A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4

Abstract

<jats:p>The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.</jats:p>

Belnap-Dunn Semantics for the Variants of BN4 and E4 which Contain Routley and Meyer’s Logic B

“…Furthermore, Brady endowed BN4 with a 2-set-up semantics when he first develop the system in [7]. As for E4, a 2-set-up semantics was developed in [20]. It is worth mentioning that a reduced Routley-Meyer semantics could be more difficult to develop for some Lti-logics due to the apparent ineliminability of disjunctive rules [cf.…”

Relational Semantics for the Paraconsistent and Paracomplete 4-valued Logic PŁ4

“…(1) The expansion of PŁ4 with necessity and possibility connectives defined by a binary accessibility relation introduced in 2bR-models, instead of defining said connectives with → and ¬ as shown in the appendix (similar to a corresponding expansion of the logic E4 as carried on in [12]).…”

“…In [2], 2 set-up RM-semantics (2RM-semantics, for short) is introduced and the logics BN4, RM3 and Łukasiewicz's 3-valued logic Ł3 are interpreted with this type of semantics. In [12], the logic E4 is also given a 2RM-semantics. The aim of this section is to add PŁ4 to this limited group of logics by endowing it with a 2RM-semantics, greatly simplifying the general RM-semantics.…”

“…2 set-up Routley-Meyer semantics (2RM-semantics) is appropriate for some 3-valued and 4-valued logics. 2RM-semantics was introduced in [2], but leaving aside [12], the topic has not been pursued, to the best of our knowledge. Finally, 2 set-up binary Routley semantics (2bR-semantics) is going to be introduced in the present paper when PŁ4 is given this kind of semantics.…”