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José M. Méndez [75]J. M. Mendez [8]Julio Raúl Mendez [8]José Méndez [5]
Julio R. Mendez [3]Juan Mendez [3]J. Mendez [3]Jorge Mendez [3]

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José M. Méndez
Universidad de Salamanca
Jorge Luis Méndez
National Autonomous University of Mexico
  1.  11
    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.  18
    Routley-Meyer Ternary Relational Semantics for Intuitionistic-Type Negations.Gemma Robles & José M. Méndez - 2018 - Elsevier, Academic Press.
    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 Morgan negations. This book provides research on particular features of intuitionistic-type of negations (...)
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  3.  23
    A Paraconsistent 3-Valued Logic Related to Godel Logic G3.G. Robles & J. M. Mendez - 2014 - Logic Journal of the IGPL 22 (4):515-538.
  4.  33
    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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  5.  11
    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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  6.  7
    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 - 2020 - Journal of Logic, Language and Information 29 (3):349-374.
    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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  7.  84
    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.  74
    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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  9.  21
    A Binary Routley Semantics for Intuitionistic De Morgan Minimal Logic HM and its Extensions.G. Robles & J. M. Mendez - 2015 - Logic Journal of the IGPL 23 (2):174-193.
  10.  33
    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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  11.  15
    A Basic Dual Intuitionistic Logic and Some of its Extensions Included in G3DH.Gemma Robles & José M. Méndez - 2021 - Journal of Logic, Language and Information 30 (1):117-138.
    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 (...)
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  12.  7
    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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  13.  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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  14.  25
    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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  15. 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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  16.  34
    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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  17.  21
    A Routley-Meyer Semantics for Truth-Preserving and Well-Determined Lukasiewicz 3-Valued Logics.G. Robles & J. M. Mendez - 2014 - Logic Journal of the IGPL 22 (1):1-23.
    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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  18.  36
    Cardiovascular Medicine at Face Value: A Qualitative Pilot Study on Clinical Axiology.Adalberto de Hoyos, Rodrigo Nava-Diosdado, Jorge Mendez, Sergio Ricco, Ana Serrano, C. Flores Cisneros, Carlos Macías-Ojeda, Héctor Cisneros, P. G. Barbara & B. J. Gilbert - 2012 - Philosophy, Ethics, and Humanities in Medicine 7:14.
    IntroductionCardiology is characterized by its state-of-the-art biomedical technology and the predominance of Evidence-Based Medicine. This predominance makes it difficult for healthcare professionals to deal with the ethical dilemmas that emerge in this subspecialty. This paper is a first endeavor to empirically investigate the axiological foundations of the healthcare professionals in a cardiology hospital. Our pilot study selected, as the target population, cardiology personnel not only because of their difficult ethical deliberations but also because of the stringent conditions in which they (...)
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  19.  58
    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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  20.  31
    The Compatibility of Relevance and Mingle.José M. Méndez - 1988 - Journal of Philosophical Logic 17 (3):279 - 297.
  21.  8
    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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  22.  11
    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.  54
    Cardiovascular Medicine at Face Value: A Qualitative Pilot Study on Clinical Axiology.Adalberto de Hoyos, Rodrigo Nava-Diosdado, Jorge Mendez, Sergio Ricco, Ana Serrano, Carmen Flores Cisneros, Carlos Macías-Ojeda, Héctor Cisneros, David Bialostozky, Nelly Altamirano-Bustamante & Myriam Altamirano-Bustamante - 2013 - Philosophy, Ethics, and Humanities in Medicine 8:3.
    Cardiology is characterized by its state-of-the-art biomedical technology and the predominance of Evidence-Based Medicine. This predominance makes it difficult for healthcare professionals to deal with the ethical dilemmas that emerge in this subspecialty. This paper is a first endeavor to empirically investigate the axiological foundations of the healthcare professionals in a cardiology hospital. Our pilot study selected, as the target population, cardiology personnel not only because of their difficult ethical deliberations but also because of the stringent conditions in which they (...)
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  24.  16
    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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  25.  2
    A Remark on Functional Completeness of Binary Expansions of Kleene’s Strong 3-Valued Logic.Gemma Robles & José M. Méndez - 2022 - Logic Journal of the IGPL 30 (1):21-33.
    A classical result by Słupecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including Łukasiewicz’s 3-valued logic Ł3, what he names the ‘$T$-function’ is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions of Kleene’s strong logic that are functionally complete for THREE.
