-
21Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated valuesJournal of Applied Non-Classical Logics 29 (1): 37-63. 2019.ABSTRACTA conditional is natural if it fulfils the three following conditions. It coincides with the classical conditional when restricted to the classical values T and F; it satisfies the Modus Ponens; and it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with …Read more
-
20Dual Equivalent Two-valued Under-determined and Over-determined Interpretations for Łukasiewicz’s 3-valued Logic Ł3Journal of Philosophical Logic 43 (2-3): 303-332. 2014.Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic…Read more
-
20A companion to Brady's 4-valued relevant logic BN4: The 4-valued logic of entailment E4Logic Journal of the IGPL 24 (5). 2016.
-
20A Class of Implicative Expansions of Kleene’s Strong Logic, a Subclass of Which Is Shown Functionally Complete Via the Precompleteness of Łukasiewicz’s 3-Valued Logic Ł3Journal of Logic, Language and Information 30 (3): 533-556. 2021.The present paper is a sequel to Robles et al. :349–374, 2020. https://doi.org/10.1007/s10849-019-09306-2). A class of implicative expansions of Kleene’s 3-valued logic functionally including Łukasiewicz’s logic Ł3 is defined. Several properties of this class and/or some of its subclasses are investigated. Properties contemplated include functional completeness for the 3-element set of truth-values, presence of natural conditionals, variable-sharing property and vsp-related properties.
-
17A Class of Implicative Expansions of Belnap-Dunn Logic in which Boolean Negation is DefinableJournal of Philosophical Logic 52 (3): 915-938. 2023.Belnap and Dunn’s well-known 4-valued logic FDE is an interesting and useful non-classical logic. FDE is defined by using conjunction, disjunction and negation as the sole propositional connectives. Then the question of expanding FDE with an implication connective is of course of great interest. In this sense, some implicative expansions of FDE have been proposed in the literature, among which Brady’s logic BN4 seems to be the preferred option of relevant logicians. The aim of this paper is to d…Read more
-
16A remark on functional completeness of binary expansions of Kleene’s strong 3-valued logicLogic Journal of the IGPL 30 (1): 21-33. 2022.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.
-
16The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łkasiewicz’s 3-Valued Logic Ł3Journal of Logic, Language and Information 29 (3): 349-374. 2020.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.
-
16Blocking the Routes to Triviality with Depth RelevanceJournal of Logic, Language and Information 23 (4): 493-526. 2014.In Rogerson and Restall’s, the “class of implication formulas known to trivialize ” is recorded. The aim of this paper is to show how to invalidate any member in this class by using “weak relevant model structures”. Weak relevant model structures verify deep relevant logics only.
-
15A note on functional relations in a certain class of implicative expansions of FDE related to Brady’s 4-valued logic BN4Logic Journal of the IGPL. forthcoming.The logic E4 is related to Brady’s BN4 in a similar way to which Anderson and Belnap’s logic of entailment E is related to their logic of the relevant implication R. In ‘A companion to Brady’s 4-valued relevant logic: the 4-valued logic of entailment E4’, quoted in this paper, three alternatives to BN4 and another three to E4 are summarily introduced in a couple of pages as the only alternatives containing Routley and Meyer’s basic logic B, provided some conditions are fulfilled. The aim of this…Read more
-
15Partiality and its dual in natural implicative expansions of Kleene’s strong 3-valued matrix with only one designated valueLogic Journal of the IGPL 27 (6): 910-932. 2019.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.
-
15Natural implicative expansions of variants of Kleene's strong 3-valued logic with Gödel-type and dual Gödel-type negationJournal of Applied Non-Classical Logics 31 (2): 130-153. 2021.Let MK3 I and MK3 II be Kleene's strong 3-valued matrix with only one and two designated values, respectively. Next, let MK3 G be defined exactly as MK3 I, except th...
-
15Two Extensions of Lewis’ S3 with Peirce’s LawTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 14 (3): 407-411. 1999.We define two extensions of Lewis’ S3 with two versions of Peirce’s Law. We prove that both of them have the Ackermann Property.
-
14Curry’s Paradox, Generalized Contraction Rule and Depth RelevanceIn Konstantinos Boudouris (ed.), Proceedings XXIII world Congress Philosophy, Philosophy Documentation Center. pp. 35-39. 2018.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 these, the Contraction rule or the Modus …Read more
-
14La Aviación Militar Española: una historia corta pero de gran intensidadArbor 171 (674): 187-216. 2002.
