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

Sandra M. López

Bulletin of the Section of Logic > 2022 > 51 > 1 > 27-56

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 specifically associated with the ternary relational semantics...

article

Four-Valued Paradefinite Logics

Ofer Arieli, Arnon Avron

Studia Logica > 2017 > 105 > 6 > 1087-1122

Paradefinite (‘beyond the definite’) logics are logics that can be used for handling contradictory or partial information. As such, paradefinite logics should be both paraconsistent and paracomplete. In this paper we consider the simplest semantic framework for introducing paradefinite logics. It consists of the four-valued matrices that expand the minimal matrix which is characteristic for first...

article

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

Gemma Robles, Sandra M. López, José M. Blanco, Marcos M. Recio, more

Bulletin of the Section of Logic > 2016 > 45 > 2

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.

article

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

Gemma Robles, José M. Blanco, Sandra M. López, Jesús R. Paradela, more

Logic and Logical Philosophy > 2016 > 25 > 2 > 173-201

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.

article

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

Gemma Robles

Logic and Logical Philosophy > 2016 > 25 > 2 > 173–201

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.

article

An Interpretation of Łukasiewicz’s 4-Valued Modal Logic

José M. Méndez, Gemma Robles, Francisco Salto

Journal of Philosophical Logic > 2016 > 45 > 1 > 73-87

A simple, bivalent semantics is defined for Łukasiewicz’s 4-valued modal logic Łm4. It is shown that according to this semantics, the essential presupposition underlying Łm4 is the following: A is a theorem iff A is true conforming to both the reductionist (rt) and possibilist (pt) theses defined as follows: rt: the value (in a bivalent sense) of modal formulas is equivalent to the value of their...

article

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

Wydawnictwo Uniwersytetu Łódzkiego, Gemma Robles, Sandra M López, José M Blanco, more

Bulletin of the Section of Logic > Bulletin of the Section of Logic 45/2 (2016)

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.

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Search results

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

Four-Valued Paradefinite Logics

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

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

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

An Interpretation of Łukasiewicz’s 4-Valued Modal Logic

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

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INFONA - science communication portal

Search results

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

Four-Valued Paradefinite Logics

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

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

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

An Interpretation of Łukasiewicz’s 4-Valued Modal Logic

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

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