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Profile: Gemma Robles (Universidad de León (Spain))
  1. José M. Méndez, Gemma Robles & Francisco Salto (forthcoming). An Interpretation of Łukasiewicz’s 4-Valued Modal Logic. Journal of Philosophical Logic:1-15.
    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 and possibilist theses defined as follows: rt: the value of modal formulas is equivalent to the value of their respective argument iff A is true , etc.); pt: everything is possible. This presupposition highlights and explains all oddities arising in (...)
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  2. Gemma Robles (forthcoming). A Simple Henkin-Style Completeness Proof for Gödel 3-Valued Logic G3. Logic and Logical Philosophy.
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  3. Gemma Robles & José M. Méndez (Forthcoming). A Routley-Meyer Semantics for Truth-Preserving and Well-Determined Łukasiewicz 3-Valued Logics. Logic Journal of the Igpl.
    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 Ł3b.
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  4. Gemma Robles & José M. Méndez (2014). Curry's Paradox, Generalized Modus Ponens Axiom and Depth Relevance. Studia Logica 102 (1):185-217.
    “Weak relevant model structures” (wr-ms) are defined on “weak relevant matrices” by generalizing Brady’s model structure ${\mathcal{M}_{\rm CL}}$ built upon Meyer’s Crystal matrix CL. It is shown how to falsify in any wr-ms the Generalized Modus Ponens axiom and similar schemes used to derive Curry’s Paradox. In the last section of the paper we discuss how to extend this method of falsification to more general schemes that could also be used in deriving Curry’s Paradox.
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  5. Gemma Robles & José M. Méndez (2014). Generalizing the Depth Relevance Condition: Deep Relevant Logics Not Included in R-Mingle. Notre Dame Journal of Formal Logic 55 (1):107-127.
  6. Gemma Robles & José M. Méndez (2014). The Non-Relevant De Morgan Minimal Logic in Routley-Meyer Semantics with No Designated Points. Journal of Applied Non-Classical Logics 24 (4):321-332.
    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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  7. Gemma Robles (2013). Admissibility of Ackermann's Rule Δ in Relevant Logics. Logic and Logical Philosophy 22 (4):411-427.
    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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  8. Gemma Robles (2013). A Routley–Meyer Semantics for Gödel 3-Valued Logic and Its Paraconsistent Counterpart. Logica Universalis 7 (4):507-532.
    Routley–Meyer semantics (RM-semantics) is defined for Gödel 3-valued logic G3 and some logics related to it among which a paraconsistent one differing only from G3 in the interpretation of negation is to be remarked. The logics are defined in the Hilbert-style way and also by means of proof-theoretical and semantical consequence relations. The RM-semantics is defined upon the models for Routley and Meyer’s basic positive logic B+, the weakest positive RM-semantics. In this way, it is to be expected that the (...)
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  9. Gemma Robles, Francisco Salto & José M. Méndez (2013). Dual Equivalent Two-Valued Under-Determined and Over-Determined Interpretations for Łukasiewicz's 3-Valued Logic Ł3. Journal of Philosophical Logic (2-3):1-30.
    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 (by using Dunn semantics) dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension of Routley (...)
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  10. José M. Méndez, Gemma Robles & Francisco Salto (2012). Ticket Entailment Plus the Mingle Axiom has the Variable-Sharing Property. Logic Journal of the Igpl 20 (1):355-364.
    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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  11. Gemma Robles (2012). A Semantical Proof of the Admissibility of the Rule Assertion in Some Relevant and Modal Logics. Bulletin of the Section of Logic 41 (1/2):51-60.
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  12. Gemma Robles (2012). Paraconsistency and Consistency Understood as the Absence of the Negation of Any Implicative Theorem. Reports on Mathematical Logic:147-171.
     
