
23Restricting the contraction axiom in Dummett's LC: a sublogic of LC with the Converse Ackermann Property, the logic LCoBulletin of the Section of Logic 30 (3): 139146. 2001.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.

31Relevance logics, paradoxes of consistency and the K rule II. A nonconstructive negationLogic and Logical Philosophy 15 (3): 175191. 2007.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 nonconstructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency

74The basic constructive logic for a weak sense of consistencyJournal of Logic, Language and Information 17 (1): 89107. 2008.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.

31Converse Ackermann croperty and semiclassical negationStudia Logica 47 (2). 1988.A prepositional logic S has the Converse Ackermann Property (CAP) if (AB)C is unprovable in S when C does not contain . In A RoutleyMeyer 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 socalled semiclassical negation. In the present paper I prove that this conjecture was right. Relational RoutleyMeyer typ…Read more

25Dual Equivalent Twovalued Underdetermined and Overdetermined Interpretations for Łukasiewicz's 3valued Logic Ł3Journal of Philosophical Logic (23): 130. 2013.Łukasiewicz threevalued logic Ł3 is often understood as the set of all 3valued valid formulas according to Łukasiewicz’s 3valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “welldetermined” Ł3a and “truthpreserving” Ł3b defined by two different consequence relations on the 3valued matrices. The aim of this paper is to provide (by using Dunn semantics) dual equivalent twovalued underdetermined and overdetermined interpretations for …Read more

20A 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

76A constructive negation for logics including TW+Journal of Applied NonClassical Logics 15 (4): 389404. 2005.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 pa…Read more

16The nonrelevant De Morgan minimal logic in RoutleyMeyer semantics with no designated pointsJournal of Applied NonClassical Logics 24 (4): 321332. 2014.Sylvan and Plumwood’s is the relevant De Morgan minimal logic in the RoutleyMeyer 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 nonrelevant De Morgan minimal logic in the RoutleyMeyer semantics without a set of designated points

24Erratum to: The compatibility of relevance and Mingle (review)Journal of Philosophical Logic 39 (3): 339339. 2010.

36Paraconsistent logics included in Lewis’ S4Review of Symbolic Logic 3 (3): 442466. 2010.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 included in S4 where the Disjunctive …Read more

25A RoutleyMeyer semantics for converse Ackermann propertyJournal of Philosophical Logic 16 (1). 1987.

20Converse Ackermann property and constructive negation defined with a negation connectiveLogic and Logical Philosophy 15 (2): 113130. 2006.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 nonnecessitive propositions from nonnecessitive 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

441A modal restriction of RMingle with the variablesharing propertyLogic and Logical Philosophy 19 (4): 341351. 2010.A restriction of RMingle with the variablesharing 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

81A natural negation completion of Urquhart's manyvalued logic CJournal of Philosophical Logic 27 (1): 7584. 1998.Etude de l'extension par la negation semiintuitionniste de la logique positive des propositions appelee logique C, developpee par A. Urquhart afin de definir une semantique relationnelle valable pour la logique des valeurs infinies de Lukasiewicz (Lw). Evitant les axiomes de contraction et de reduction propres a la logique classique de Dummett, l'A. propose une semantique de type RoutleyMeyer pour le systeme d'Urquhart (CI) en tant que cellela ne fournit que des theories consistantes pour la …Read more

39Two extensions of Lewis' s3 with Peirce's lawTheoria 14 (3): 407411. 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

34Strengthening Brady’s Paraconsistent 4Valued Logic BN4 with TruthFunctional Modal OperatorsJournal of Logic, Language and Information 25 (2): 163189. 2016.Łukasiewicz presented two different analyses of modal notions by means of manyvalued logics: the linearly ordered systems Ł3,..., Open image in new window,..., \; the 4valued 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 4valued logic BN4 is the basic 4valued bilattice logic. The aim of this paper is to show that BN4 can be strengthened with modal operators following Łukasiewicz’s strategy…Read more

23The basic constructive logic for weak consistency and the reductio axiomsBulletin of the Section of Logic 38 (1/2): 6176. 2009.

30Constructive RBulletin of the Section of Logic 16 (4): 167173. 1987.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 variablesharing property. Moreover, each of there systems is given a semantics in the RoutleyMeyer style. In describing in [2] the models for RMO+ plus minimal negation, we noted that a similar strategy would give us a semantics for R+…Read more

Exhaustively Axiomatizing S3 (>) degrees and S4 (>) degreesTeorema: International Journal of Philosophy 27 (2): 7989. 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.

84A RoutleyMeyer type semantics for relevant logics including B r plus the disjunctive syllogismJournal of Philosophical Logic 39 (2): 139158. 2010.RoutleyMeyer 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.

28Axiomatizing E→ and R→ with Anderson and Belnap's 'strong and natural'list of valid entailmentsBulletin of the Section of Logic 16 (1): 27. 1987.We provide all possible axiomatizations with independent axioms of E→ and R→ formulable with Anderson and Belnap’s list

19A Class of Simpler Logical Matrices for the VariableSharing PropertyLogic and Logical Philosophy 20 (3): 241249. 2011.In our paper “A general characterization of the variablesharing property by means of logical matrices”, a general class of socalled “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 variablesharing property and related properties predicable of the logic of entailment E and of the logic of relevance R

15Ticket Entailment plus the mingle axiom has the variablesharing propertyLogic Journal of the IGPL 20 (1): 355364. 2012.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 variablesharing property . Ternary relational semantics for TM is provided. Finally, an interesting extension of TM with the vsp is briefly discussed

110Two versions of minimal intuitionism with the cap. A noteTheoria 20 (2): 183190. 2005.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

32Intuitionistic propositional logic without 'contraction' but with 'reductio'Studia Logica 66 (3): 409418. 2000.Routley Meyer type relational complete semantics are constructed for intuitionistic contractionless logic with reductio. Different negation completions of positive intuitionistic logic without contraction are treated in a systematical, unified and semantically complete setting

19Relational ternary semantics for a logic equivalent to Involutive Monoidal tnorm based logic IMTLBulletin of the Section of Logic 34 (2): 101116. 2005.

Universidad de SalamancaRegular Faculty