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José M. Méndez
Universidad de Salamanca
  1.  10
    Belnap-Dunn Semantics for Natural Implicative Expansions of Kleene's Strong Three-Valued Matrix with Two Designated Values.Gemma Robles & José M. Méndez - 2019 - Journal of Applied Non-Classical Logics 29 (1):37-63.
    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 two (...)
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  2.  8
    Belnap-Dunn Semantics for Natural Implicative Expansions of Kleene's Strong Three-Valued Matrix II. Only One Designated Value.Gemma Robles, Francisco Salto & José M. Méndez - 2019 - Journal of Applied Non-Classical Logics 29 (3):307-325.
    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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  3.  27
    An Interpretation of Łukasiewicz’s 4-Valued Modal Logic.José M. Méndez, Gemma Robles & Francisco Salto - 2016 - 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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  4.  67
    The Basic Constructive Logic for a Weak Sense of Consistency.Gemma Robles & José M. Méndez - 2008 - 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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  5. A Modal Restriction of R-Mingle with the Variable-Sharing Property.Gemma Robles, José M. Méndez & Francisco Salto - 2010 - 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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  6. A Routley-Meyer Semantics for Ackermann's Logics of “Strenge Implication”.José M. Méndez - 2009 - 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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  7.  73
    A Routley-Meyer Type Semantics for Relevant Logics Including B R Plus the Disjunctive Syllogism.Gemma Robles & José M. Méndez - 2010 - 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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  8.  5
    Partiality and its Dual in Natural Implicative Expansions of Kleene’s Strong 3-Valued Matrix with Only One Designated Value.Gemma Robles & José M. Méndez - 2019 - Logic Journal of the IGPL 27 (6):910-932.
    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.
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  9.  5
    Dual Equivalent Two-Valued Under-Determined and Over-Determined Interpretations for Łukasiewicz’s 3-Valued Logic Ł3.Gemma Robles, Francisco Salto & José M. Méndez - 2014 - Journal of Philosophical Logic 43 (2-3):303-332.
    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 Ł3 is axiomatized as an extension of Routley and Meyer’s basic positive (...)
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  10.  24
    A General Characterization of the Variable-Sharing Property by Means of Logical Matrices.Gemma Robles & José M. Méndez - 2012 - 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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  11.  17
    Minimal Negation in the Ternary Relational Semantics.Gemma Robles, José M. Méndez & Francisco Salto - 2005 - Reports on Mathematical Logic 39:47-65.
    Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Thus, by defining a number of subminimal negations in the B+ context, principles of weak negation are shown to be isolable. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable (in ternary frames) without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended positive logic are offered.
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  12.  24
    Dual Equivalent Two-Valued Under-Determined and Over-Determined Interpretations for Łukasiewicz's 3-Valued Logic Ł3.Gemma Robles, Francisco Salto & José M. Méndez - 2013 - 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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  13.  31
    A Strong and Rich 4-Valued Modal Logic Without Łukasiewicz-Type Paradoxes.José M. Méndez & Gemma Robles - 2015 - 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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  14. A Routley-Meyer Semantics for Relevant Logics Including TWR Plus the Disjunctive Syllogism.Gemma Robles & José M. Méndez - 2011 - 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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  15.  16
    The Non-Relevant De Morgan Minimal Logic in Routley-Meyer Semantics with No Designated Points.Gemma Robles & José M. Méndez - 2014 - 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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  16.  27
    Strengthening Brady’s Paraconsistent 4-Valued Logic BN4 with Truth-Functional Modal Operators.José M. Méndez & Gemma Robles - 2016 - 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,..., Open image in new window,..., \; 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 (...)
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  17.  18
    The Logic Determined by Smiley’s Matrix for Anderson and Belnap’s First-Degree Entailment Logic.José M. Méndez & Gemma Robles - 2016 - Journal of Applied Non-Classical Logics 26 (1):47-68.
    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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  18.  30
    Relevance Logics, Paradoxes of Consistency and the K Rule II. A Non-Constructive Negation.José M. Méndez & Gemma Robles - 2007 - 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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  19.  16
    The Logic B and the Reductio Axioms.Gemma Robles & José M. Méndez - 2004 - Bulletin of the Section of Logic 33 (2):87-94.
  20.  12
    Ticket Entailment Plus the Mingle Axiom has the Variable-Sharing Property.José M. Méndez, Gemma Robles & Francisco Salto - 2012 - 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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  21.  55
    Curry’s Paradox, Generalized Modus Ponens Axiom and Depth Relevance.Gemma Robles & José M. Méndez - 2014 - 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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  22.  8
    Blocking the Routes to Triviality with Depth Relevance.Gemma Robles & José M. Méndez - 2014 - Journal of Logic, Language and Information 23 (4):493-526.
    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.
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  23.  98
    Two Versions of Minimal Intuitionism with the Cap. A Note.Gemma Robles & José M. Méndez - 2005 - 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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  24.  23
    Erratum To: The Compatibility of Relevance and Mingle. [REVIEW]José M. Méndez - 2010 - Journal of Philosophical Logic 39 (3):339-339.
  25.  21
    Restricting the Contraction Axiom in Dummett's LC: A Sublogic of LC with the Converse Ackermann Property, the Logic LCo.Francisco Salto, José M. Méndez & Gemma Robles - 2001 - Bulletin of the Section of Logic 30 (3):139-146.
  26.  13
    Generalizing the Depth Relevance Condition: Deep Relevant Logics Not Included in R-Mingle.Gemma Robles & José M. Méndez - 2014 - Notre Dame Journal of Formal Logic 55 (1):107-127.
