the interpretation of the parameters as probability values. A formula [.5]F may for example express the fact that in at least 50\% of all cases (worlds) F holds. These probability values can be numbers, qualitative descriptions and even arbitrary terms. Secondly a general theory of the parameters and in particular of the characteristic operations on the parameters is developed which unifies for example the multiplication of numbers in the probabilistic interpretation of the parameters and the sequencing of actions in the dynamic logic interpretation.

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Last Modified: Thursday, 06-Apr-2000 18:00:08 CEST