# Operational semantics for positive relevance logics

## Katalin Bimbó

The relational semantics for relevance logics that was introduced by Meyer and Routley in the 1970s, utilizes a ternary relation, although it emerged from the idea of an operational semantics (cf. [2]). A binary operation in place of the ternary relation provides a certain simplification; however, the set of prime filters (or prime theories) is not closed under the fusion operation. For an informational interpretation of the semantics, it is desirable to use operations applicable to situations that have less structure than prime theories have. In this talk, I define an operational semantics for the main positive relevance logics \(\mathbf{T_+}\), \(\mathbf{E_+}\) and \(\mathbf{R_+}\), that is, the positive fragments of the logics of ticket entailment, of entailment and of relevant implication. The operational structure for these logics is based on pieces of information and it is augmented with a topology (which is similar to the topology used in [1]). The logics are proved to be sound and complete for these operational semantics.

## Bibliography

- Bimbó, Katalin,
*Dual gaggle semantics for entailment*,, vol. 50 (2009), no. 1, pp. 23–41.*Notre Dame Journal of Formal Logic* - Bimbó, Katalin and J. Michael Dunn,
*The emergence of set-theoretical semantics for relevance logicsaround 1970*,, (Bimbó, K. and J. M. Dunn, editors), special issue of the*Proceedings of the Third Workshop, May 16–17, 2016,Edmonton, Canada*, vol. 4 (2017), no. 3, pp. 557–589.*IFCoLog Journal of Logics and theirApplications*