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  13. Gemma Robles & José M. Méndez (2012). A General Characterization of the Variable-Sharing Property by Means of Logical Matrices. Notre Dame Journal of Formal Logic 53 (2):223-244.
    As is well known, the variable-sharing property (vsp) is, according to Anderson and Belnap, a necessary property of any relevant logic. In this paper, we shall consider two versions of the vsp, what we label the "weak vsp" (wvsp) and the "strong vsp" (svsp). In addition, the "no loose pieces property," a property related to the wvsp and the svsp, will be defined. Each one of these properties shall generally be characterized by means of a class of logical matrices. In (...)
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  14. Jose M. Mendez, Gemma Robles & Francisco Salto (2011). Adding the Disjunctive Syllogism to Relevant Logics Including TW Plus the Contraction and Reductio Rules. Logique Et Analyse 215:343-358.
     
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  15. Gemma Robles & José M. Méndez (2011). A Routley-Meyer Semantics for Relevant Logics Including TWR Plus the Disjunctive Syllogism. Logic Journal of the Igpl 19 (1):18-32.
    We provide Routley-Meyer type semantics for relevant logics including Contractionless Ticket Entailment TW (without the truth constant t and o) plus reductio R and Ackermann’s rule γ (i.e., disjunctive syllogism). These logics have the following properties. (i) All have the variable sharing property; some of them have, in addition, the Ackermann Property. (ii) They are stable. (iii) Inconsistent theories built upon these logics are not necessarily trivial.
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  16. Gemma Robles, Francisco Salto & José M. Méndez (2011). A Weak Logic with the Axiom Mingle Lacking the Variable-Sharing Property. Bulletin of the Section of Logic 40 (3/4):195-202.
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  17. Gemma Robles (2010). Minimal Non-Relevant Logics Without the K Axiom II. Negation Introduced Via the Unary Connective. Reports on Mathematical Logic:97-118.
     
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  18. Gemma Robles (2010). The Non-Involutive Routley Star: Relevant Logics Without Weak Double Negation. Teorema: Revista Internacional de Filosofía 29 (3):103-116.
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  19. Gemma Robles & José M. Méndez (2010). A Routley-Meyer Type Semantics for Relevant Logics Including B R Plus the Disjunctive Syllogism. Journal of Philosophical Logic 39 (2):139 - 158.
    Routley-Meyer type ternary relational semantics are defined for relevant logics including Routley and Meyer’s basic logic B plus the reductio rule and the disjunctive syllogism. Standard relevant logics such as E and R (plus γ ) and Ackermann’s logics of ‘strenge Implikation’ Π and Π ′ are among the logics considered.
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  20. Gemma Robles & José M. Méndez (2010). Axiomatizing S4+ and J+ Without the Suffixing, Prefixing and Self-Distribution of the Conditional Axioms. Bulletin of the Section of Logic 39 (1/2):79-91.
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  21. Gemma Robles & José M. Méndez (2010). Paraconsistent Logics Included in Lewis’ S4. Review of Symbolic Logic 3 (03):442-466.
    As is known, a logic S is paraconsistent if the rule ECQ (E contradictione quodlibet) is not a rule of S. Not less well known is the fact that Lewis’ modal logics are not paraconsistent. Actually, Lewis vindicates the validity of ECQ in a famous proof currently known as the “Lewis’ proof” or “Lewis’ argument.” This proof essentially leans on the Disjunctive Syllogism as a rule of inference. The aim of this paper is to define a series of paraconsistent logics (...)
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  22. Gemma Robles, José M. Méndez & Francisco Salto (2010). A Modal Restriction of R-Mingle with the Variable-Sharing Property. Logic and Logical Philosophy 19 (4):341-351.
    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.
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  23. José M. Méndez & Gemma Robles (2009). The Basic Constructive Logic for Absolute Consistency. Journal of Logic, Language and Information 18 (2):199-216.
    In this paper, consistency is understood as absolute consistency (i.e. non-triviality). The basic constructive logic BKc6, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending BKc6 up to contractionless intuitionistic logic. All logics defined in this paper are paraconsistent logics.
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  24. Gemma Robles (2009). Negation Introduced with the Unary Connective. Journal of Applied Non-Classical Logics 19 (3):371-388.
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  25. Gemma Robles & José M. Méndez (2009). Strong Paraconsistency and the Basic Constructive Logic for an Even Weaker Sense of Consistency. Journal of Logic, Language and Information 18 (3):357-402.
    In a standard sense, consistency and paraconsistency are understood as the absence of any contradiction and as the absence of the ECQ (‘E contradictione quodlibet’) rule, respectively. The concepts of weak consistency (in two different senses) as well as that of F -consistency have been defined by the authors. The aim of this paper is (a) to define alternative (to the standard one) concepts of paraconsistency in respect of the aforementioned notions of weak consistency and F -consistency; (b) to define (...)
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  26. Gemma Robles & José M. Méndez (2009). The Basic Constructive Logic for Weak Consistency and the Reductio Axioms. Bulletin of the Section of Logic 38 (1/2):61-76.
  27. José M. Méndez & Gemma Robles (2008). Relevance Logics and Intuitionistic Negation. Journal of Applied Non-Classical Logics 18 (1):49-65.
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  28. Gemma Robles (2008). A Note on the Non-Involutive Routley Star. Bulletin of the Section of Logic 37 (1):19-27.
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  29. Gemma Robles (2008). Extensions of the Basic Constructive Logic for Weak Consistency BKc1 Defined with a Falsity Constant. Logic and Logical Philosophy 16 (4):311-322.
    The logic BKc1 is the basic constructive logic for weak consistency (i.e., absence of the negation of a theorem) in the ternary relational semantics without a set of designated points. In this paper, a number of extensions of B Kc1 defined with a propositional falsity constant are defined. It is also proved that weak consistency is not equivalent to negation-consistency or absolute consistency (i.e., non-triviality) in any logic included in positive contractionless intermediate logic LC plus the constructive negation of BKc1 (...)
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  30. Gemma Robles (2008). Extensions of the Basic Constructive Logic for Negation-Consistency BKc4. Logique Et Analyse 51.
     
