# Deciding Intuitionistic Propositional Logic via Translation into Classical Logic

@inproceedings{Korn1997DecidingIP, title={Deciding Intuitionistic Propositional Logic via Translation into Classical Logic}, author={Daniel S. Korn and Christoph Kreitz}, booktitle={CADE}, year={1997} }

We present a technique that efficiently translates prepositional intuitionistic formulas into propositional classical formulas. This technique allows the use of arbitrary classical theorem provers for deciding the intuitionistic validity of a given propositional formula. The translation is based on the constructive description of a finite counter-model for any intuitionistic non-theorem. This enables us to replace universal quantification over all accessible worlds by a conjunction over the…

## 8 Citations

### A Constructively Adequate Refutation System for Intuitionistic Logic

- Computer Science
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A refutation system for intuitionistic logic which allows to locate situations where constructive reasoning is unnecessary and back- tracking over choicepoints for dierent orderings of non-permutable rules can often be avoided and the search space will be reduced considerably.

### Deciding Regular Grammar Logics with Converse Through First-Order Logic

- Philosophy, Computer ScienceJ. Log. Lang. Inf.
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The results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators.

### On the Advantage of a Non-Clausal Davis-Putnam Procedure

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A non-clausal decision procedure for classical propositional logic that deals with formulae which are not necessarily in clausal form and is compared with a clausalbased Davis-Putnam prover using the standard translation into clausalform as well as the definitional translation.

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- Computer Science
- 1996

An overall view of an approach to developing a coherent ATP-system which can deal with a variety of logics and with diierent applications in a tailored way is provided.

### Problem-Oriented Applications of Automated Theorem Proving

- Computer ScienceDISCO
- 1996

An overall view of an approach to developing a coherent ATP-system which can deal with a variety of logics and with different applications in a tailored way is provided.

### A Multi-level Approach to Program Synthesis

- Computer ScienceLOPSTR
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We present an approach to a coherent program synthesis system which integrates a variety of interactively controlled and automated techniques from theorem proving and algorithm design at different…

### A Multi-level Approach to Program Synthesis a Multi-level Approach to Program Synthesis

- Computer Science
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We present an approach to a coherent program synthesis system which integrates a variety of interactively controlled and automated techniques from theorem proving and algorithm design at diierent…

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A refutation system for intuitionistic logic which allows to locate situations where constructive reasoning is unnecessary and back- tracking over choicepoints for dierent orderings of non-permutable rules can often be avoided and the search space will be reduced considerably.

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