Natural implicative expansions of variants of Kleene's strong 3-valued logic with Gödel-type and dual Gödel-type negation

Robles, Gemma; Méndez, José M.

doi:10.1080/11663081.2021.1948285

Cited by 2 publications

(1 citation statement)

References 24 publications

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“…By using a Belnap-Dunn bivalent semantics (cf. [7], [8], [12], [13]), Hilbert-style axiomatic systems corresponding to TI 0 -logics (resp., TII 0logics; resp., TIV 0 -logics) are defined in [31] (resp., in [35]; resp., in [33]) in a general and unified way (cf. also [30], [32], [34] and [26]).…”

Section: Discussionmentioning

confidence: 99%

The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łkasiewicz’s 3-Valued Logic Ł3

Robles

Méndez

2019

J of Log Lang and Inf

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We consider the logics determined by the set of all natural implicative expansions of Kleene's strong 3-valued matrix (with both only one and two designated values) and select the class of all logics functionally equivalent to Łukasiewicz's 3-valued logic Ł3. The concept of a "natural implicative matrix" is based upon the notion of a "natural conditional" defined in Tomova (2012), "A lattice of implicative extensions of regular Kleene's logics", Reports on Mathematical Logic 47, pp. 173-182.

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Section: Discussionmentioning

confidence: 99%

The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łkasiewicz’s 3-Valued Logic Ł3

Robles

Méndez

2019

J of Log Lang and Inf

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Two 4-valued implicative expansions of first-degree entailment logic: The relevant logic BN4VSP and the (relevant) entailment logic BN4AP

Robles

2023

Journal of Logic and Computation

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A logic L has the ‘variable-sharing property’ (VSP) if in all L-theorems of the form $A\rightarrow B$, $A$ and $B$ share at least a propositional variable. A logic L has the ‘Ackermann property’ (AP) if in all L-theorems of the form $A\rightarrow (B\rightarrow C)$, $A$ contains at least a conditional connective ($\rightarrow $). Anderson and Belnap consider the VSP a necessary property of any relevant logic, and both the VSP and the AP necessary properties of any (relevant) entailment logic. Now, among relevant logicians, Brady’s logic BN4 is widely viewed as the adequate 4-valued implicative logic. But BN4 lacks the VSP and the AP. The aim of this paper is to define the logics BN4$^{\text {VSP}}$ and BN4$^{\text {AP}}$. The former one has the VSP, whereas the latter one has the VSP and the AP. Moreover, both logics have some properties that do not support their consideration as mere artificial constructs.

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Natural implicative expansions of variants of Kleene's strong 3-valued logic with Gödel-type and dual Gödel-type negation

Cited by 2 publications

References 24 publications

The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łkasiewicz’s 3-Valued Logic Ł3

The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łkasiewicz’s 3-Valued Logic Ł3

Two 4-valued implicative expansions of first-degree entailment logic: The relevant logic BN4VSP and the (relevant) entailment logic BN4AP

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