Logic, Reasoning, and Rationality pp 95-123 | Cite as

# A Method of Generating Modal Logics Defining Jaśkowski’s Discussive D_{2} Consequence

## Abstract

Jaśkowski’s logic **D** _{ 2 } is usually understood as a set of discussive formulae. Studying Jaśkowski’s paper one can also find a consequence relation (the **D** _{ 2 }-consequence). The logic **D** _{ 2 } was meant to express this consequence relation. Since the logic **D** _{ 2 } was formulated with the help of a modal logic, the consequence relation is also defined in the modal language. It is known that the logic **D** _{ 2 } can be defined by other modal logics than **S5**. A similar question arises as regards the consequence relation. In Nasieniewski and Pietruszczak (On modal logics defining Jaśkowski’s D_{2}-consequence. In: Tanaka K, Berto F, Mares E, Paoli F (eds) Paraconsistency: logic and applications. Logic, epistemology and the unity of science, chap 8, vol 26. Springer, Dordrecht/New York, pp 141–161, 2013) there are given modal logics other than **S5** which define exactly the same consequence relation. In the present paper we try to develop a more general method of defining modal logics which also allow to define the **D** _{ 2 }-consequence.

## Keywords

Jaśkowski’s logic**D**

_{2}

**D**

_{2}-consequence Deducibility in

**D**

_{2}

## Notes

### Acknowledgements

We would like to thank both anonymous referees for their valuable remarks on an earlier version of this paper.

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