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Profile: José M. Méndez (Universidad de Salamanca)
  1. 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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  2. José M. Méndez (2010). A Routley-Meyer Semantics for Ackermann's Logics of “Strenge Implication”. Logic and Logical Philosophy 18 (3-4):191-219.
    The aim of this paper is to provide a Routley-Meyer semantics for Ackermann’s logics of “strenge Implikation” Π ′ and Π ′′ . Besides the Disjunctive Syllogism, this semantics validates the rules Necessitation and Assertion. Strong completeness theorems for Π ′ and Π ′′ are proved. A brief discussion on Π ′ , Π ′′ and paraconsistency is included.
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  3.  20
    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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  4. 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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  5.  3
    José M. Méndez & Gemma Robles (forthcoming). The Logic Determined by Smiley’s Matrix for Anderson and Belnap’s First-Degree Entailment Logic. Journal of Applied Non-Classical Logics:1-22.
    The aim of this paper is to define the logical system Sm4 characterised by the degree of truth-preserving consequence relation defined on the ordered set of values of Smiley’s four-element matrix MSm4. The matrix MSm4 has been of considerable importance in the development of relevant logics and it is at the origin of bilattice logics. It will be shown that Sm4 is a most interesting paraconsistent logic which encloses a sound theory of logical necessity similar to that of Anderson and (...)
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  6.  16
    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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  7.  28
    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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  8.  16
    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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  9.  16
    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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  10.  7
    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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  11.  8
    José M. Méndez & Gemma Robles (2015). A Strong and Rich 4-Valued Modal Logic Without Łukasiewicz-Type Paradoxes. Logica Universalis 9 (4):501-522.
    The aim of this paper is to introduce an alternative to Łukasiewicz’s 4-valued modal logic Ł. As it is known, Ł is afflicted by “Łukasiewicz type paradoxes”. The logic we define, PŁ4, is a strong paraconsistent and paracomplete 4-valued modal logic free from this type of paradoxes. PŁ4 is determined by the degree of truth-preserving consequence relation defined on the ordered set of values of a modification of the matrix MŁ characteristic for the logic Ł. On the other hand, PŁ4 (...)
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  12.  10
    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. (...)
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  13.  4
    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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  14.  13
    José M. Mendez (1988). 1. Select List of Representative Theses. Bulletin of the Section of Logic 17 (1):15-20.
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  15.  13
    Gemma Robles & José M. Méndez (2005). A Constructive Negation for Logics Including TW+. Journal of Applied Non-Classical Logics 15 (4):389-404.
  16.  13
    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.
  17.  13
    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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  18.  3
    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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  19.  15
    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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  20.  13
    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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  21. Gemma Robles & José M. Méndez (2010). A Routley-Meyer Type Semantics for Relevant Logics Including Br Plus the Disjunctive Syllogism. Journal of Philosophical Logic 39 (2):139-158.
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  22.  9
    Francisco Salto & José M. Méndez (1999). Two Extensions of Lewis' S3 with Peirce's Law. Theoria 14 (3):407-411.
    We define two extensions of Lewis’ S3 with two versions of Peirce’s Law. We prove that both of them have the Ackermann Property.
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  23.  25
    José M. Méndez, A Note on "Recent Work in Relevant Logic".
    In his paper “Recent work in relevant logic”, Jago includes a section on Disjunctive Syllogism . The content of the section essentially consists of (a) a valuation of some work by Robles and Méndez on the topic as “not particularly interesting in itself”; (b) a statement establishing that “What would be interesting is to discover just how weak a relevant logic needs to be before disjunctive syllogism becomes inadmissible”. The main problem with this section of Jago’s paper on DS is (...)
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  24.  2
    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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  25.  26
    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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  26.  10
    José M. Méndez (1987). Axiomatizing E→ and R→ with Anderson and Belnap's 'Strong and Natural'list of Valid Entailments. Bulletin of the Section of Logic 16 (1):2-7.
    We provide all possible axiomatizations with independent axioms of E→ and R→ formulable with Anderson and Belnap’s list.
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  27.  1
    José M. Méndez & Gemma Robles (2016). Strengthening Brady’s Paraconsistent 4-Valued Logic BN4 with Truth-Functional Modal Operators. Journal of Logic, Language and Information 25 (2):163-189.
    Łukasiewicz presented two different analyses of modal notions by means of many-valued logics: the linearly ordered systems Ł3,...,,..., \; the 4-valued logic Ł he defined in the last years of his career. Unfortunately, all these systems contain “Łukasiewicz type paradoxes”. On the other hand, Brady’s 4-valued logic BN4 is the basic 4-valued bilattice logic. The aim of this paper is to show that BN4 can be strengthened with modal operators following Łukasiewicz’s strategy for defining truth-functional modal logics. The systems we (...)
