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32Routley-Meyer ternary relational semantics for intuitionistic-type negationsElsevier, Academic Press. 2018.Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations examines how to introduce intuitionistic-type negations into RM-semantics. RM-semantics is highly malleable and capable of modeling families of logics which are very different from each other. This semantics was introduced in the early 1970s, and was devised for interpreting relevance logics. In RM-semantics, negation is interpreted by means of the Routley operator, which has been almost exclusively used for modeling De…Read more
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32A Routley-Meyer semantics for truth-preserving and well-determined Lukasiewicz 3-valued logicsLogic Journal of the IGPL 22 (1): 1-23. 2014.Łukasiewicz 3-valued logic Ł3 is often understood as the set of all valid formulas according to Łukasiewicz 3-valued matrices MŁ3. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: ‘truth-preserving’ Ł3a and ‘well-determined’ Ł3b defined by two different consequence relations on the 3-valued matrices MŁ3. The aim of this article is to provide a Routley–Meyer ternary semantics for each one of these three versions of Łukasiewicz 3-valued logic: Ł3, Ł3a and Ł…Read more
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31Basic Quasi-Boolean Expansions of Relevance LogicsJournal of Philosophical Logic 50 (4): 727-754. 2021.The basic quasi-Boolean negation expansions of relevance logics included in Anderson and Belnap’s relevance logic R are defined. We consider two types of QB-negation: H-negation and D-negation. The former one is of paraintuitionistic or superintuitionistic character, the latter one, of dual intuitionistic nature in some sense. Logics endowed with H-negation are paracomplete; logics with D-negation are paraconsistent. All logics defined in the paper are given a Routley-Meyer ternary relational se…Read more
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31A paraconsistent 3-valued logic related to Godel logic G3Logic Journal of the IGPL 22 (4): 515-538. 2014.
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31A weak logic with the axiom Mingle lacking the variable-sharing propertyBulletin of the Section of Logic 40 (3/4): 195-202. 2011.As it is well known, Relevance Logic R plus the axiom mingle (R-Mingle) does not have the variable-sharing property (vsp). The aim of this paper is to improve this result by defining a weak logic with the axiom mingle and not included in minimal logic BM lacking the vsp.
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31Axiomatizing s4+ and j+ without the suffixing, prefixing and self-distribution of the conditional axiomsBulletin of the Section of Logic 39 (1/2): 79-91. 2010.
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30Ticket Entailment plus the mingle axiom has the variable-sharing propertyLogic Journal of the IGPL 20 (1): 355-364. 2012.The logic TM is the result of adding the mingle axiom, M to Ticket Entailment logic, T. In the present study, it is proved that TM has the variable-sharing property . Ternary relational semantics for TM is provided. Finally, an interesting extension of TM with the vsp is briefly discussed
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30Converse Ackermann property and constructive negation defined with a negation connectiveLogic and Logical Philosophy 15 (2): 113-130. 2006.The Converse Ackermann Property is the unprovability of formulas of the form (A -> B) -> C when C does contain neither -> nor ¬. Intuitively, the CAP amounts to rule out the derivability of pure non-necessitive propositions from non-necessitive ones. A constructive negation of the sort historically defined by, e.g., Johansson is added to positive logics with the CAP in the spectrum delimited by Ticket Entailment and Dummett’s logic LC
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30Admissibility of Ackermann's rule δ in relevant logicsLogic and Logical Philosophy 22 (4): 411-427. 2013.It is proved that Ackermann’s rule δ is admissible in a wide spectrum of relevant logics satisfying certain syntactical properties
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28A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4Bulletin 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 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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28Generalizing the Depth Relevance Condition: Deep Relevant Logics Not Included in R-MingleNotre Dame Journal of Formal Logic 55 (1): 107-127. 2014.
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27The basic constructive logic for weak consistency and the reductio axiomsBulletin of the Section of Logic 38 (1/2): 61-76. 2009.
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27Relational ternary semantics for a logic equivalent to Involutive Monoidal t-norm based logic IMTLBulletin of the Section of Logic 34 (2): 101-116. 2005.
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27A binary Routley semantics for intuitionistic De Morgan minimal logic HM and its extensionsLogic Journal of the IGPL 23 (2): 174-193. 2015.
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26The non-relevant De Morgan minimal logic in Routley-Meyer semantics with no designated pointsJournal of Applied Non-Classical Logics 24 (4): 321-332. 2014.Sylvan and Plumwood’s is the relevant De Morgan minimal logic in the Routley-Meyer semantics with a set of designated points. The aim of this paper is to define the logic and some of its extensions. The logic is the non-relevant De Morgan minimal logic in the Routley-Meyer semantics without a set of designated points
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26A Variety of DeMorgan Negations in Relevant LogicsAustralasian Journal of Logic 20 (2): 348-374. 2023.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 se…Read more
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25Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix II. Only one designated valueJournal of Applied Non-Classical Logics 29 (3): 307-325. 2019.This paper is a sequel to ‘Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values’, where a ‘bivalent’ Belnap-Dunn semantics is provided for all the expansions referred to in its title. The aim of the present paper is to carry out a parallel investigation for all natural implicative expansions of Kleene's strong 3-valued matrix now with only one designated value.