-
12The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic BdLogic Journal of the IGPL. forthcoming.The well-known logic first degree entailment logic (FDE), introduced by Belnap and Dunn, is defined with |$\wedge $|, |$\vee $| and |$\sim $| as the sole primitive connectives. The aim of this paper is to establish the lattice formed by the class of all 4-valued C-extending implicative expansions of FDE verifying the axioms and rules of Routley and Meyer’s basic logic B and its useful disjunctive extension B|$^{\textrm {d}}$|. It is to be noted that Boolean negation (so, classical propositiona…Read more
-
11Exhaustively axiomatizing RMO with an appropiate extension of Anderson and Belnap’s “strong and natural list of valid entailments”Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 5 (1-2): 223-228. 1990.RMO -> is the result of adding the ‘mingle principle’ ) 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.
-
10Two versions of minimal intuitionism with the CAP. A noteTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 20 (2): 183-190. 2010.La "Conversa de la Propiedad Ackermann" (CAP) es la no demostrabilidad de proposiciones puramente no-necesitivas a partir de proposiciones necesitivas. En nuestro trabajo definimos las dos restricciones básicas de la lógica intuicionista mínima con la CAP.
-
10A Note on Gödel-Dummet Logic LCBulletin of the Section of Logic 50 (3): 325-335. 2021.Let \ be distintict wffs, \ being an odd number equal to or greater than 1. Intuitionistic Propositional Logic IPC plus the axiom \\vee...\vee \vee \) is equivalent to Gödel-Dummett logic LC. However, if \ is an even number equal to or greater than 2, IPC plus the said axiom is a sublogic of LC.
-
8The Basic Constructive Logic for a Weak Sense of Consistency defined with a Propositional Falsity ConstantLogic Journal of the IGPL 16 (1): 33-41. 2008.The logic BKc1 is the basic constructive logic in the ternary relational semantics adequate to consistency understood as the absence of the negation of any theorem. Negation is introduced in BKc1 with a negation connective. The aim of this paper is to define the logic BKc1F. In this logic negation is introduced via a propositional falsity constant. We prove that BKc1 and BKc1F are definitionally equivalent.
-
8Aportes para la revisión curricular desde la perspectiva interculturalCuestiones de Filosofía 8 (31): 73-87. 2022.Los instrumentos curriculares suelen ser objeto de luchas políticas; están atravesados por opciones, renuncias y escogencias. No son nunca neutros. Estas páginas quieren ser una contribución a la urgente tarea de revisión curricular desde una perspectiva intercultural. En este artículo se presenta el currículo como “un camino” en el que las personas ‘aprendientes’ pueden encontrarse, dialogar y aprender gracias a su diversidad, y en el que es posible promover el diálogo de saberes y culturas. No…Read more
-
4A 2 Set-Up Binary Routley Semantics for Gödelian 3-Valued Logic G3 and Its Paraconsistent Counterpart G3\(_\text{Ł}^\leq\) (review)Bulletin of the Section of Logic 51 (4): 487-505. 2022.G3 is Gödelian 3-valued logic, G3\(_\text{Ł}^\leq\) is its paraconsistent counterpart and G3\(_\text{Ł}^1\) is a strong extension of G3\(_\text{Ł}^\leq\). The aim of this paper is to endow each one of the logics just mentioned with a 2 set-up binary Routley semantics.
-
Exhaustively Axiomatizing S3 (->) degrees and S4 (->) degreesTeorema: International Journal of Philosophy 27 (2): 79-89. 2008.S3o and S4o are the restrictions with the Converse Ackermann Property of the implicative fragments of Lewis' S3 and S4 respectively. The aim of this paper is to provide all possible axiomatizations with independent axioms of S3o and S40 that can be formulated with a modification of Anderson and Belnap's list of valid entailments.
-
Constructive negation defined with a falsity constant for positive logics with the CAP defined with a truth constant ALogique Et Analyse 48 (192): 87-100. 2005.
-
Adding the Disjunctive Syllogism to Relevant Logics Including TW Plus the Contraction and Reductio RulesLogique Et Analyse 54 (215): 343-358. 2011.
-
Minimal Non-relevant Logics Without The K AxiomReports on Mathematical Logic. 2007.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.
-
Exhaustively axiomatizing S3-> and S4-> with a select list of representative thesesBulletin of the Section of Logic 17 (1): 15-20. 1988.This paper is a sequel to [2]. We extend Anderson and Belnap’s list with the characteristic axioms of S3→ and S4→ . Then we exhaustively axiomatize these systems with the list thus extended
-
Universidad de SalamancaRegular Faculty