Reduced Routley-Meyer semantics for the logics characterized by natural implicative expansions of Kleene's strong 3-valued matrix

15 p.The aim of this paper is to provide a reduced Routley-Meyer semantics for the logics characterized by all natural implicative expansions of Kleene’s strong 3-valued matrix (with two designated values, as well as with only one) susceptible to be interpreted in Routley-Meyer semantics.S

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

The paraconsistent and paracomplete 4-valued logic PŁ4 is originally interpreted with a two-valued Belnap-Dunn semantics. In the present paper, PŁ4 is endowed with both a ternary Routley-Meyer semantics and a binary Routley semantics together with their respective restriction to the 2 set-up cases

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

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

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

[EN] The paraconsistent and paracomplete 4-valued logic PŁ4 is originally interpreted with a two-valued Belnap-Dunn semantics. In the present paper, PŁ4 is endowed with both a ternary Routley-Meyer semantics and a binary Routley semantics together with their respective restriction to the 2 set-up cases.SIMinisterio de Ciencia e Innovación (MCIN/AEI/ 10.13039/501100011033

Some Concerns Regarding Ternary-relation Semantics and Truth-theoretic Semantics in General

This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment

Ternary Relational Semantics for the Variants of BN4 and E4 which Contain Routley and Meyer's Logic B

[EN]Six interesting variants of the logics BN4 and E4|which can be considered as the 4-valued logics of the relevant conditional and (relevant) entailment, respectively| were previously developed in the literature. All these systems are related to the family of relevant logics and contain Routley and Meyer's basic logic B, which is well-known to be speci cally associated with the ternary relational semantics. The aim of this paper is to develop reduced general Routley-Meyer semantics for them. Strong soundness and completeness theorems are proved for each one of the logics

The Relevant Logic E and Some Close Neighbours: A Reinterpretation

This paper has two aims. First, it sets out an interpretation of the relevant logic E of relevant entailment based on the theory of situated inference. Second, it uses this interpretation, together with Anderson and Belnap’s natural deduc- tion system for E, to generalise E to a range of other systems of strict relevant implication. Routley–Meyer ternary relation semantics for these systems are produced and completeness theorems are proven

A Variety of DeMorgan Negations in Relevant Logics

The present paper is inspired by Sylvan and Plumwood’s logicBM defined in “Non-normal relevant logics” and by their treatmentof negation with the ∗-operator in “The semantics of first-degree en-tailment”. Given a positive logic L including Routley and Meyer’sbasic positive logic and included in either the positive fragment of Eor in that of RW, we investigate the essential De Morgan negation ex-pansions of L and determine all the deductive relations they maintainto each other. A Routley-Meyer semantics is provided for each logicdefined in the paper

Logically Impossible Worlds

What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically impossible world, the laws of logic fail. In this paper, I provide a definition of logically impossible worlds. I then show that there is nothing strange about admitting such worlds