Universidad de León
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Universidad de LeónRegular Faculty
León, CL, Spain
Areas of Specialization
Logic and Philosophy of Logic 
Areas of Interest
Logic and Philosophy of Logic 

Reduced Routley–Meyer semantics for the logics characterized by natural implicative expansions of Kleene’s strong 3valued matrixLogic Journal of the IGPL. forthcoming.

Converse Ackermann Property and Minimal NegationTeorema: International Journal of Philosophy 24 (1). 2005.

RoutleyMeyer ternary relational semantics for intuitionistictype negationsElsevier, Academic Press. 2018.RoutleyMeyer Ternary Relational Semantics for Intuitionistictype Negations examines how to introduce intuitionistictype negations into RMsemantics. RMsemantics 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 RMsemantics, negation is interpreted by means of the Routley operator, which has been almost exclusively used for modeling De…Read more

Relational semantics for the 4valued relevant logics BN4 and E4Logic and Logical Philosophy 25 (2): 173201. 2016.

Two versions of minimal intuitionism with the CAP. A noteTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 20 (2): 183190. 2005.

Dual Equivalent Twovalued Underdetermined and Overdetermined Interpretations for Łukasiewicz’s 3valued Logic Ł3Journal of Philosophical Logic 43 (23): 303332. 2014.

El sistema Bp+ : una lógica positiva mínima para la negación mínimaTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 22 (1): 8191. 2007.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,…Read more

A simple Henkinstyle completeness proof for Gödel 3valued logic G3Logic and Logical Philosophy 23 (4): 371390. 2014.A simple Henkinstyle completeness proof for Gödel 3valued propositional logic G3 is provided. The idea is to endow G3 with an underdetermined semantics of the type defined by Dunn. The key concept in usemantics is that of “underdetermined interpretation”. It is shown that consistent prime theories built upon G3 can be understood as uinterpretations. In order to prove this fact we follow Brady by defining G3 as an extension of Anderson and Belnap’s positive fragment of First Degree Entailme…Read more

Exhaustively Axiomatizing S3°→ and S4°→Teorema: International Journal of Philosophy 27 (2): 7989. 2008.

An Interpretation of Łukasiewicz’s 4Valued Modal LogicJournal of Philosophical Logic 45 (1): 7387. 2016.A simple, bivalent semantics is defined for Łukasiewicz’s 4valued 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 arisi…Read more

A semantical proof of the admissibility of the rule assertion in some relevant and modal logicsBulletin of the Section of Logic 41 (1/2): 5160. 2012.

A RoutleyMeyer semantics for relevant logics including TWR plus the disjunctive syllogismLogic Journal of the IGPL 19 (1): 1832. 2011.

Two versions of minimal intuitionism with the cap. A noteTheoria 20 (2): 183190. 2005.

The basic constructive logic for negationconsistencyJournal of Logic, Language and Information 17 (2): 161181. 2008.

A binary Routley semantics for intuitionistic De Morgan minimal logic HM and its extensionsLogic Journal of the IGPL 23 (2): 174193. 2015.

Minimal negation in the ternary relational semanticsReports on Mathematical Logic 4765. 2005.

Relevance logics, paradoxes of consistency and the K rule II. A nonconstructive negationLogic and Logical Philosophy 15 (3): 175191. 2007.

Curry's Paradox, Generalized Modus Ponens Axiom and Depth RelevanceStudia Logica 102 (1): 185217. 2014.

Strong paraconsistency and the basic constructive logic for an even weaker sense of consistencyJournal of Logic, Language and Information 18 (3): 357402. 2009.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…Read more

A RoutleyMeyer type semantics for relevant logics including B r plus the disjunctive syllogismJournal of Philosophical Logic 39 (2): 139158. 2010.

A companion to Brady's 4valued relevant logic BN4: The 4valued logic of entailment E4Logic Journal of the IGPL 24 (5). 2016.

Paraconsistency and consistency understood as the absence of the negation of any implicative theoremReports on Mathematical Logic 147171. 2012.

The basic constructive logic for negationconsistency defined with a propositional falsity constantBulletin of the Section of Logic 36 (12): 4558. 2007.

Extensions of the basic constructive logic for weak consistency BKc1 defined with a falsity constantLogic and Logical Philosophy 16 (4): 311322. 2007.

A Strong and Rich 4Valued Modal Logic Without ŁukasiewiczType ParadoxesLogica Universalis 9 (4): 501522. 2015.The aim of this paper is to introduce an alternative to Łukasiewicz’s 4valued 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 4valued modal logic free from this type of paradoxes. PŁ4 is determined by the degree of truthpreserving 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 is a rich logic i…Read more

A weak logic with the axiom Mingle lacking the variablesharing propertyBulletin of the Section of Logic 40 (3/4): 195202. 2011.

A RoutleyMeyer semantics for truthpreserving and welldetermined Lukasiewicz 3valued logicsLogic Journal of the IGPL 22 (1): 123. 2014.Łukasiewicz 3valued logic Ł3 is often understood as the set of all valid formulas according to Łukasiewicz 3valued matrices MŁ3. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: ‘truthpreserving’ Ł3a and ‘welldetermined’ Ł3b defined by two different consequence relations on the 3valued matrices MŁ3. The aim of this article is to provide a Routley–Meyer ternary semantics for each one of these three versions of Łukasiewicz 3valued logic: Ł3, Ł3a and Ł…Read more

Admissibility of Ackermann's rule δ in relevant logicsLogic and Logical Philosophy 22 (4): 411427. 2013.