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  31. Gemma Robles (2008). The Basic Constructive Logic for Negation-Consistency. Journal of Logic, Language and Information 17 (2):161-181.
    In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction. The basic constructive logic BKc4, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending BKc4 up to minimal intuitionistic logic. All logics defined in this paper are paraconsistent logics.
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  32. Gemma Robles (2008). The Basic Constructive Logic for Absolute Consistency Defined with a Propositional Falsity Constant. Logic Journal of the Igpl 16 (3):275-291.
    The logic BKc6 is the basic constructive logic in the ternary relational semantics adequate to consistency understood as absolute consistency, i.e., non-triviality. Negation is introduced in BKc6 with a negation connective. The aim of this paper is to define the logic BKc6F. In this logic negation is introduced via a propositional falsity constant. We prove that BKc6 and BKc6F are definitionally equivalent. Then, we show how to extend BKc6F within the spectrum of logics delimited by contractionless intuitionistic logic. All logics (...)
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  33. Gemma Robles & José M. Méndez (2008). The Basic Constructive Logic for a Weak Sense of Consistency. Journal of Logic, Language and Information 17 (1):89-107.
    In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic BKc1 adequate to this sense of consistency in the ternary relational semantics without a set of designated points. Then we show how to define a series of logics extending BKc1 within the spectrum delimited by contractionless minimal intuitionistic logic. All logics defined in the paper are paraconsistent logics.
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  34. Gemma Robles, Francisco Salto & Jose M. Mendez (2008). Exhaustively Axiomatizing S3 (->) Degrees and S4 (->) Degrees. Teorema 27 (2):79-89.
     