  27.  26
    The Compatibility of Relevance and Mingle.José M. Méndez - 1988 - Journal of Philosophical Logic 17 (3):279 - 297.
  28.  16
    Converse Ackermann Property and Constructive Negation Defined with a Negation Connective.Gemma Robles & José M. Méndez - 2006 - 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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  29.  19
    Relational Ternary Semantics for a Logic Equivalent to Involutive Monoidal T-Norm Based Logic IMTL.Gemma Robles & José M. Méndez - 2005 - Bulletin of the Section of Logic 34 (2):101-116.
  30.  66
    A Constructive Negation for Logics Including TW+.Gemma Robles & José M. Méndez - 2005 - Journal of Applied Non-Classical Logics 15 (4):389-404.
    The logic TW+ is positive Ticket Entailment without the contraction axiom. Constructive negation is understood in the intuitionistic sense but without paradoxes of relevance. It is shown how to introduce a constructive negation of this kind in positive logics at least as strong as TW+. Special attention is paid to the reductio axioms. Concluding remarks about relevance, modal and entailment logics are stated. Complete relational ternary semantics are provided for the logics introduced in this paper.
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  31.  23
    Axiomatizing S4+ and J+ Without the Suffixing, Prefixing and Self-Distribution of the Conditional Axioms.Gemma Robles & José M. Méndez - 2010 - Bulletin of the Section of Logic 39 (1/2):79-91.
  32.  35
    Paraconsistent Logics Included in Lewis’ S4.Gemma Robles & José M. Méndez - 2010 - Review of Symbolic Logic 3 (3):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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  33.  43
    Systems with the Converse Ackermann Property.José M. Méndez - 1985 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 1 (1):253-258.
    A system S has the “converse Ackermann property” if -> 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 the C.A.P. Thus, we (...)
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  34.  20
    A Routley-Meyer Semantics for Converse Ackermann Property.José M. Méndez - 1987 - Journal of Philosophical Logic 16 (1):65 - 76.
  35.  24
    Relevance Logics and Intuitionistic Negation.José M. Méndez & Gemma Robles - 2008 - Journal of Applied Non-Classical Logics 18 (1):49-65.
    The logic B+ is Routley and Meyer's basic positive logic. We show how to introduce a minimal intuitionistic negation and an intuitionistic negation in B+. The two types of negation are introduced in a wide spectrum of relevance logics built up from B+. It is proved that although all these logics have the characteristic paradoxes of consistency, they lack the K rule.
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  36.  16
    Urquhart's C with Intuitionistic Negation: Dummett's LC Without the Contraction Axiom.José M. Méndez & Francisco Salto - 1995 - Notre Dame Journal of Formal Logic 36 (3):407-413.
    This paper offers a particular intuitionistic negation completion of Urquhart's system C resulting in a super-intuitionistic contractionless propositional logic equivalent to Dummett's LC without contraction.
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  37.  44
    Strong Paraconsistency and the Basic Constructive Logic for an Even Weaker Sense of Consistency.Gemma Robles & José M. Méndez - 2009 - 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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  38.  25
    The Basic Constructive Logic for Negation-Consistency Defined with a Propositional Falsity Constant.José M. Méndez, Gemma Robles & Francisco Salto - 2007 - Bulletin of the Section of Logic 36 (1-2):45-58.
  39.  38
    The Basic Constructive Logic for Absolute Consistency.José M. Méndez & Gemma Robles - 2009 - 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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  40.  26
    Converse Ackermann Croperty and Semiclassical Negation.José M. Méndez - 1988 - 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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  41.  38
    Two Extensions of Lewis' S3 with Peirce's Law.Francisco Salto & José M. Méndez - 1999 - 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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  42.  3
    The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łkasiewicz’s 3-Valued Logic Ł3.Gemma Robles & José M. Méndez - forthcoming - Journal of Logic, Language and Information:1-26.
    We consider the logics determined by the set of all natural implicative expansions of Kleene’s strong 3-valued matrix 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.
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  43.  27
    Axiomatizing E→ and R→ with Anderson and Belnap's 'Strong and Natural'list of Valid Entailments.José M. Méndez - 1987 - 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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  44.  21
    1. Select List of Representative Theses.José M. Mendez - 1988 - Bulletin of the Section of Logic 17 (1):15-20.
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  45.  39
    A Note on "Recent Work in Relevant Logic".José M. Méndez - manuscript
    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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  46.  31
    El Sistema Bp+ : Una Lógica Positiva Mínima Para la Negación Mínima (the System Bp+: A Minimal Positive Logic for Minimal Negation).José M. Méndez, Francisco Salto & Gemma Robles - 2007 - 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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  47.  24
    A Weak Logic with the Axiom Mingle Lacking the Variable-Sharing Property.Gemma Robles, Francisco Salto & José M. Méndez - 2011 - Bulletin of the Section of Logic 40 (3/4):195-202.
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  48.  11
    Una crítica inmanente de la lógica de la relevancia.José M. Méndez - 1986 - Critica 18 (52):61-94.
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  49.  23
    The Basic Constructive Logic for Weak Consistency and the Reductio Axioms.Gemma Robles & José M. Méndez - 2009 - Bulletin of the Section of Logic 38 (1/2):61-76.
  50.  27
    Exhaustively Axiomatizing RMO with an Appropiate Extension of Anderson and Belnap's “Strong and Natural List of Valid Entailments”.José M. Méndez - 1990 - 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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