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  28.  7
    Francisco Salto, Gemma Robles & José M. Méndez (1999). Exhaustively Axiomatizing Rmo→ with a Select List of Representative Theses Including Restricted Mingle Principles. Bulletin of the Section of Logic 28 (4):195-206.
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  29.  8
    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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  30.  24
    José M. Mendez & Francisco Salto (1998). A Natural Negation Completion of Urquhart's Many-Valued Logic C. Journal of Philosophical Logic 27 (1):75-84.
  31.  10
    José M. Méndez (1985). Systems with the Converse Ackermann Property. Theoria 1 (1):253-258.
    A system S has the “converse Ackermann property” (C.A.P.) if (A -> B) -> C is unprovable in S whenever C is a propositional variable. In this paper we define the fragments with the C.A.P. of some well-know propositional systems in the spectrum between the minimal and classical logic. In the first part we succesively study the implicative and positive fragments and the full calculi. In the second, we prove by a matrix method that each one of the systems has (...)
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  32.  10
    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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  33.  10
    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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  34.  9
    José M. Méndez (1990). Exhaustively Axiomatizing RMO with an Appropiate Extension of Anderson and Belnap's “Strong and Natural List of Valid Entailments”. Theoria 5 (1):223-228.
    RMO -> is the result of adding the ‘mingle principle’ (viz. A-> (A -> A)) to Anderson and Belnap’s implicative logic of relevance R->. The aim of this paper is to provide all possible axiomatizations with independent axioms of RMO -> formulable with Anderson and Belnap’s list extended with three characteristic minglish principles.
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  35.  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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  36.  8
    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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  37.  4
    José M. Méndez (1987). Constructive R. Bulletin of the Section of Logic 16 (4):167-173.
    Let R+ be the positive fragment of Anderson and Belnap’s Logic of Relevance, R. And let RMO+ be the result of adding the Mingle principle ) to R+. We have shown in [2] that either a minimal negation or else a semiclassical one can be added to RMO+ preserving the variable-sharing property. Moreover, each of there systems is given a semantics in the Routley-Meyer style. In describing in [2] the models for RMO+ plus minimal negation, we noted that a similar (...)
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  38.  23
    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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  39.  5
    José M. Méndez (1987). A Routley-Meyer Semantics for Converse Ackermann Property. Journal of Philosophical Logic 16 (1):65 - 76.
  40.  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 (...)
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  41.  5
    José M. Méndez (1990). Urquhart'sc with Minimal Negation. Bulletin of the Section of Logic 19 (1):15-20.
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  42.  2
    José M. Méndez, Gemma Robles & Francisco Salto (2016). An Interpretation of Łukasiewicz’s 4-Valued Modal Logic. Journal of Philosophical Logic 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 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 Łm4.
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  43.  2
    José M. Méndez (1986). Una crítica inmanente de la lógica de la relevancia. Critica 18 (52):61 - 94.
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  44.  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.
  45.  11
    José M. Méndez (1988). Converse Ackermann Croperty and Semiclassical Negation. Studia Logica 47 (2):159 - 168.
    A prepositional logic S has the Converse Ackermann Property (CAP) if (AB)C is unprovable in S when C does not contain . In A Routley-Meyer semantics for Converse Ackermann Property (Journal of Philosophical Logic, 16 (1987), pp. 65–76) I showed how to derive positive logical systems with the CAP. There I conjectured that each of these positive systems were compatible with a so-called semiclassical negation. In the present paper I prove that this conjecture was right. Relational Routley-Meyer type semantics are (...)
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  46.  9
    José M. Méndez (2010). Erratum To: The Compatibility of Relevance and Mingle. [REVIEW] Journal of Philosophical Logic 39 (3):339-339.
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  47.  1
    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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  48.  4
    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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  49.  8
    José M. Méndez (1988). The Compatibility of Relevance and Mingle. Journal of Philosophical Logic 17 (3):279 - 297.
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  50. Vladimir Markin, Dmitry Zaitsev, Imaginary Logic, Lloyd Humberstone, Implicational Converses, Jose M. Mendez, Francisco Salto, Pedro Mendez, Roger Vergauwen & Ray Lam (2002). Tjeerd B. Jongeling, Teun Koetsier & Evert Wattel, a Logical Approach to Qualitative Reasoning With'several'... 15. Logique Et Analyse 45:1.
     
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