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  35. Gemma Robles, Francisco Salto & José M. Méndez (2008). Exhaustively Axiomatizing S3°→ and S4°→. Teorema 27 (2):79-89.
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  36. José M. Méndez & Gemma Robles (2007). Relevance Logics, Paradoxes of Consistency and the K Rule II. A Non-Constructive Negation. Logic and Logical Philosophy 15 (3):175-191.
    The logic B+ is Routley and Meyer’s basic positive logic. We define the logics BK+ and BK'+ by adding to B+ the K rule and to BK+ the characteristic S4 axiom, respectively. These logics are endowed with a relatively strong non-constructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency.
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  37. José M. Méndez, Gemma Robles & Francisco Salto (2007). The Basic Constructive Logic for Negation-Consistency Defined with a Propositional Falsity Constant. Bulletin of the Section of Logic 36 (1-2):45-58.
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  38. José M. Méndez, Francisco Salto & Gemma Robles (2007). El Sistema Bp+ : Una Lógica Positiva Mínima Para la Negación Mínima (the System Bp+: A Minimal Positive Logic for Minimal Negation). Theoria 22 (1):81-91.
    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, some of (...)
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  39. Gemma Robles & Jose Mendez (2007). Minimal Non-Relevant Logics Without The K Axiom. Reports on Mathematical Logic.
    The logic B$_{+}$ is Routley and Meyer's basic positive logic. The logic B$_{K+}$ is B$_{+}$ plus the $K$ rule. We add to B$_{K+}$ four intuitionistic-type negations. We show how to extend the resulting logics within the modal and relevance spectra. We prove that all the logics defined lack the K axiom.
     
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  40. José Méndez & Gemma Robles (2006). Relevance Logics, Paradoxes Of Consistency And The K Rule Ii. Logic and Logical Philosophy 15:175-191.
    The logic B+ is Routley and Meyer’s basic positive logic. Wedefine the logics BK+ and BK′+ by adding to B+ the K rule and to BK+the characteristic S4 axiom, respectively. These logics are endowed witha relatively strong non-constructive negation. We prove that all the logicsdefined lack the K axiom and the standard paradoxes of consistency.
     
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  41. Gemma Robles & José M. Méndez (2006). Converse Ackermann Property and Constructive Negation Defined with a Negation Connective. Logic and Logical Philosophy 15 (2):113-130.
    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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  42. Gemma Robles & José M. Méndez (2005). A Constructive Negation for Logics Including TW+. Journal of Applied Non-Classical Logics 15 (4):389-404.
  43. Gemma Robles & José M. Méndez (2005). Constructive Negation Defined with a Falsity Constant for Positive Logics with the CAP Defined with a Truth Constant A. Logique Et Analyse 48 (192):87-100.
     
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  44. Gemma Robles & José M. Méndez (2005). Relational Ternary Semantics for a Logic Equivalent to Involutive Monoidal T-Norm Based Logic IMTL. Bulletin of the Section of Logic 34 (2):101-116.
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  45. Gemma Robles & José M. Méndez (2005). Two Versions of Minimal Intuitionism with the Cap. A Note. Theoria 20 (2):183-190.
    Two versions of minimal intuitionism are defined restricting Contraction. Both are defined by means of a falsity constant F. The first one follows the historical trend, the second is the result of imposing specialconstraints on F. RelationaI ternary semantics are provided.
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  46. Gemma Robles, Francisco Salto & José M. Méndez (2005). A Constructive Negation Defined with a Negation Connective for Logics Including Bp+. Bulletin of the Section of Logic 34 (3):177-190.
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  47. José Manuel Méndez Rodríguez & Gemma Robles (2005). Two Versions of Minimal Intuitionism with the CAP. A Note. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 20 (53):183-190.
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  48. Gemma Robles & José M. Méndez (2004). The Logic B and the Reductio Axioms. Bulletin of the Section of Logic 33 (2):87-94.
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  49. Gemma Robles (2003). Intutionistic Propositional Logic with the Converse Ackerman Poperty. Teorema 22 (1-2):46-54.
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  50. Francisco Salto, José M. Méndez & Gemma Robles (2001). Restricting the Contraction Axiom in Dummett's LC: A Sublogic of LC with the Converse Ackermann Property, the Logic LCo. Bulletin of the Section of Logic 30 (3):139-146.
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