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  26. 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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  27. 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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  28.  31
    Anderson And Belnap's Minimal Positive Logic With Minimal Negation.J. Mendez, F. Salto & G. Robles - 2002 - Reports on Mathematical Logic 36:117-130.
    Our question is: can we embed minimal negation in implicative logics weaker than I→? Previous results show how to define minimal negation in the positive fragment of the logic of relevance R and in contractionless intuitionistic logic. Is it possible to endow weaker positive logics with minimal negation? This paper prooves that minimal negation can be embedded in even such a weak system as Anderson and Belnap’s minimal positive logic.
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  29.  31
    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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  30.  9
    A Companion to Brady's 4-Valued Relevant Logic BN4: The 4-Valued Logic of Entailment E4.Gemma Robles & José M. Méndez - 2016 - Logic Journal of the IGPL 24 (5).
  31.  19
    A Class of Simpler Logical Matrices for the Variable-Sharing Property.G. Robles & J. M. Méndez - 2011 - Logic and Logical Philosophy 20 (3):241-249.
    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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  32.  24
    Erratum To: The Compatibility of Relevance and Mingle. [REVIEW]José M. Méndez - 2010 - Journal of Philosophical Logic 39 (3):339-339.
  33.  25
    A Routley-Meyer Semantics for Converse Ackermann Property.José M. Méndez - 1987 - Journal of Philosophical Logic 16 (1):65 - 76.
  34.  18
    The Logic B and the Reductio Axioms.Gemma Robles & José M. Méndez - 2004 - Bulletin of the Section of Logic 33 (2):87-94.
  35.  34
    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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  36.  2
    Curry’s Paradox, Generalized Contraction Rule and Depth Relevance.Francisco Salto, Gemma Robles & José M. Méndez - 2018 - In Konstantinos Boudouris (ed.), Proceedings XXIII world Congress Philosophy. Charlottesville: Philosophy Documentation Center. pp. 35-39.
    As it is well known, in the forties of the past century, Curry proved that in any logic S closed under Modus Ponens, uniform substitution of propositional variables and the Contraction Law, the naïve Comprehension axiom trivializes S in the sense that all propositions are derivable in S plus CA. Not less known is the fact that, ever since Curry published his proof, theses and rules weaker than W have been shown to cause the same effect as W causes. Among (...)
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  37.  26
    Minimal Negation in the Ternary Relational Semantics.G. Robles, J. Mendez & F. Salto - 2005 - Reports on Mathematical Logic: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 without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended positive logic are offered.
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  38.  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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  39.  2
    Cardiovascular Medicine at Face Value: A Qualitative Pilot Study on Clinical Axiology.Myriam M. Altamirano-Bustamante, Nelly Altamirano-Bustamante, David Bialostozky, Héctor Cisneros, Carlos Macías-Ojeda, Carmen Flores Cisneros, Ana Serrano, Sergio Ricco, Jorge Mendez, Rodrigo Nava-Diosdado & Adalberto de Hoyos - 2013 - Philosophy, Ethics, and Humanities in Medicine 8 (1).
    IntroductionCardiology is characterized by its state-of-the-art biomedical technology and the predominance of Evidence-Based Medicine. This predominance makes it difficult for healthcare professionals to deal with the ethical dilemmas that emerge in this subspecialty. This paper is a first endeavor to empirically investigate the axiological foundations of the healthcare professionals in a cardiology hospital. Our pilot study selected, as the target population, cardiology personnel not only because of their difficult ethical deliberations but also because of the stringent conditions in which they (...)
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  40.  23
    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.
    LCo with the Converse Ackermann Property is defined as the result of restricting Contraction in LC. Intuitionistic and Superintuitionistic Negation is shown to be compatible with the CAP.
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  41.  14
    Perpetuating the Double Helix: Molecular Machines at Eukaryotic DNA Replication Origins.Juan Méndez & Bruce Stillman - 2003 - Bioessays 25 (12):1158-1167.
  42.  31
    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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  43.  17
    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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  44. De Rijke, M., 109 Di Maio, MC, 435 Doria, FA, 553 French, S., 603.E. M. Hammer, J. Hawthorne, M. Kracht, E. Martino, J. M. Mendez, R. K. Meyer, L. S. Moss, A. Tzouvaras, J. van Benthem & F. Wolter - 1998 - Journal of Philosophical Logic 27 (661).
  45.  20
    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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  46.  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.
  47.  46
    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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  48.  14
    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.
  49. 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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  50.  8
    A 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 Ł3.Gemma Robles & José M. Méndez - 2021 - Journal of Logic, Language and Information 30 (3):533-556.
    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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