53 research outputs found

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

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    The logics BN4 and E4 can be considered as the 4-valued logics of the relevant conditional and (relevant) entailment, respectively. The logic BN4 was developed by Brady in 1982 and the logic E4 by Robles and Méndez in 2016. The aim of this paper is to investigate the implicative variants (of both systems) which contain Routley and Meyer’s logic B and endow them with a Belnap-Dunn type bivalent semantics

    Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values

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    27 p.A conditional is natural if it fulfils the three following conditions. (1) It coincides with the classical conditional when restricted to the classical values T and F; (2) it satisfies the Modus Ponens; and (3) it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two designated elements. (We understand the notion ‘natural conditional’ according to N. Tomova, ‘A lattice of implicative extensions of regular Kleene's logics’, Reports on Mathematical Logic, 47, 173–182, 2012.)S

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

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    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

    Partiality and its dual in natural implicative expansions of Kleene’s strong 3-valued matrix with only one designated value

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    26 p.Equivalent overdetermined and underdetermined bivalent Belnap–Dunn type semantics for the logics determined by all natural implicative expansions of Kleene’s strong 3-valued matrix with only one designated value are provided.S

    The class of all 3-valued natural conditional variants of RM3 that are Plumwood Algebras

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    Valerie Plumwood introduced in "Some false laws of logic" a series of arguments on how the rules Exported Syllogism, Disjunctive Syllogism, Commutation, and Exportation are not acceptable. Based on this we define the class of Plumwood algebras - logical matrices that do not verify any of these theses. Afterwards we provide conditional variants of the characteristic matrix of the logic RM3 that are also Plumwood algebras. These matrices are given an axiomatization based on First Degree Entailment and are endowed with Belnap-Dunn Semantics. Finally we provide results of Soundness and Completeness in the strong sense for each of the defined variants

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

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    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
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