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1

Relational semantics for the 4-valued relevant logics BN4 and E4

100%
Robles G.
Logic and Logical Philosophy
|
2016
|
vol. 25
|
issue 2
173–201
EN
The logic BN4 was defined by R.T. Brady in 1982. It can be considered as the 4-valued logic of the relevant conditional. E4 is a variant of BN4 that can be considered as the 4-valued logic of (relevant) entailment. The aim of this paper is to define reduced general Routley-Meyer semantics for BN4 and E4. It is proved that BN4 and E4 are strongly sound and complete w.r.t. their respective semantics.
2

A simple Henkin-style completeness proof for Gödel 3-valued logic G3

100%
Robles G.
Logic and Logical Philosophy
|
2014
|
vol. 23
|
issue 4
371–390
EN
A simple Henkin-style completeness proof for Gödel 3-valued propositional logic G3 is provided. The idea is to endow G3 with an under-determined semantics (u-semantics) of the type defined by Dunn. The key concept in u-semantics is that of “under-determined interpretation” (u-interpretation). It is shown that consistent prime theories built upon G3 can be understood as (canonical) u-interpretations. In order to prove this fact we follow Brady by defining G3 as an extension of Anderson and Belnap’s positive fragment of First Degree Entailment Logic.
3

A modal restriction of R-Mingle with the variable-sharing property

51%
Robles G., Méndez J. M., Salto F.
Logic and Logical Philosophy
|
2010
|
vol. 19
|
issue 4
341–351
EN
A restriction of R-Mingle with the variable-sharing property and the Ackermann properties is defined. From an intuitive semantical point of view, this restriction is an alternative to Anderson and Belnap’s logic of entailment E.
4
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Relational semantics for the 4-valued relevant logics BN4 and E4

45%
Robles G., Blanco J. M., López S. M., Paradela J. R., Recio M. M.
Logic and Logical Philosophy
|
2016
|
vol. 25
|
issue 2
173-201
EN
The logic BN4 was defined by R.T. Brady in 1982. It can be considered as the 4-valued logic of the relevant conditional. E4 is a variant of BN4 that can be considered as the 4-valued logic of (relevant) entailment. The aim of this paper is to define reduced general Routley-Meyer semantics for BN4 and E4. It is proved that BN4 and E4 are strongly sound and complete w.r.t. their respective semantics.
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