# From Kripke Models to Algebraic Counter-Valuations

@inproceedings{Negri1998FromKM, title={From Kripke Models to Algebraic Counter-Valuations}, author={Sara Negri and Jan von Plato}, booktitle={TABLEAUX}, year={1998} }

Starting with a derivation in the refutation calculus CRIP of Pinto and Dyckhoff, we give a constructive algebraic method for determining the values of formulas of intuitionistic propositional logic in a counter-model. The values of compound formulas are computed point-wise from the values on atoms, in contrast to the non-local determination of forcing relations in a Kripke model based on classical reasoning.

## 3 Citations

### Admissibility of structural rules for contraction-free systems of intuitionistic logic

- Philosophy, MathematicsJournal of Symbolic Logic
- 2000

This proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs, i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

### Sequent calculus proof theory of intuitionistic apartness and order relations

- MathematicsArch. Math. Log.
- 1999

Contraction-free sequent calculi for intuitionistic theories of apartness and order are given and cut-elimination for the calculi proved and conservativity results for the theories of constructive order over the usual theories of order are extended.

### Reasoning with Diagrams: Track Record

- Computer Science
- 2001

The team is ideally positioned to carry out the proposed programme of research, offering a combination of skills in diagrammatic reasoning, visual modelling, logic and automated reasoning, and tools for diagram manipulation and visualisation.

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- 1999

Contraction-free sequent calculi for intuitionistic theories of apartness and order are given and cut-elimination for the calculi proved and conservativity results for the theories of constructive order over the usual theories of order are extended.

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An equivalent calculus is described below, yet another variant on these systems, where the problem no longer arises: this gives a simple but effective decision procedure for IPC.

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