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25A Class of Simpler Logical Matrices for the Variable-Sharing PropertyLogic and Logical Philosophy 20 (3): 241-249. 2011.In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′serving the same purpose that RMLs, to wit: any logic verified by an RML′has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R
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24A Basic Dual Intuitionistic Logic and Some of its Extensions Included in G3DHJournal of Logic, Language and Information 30 (1): 117-138. 2020.The logic DHb is the result of extending Sylvan and Plumwood’s minimal De Morgan logic BM with a dual intuitionistic negation of the type Sylvan defined for the extension CCω of da Costa’s paraconsistent logic Cω. We provide Routley–Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3DH, the expansion of G3+ with a dual intuitionistic negation of the kind considered by Sylvan (G3+ is the positive fragment of Gödelian 3-valued lo…Read more
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24El sistema Bp+ : una lógica positiva mínima para la negación mínima (The system Bp+: a minimal positive logic for minimal negation)Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 22 (1): 81-91. 2007.Entendemos el concepto de “negación mínima” en el sentido clásico definido por Johansson. El propósito de este artículo es definir la lógica positiva mínima Bp+, y probar que la negación mínima puede introducirse en ella. Además, comentaremos algunas de las múltiples extensiones negativas de Bp+.“Minimal negation” is classically understood in a Johansson sense. The aim of this paper is to define the minimal positive logic Bp+ and prove that a minimal negation can be inroduced in it. In addition,…Read more
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23Exhaustively Axiomatizing S3°→ and S4°→Teorema: International Journal of Philosophy 27 (2): 79-89. 2008.S3o and S4o are the restrictions with the Converse Ackermann Property of the implicative fragments of Lewis' S3 and S4 respectively. The aim of this paper is to provide all possible axiomatizations with independent axioms of S3o and S4o that can be formulated with a modification of Anderson and Belnap's list of valid entailments.
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22A constructive negation defined with a negation connective for logics including Bp+Bulletin of the Section of Logic 34 (3): 177-190. 2005.The concept of constructive negation we refer to in this paper is (minimally) intuitionistic in character (see [1]). The idea is to understand the negation of a proposition A as equivalent to A implying a falsity constant of some sort. Then, negation is introduced either by means of this falsity constant or, as in this paper, by means of a propositional connective defined with the constant. But, unlike intuitionisitc logic, the type of negation we develop here is, of course, devoid of paradoxes …Read more
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21Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated valuesJournal of Applied Non-Classical Logics 29 (1): 37-63. 2019.ABSTRACTA conditional is natural if it fulfils the three following conditions. It coincides with the classical conditional when restricted to the classical values T and F; it satisfies the Modus Ponens; and 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 …Read more
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21Exhaustively axiomatizing rmo→ with a select list of representative theses including restricted Mingle principlesBulletin of the Section of Logic 28 (4): 195-206. 1999.
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20A companion to Brady's 4-valued relevant logic BN4: The 4-valued logic of entailment E4Logic Journal of the IGPL 24 (5). 2016.
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20A Class of Implicative Expansions of Kleene’s Strong Logic, a Subclass of Which Is Shown Functionally Complete Via the Precompleteness of Łukasiewicz’s 3-Valued Logic Ł3Journal of Logic, Language and Information 30 (3): 533-556. 2021.The present paper is a sequel to Robles et al. :349–374, 2020. https://doi.org/10.1007/s10849-019-09306-2). A class of implicative expansions of Kleene’s 3-valued logic functionally including Łukasiewicz’s logic Ł3 is defined. Several properties of this class and/or some of its subclasses are investigated. Properties contemplated include functional completeness for the 3-element set of truth-values, presence of natural conditionals, variable-sharing property and vsp-related properties.
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20Dual Equivalent Two-valued Under-determined and Over-determined Interpretations for Łukasiewicz’s 3-valued Logic Ł3Journal of Philosophical Logic 43 (2-3): 303-332. 2014.Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic…Read more
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17A Class of Implicative Expansions of Belnap-Dunn Logic in which Boolean Negation is DefinableJournal of Philosophical Logic 52 (3): 915-938. 2023.Belnap and Dunn’s well-known 4-valued logic FDE is an interesting and useful non-classical logic. FDE is defined by using conjunction, disjunction and negation as the sole propositional connectives. Then the question of expanding FDE with an implication connective is of course of great interest. In this sense, some implicative expansions of FDE have been proposed in the literature, among which Brady’s logic BN4 seems to be the preferred option of relevant logicians. The aim of this paper is to d…Read more
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16Blocking the Routes to Triviality with Depth RelevanceJournal of Logic, Language and Information 23 (4): 493-526. 2014.In Rogerson and Restall’s, the “class of implication formulas known to trivialize ” is recorded. The aim of this paper is to show how to invalidate any member in this class by using “weak relevant model structures”. Weak relevant model structures verify deep relevant logics only.
Gemma Robles
Universidad de León
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Universidad de LeónRegular Faculty
León, CL, Spain
Areas of Specialization
Logic and Philosophy of Logic |
Areas of Interest
Logic and Philosophy of Logic |