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Extensions of the basic constructive logic for negation-consistency BKc4Logique Et Analyse 51. 2008.
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29Converse Ackermann property and constructive negation defined with a negation connectiveLogic and Logical Philosophy 15 (2): 113-130. 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 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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30Admissibility of Ackermann's rule δ in relevant logicsLogic and Logical Philosophy 22 (4): 411-427. 2013.It is proved that Ackermann’s rule δ is admissible in a wide spectrum of relevant logics satisfying certain syntactical properties
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26A binary Routley semantics for intuitionistic De Morgan minimal logic HM and its extensionsLogic Journal of the IGPL 23 (2): 174-193. 2015.
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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.
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32Relevance logics and intuitionistic negationJournal of Applied Non-Classical Logics 18 (1): 49-65. 2008.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 (and so, the K axioms).
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11Negation introduced with the unary connectiveJournal of Applied Non-Classical Logics 19 (3): 371-388. 2009.In the first part of this paper (Méndez and Robles 2008) a minimal and an intuitionistic negation is introduced in a wide spectrum of relevance logics extending Routley and Meyer's basic positive logic B+. It is proved that although all these logics have the characteristic paradoxes of consistency, they lack the K rule (and so, the K axiom). Negation is introduced with a propositional falsity constant. The aim of this paper is to build up logics definitionally equivalent to those in the aforemen…Read more
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48Paraconsistent logics included in Lewis’ S4Review of Symbolic Logic 3 (3): 442-466. 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
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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.
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31Axiomatizing s4+ and j+ without the suffixing, prefixing and self-distribution of the conditional axiomsBulletin of the Section of Logic 39 (1/2): 79-91. 2010.
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20A companion to Brady's 4-valued relevant logic BN4: The 4-valued logic of entailment E4Logic Journal of the IGPL 24 (5). 2016.
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118Two versions of minimal intuitionism with the cap. A noteTheoria 20 (2): 183-190. 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
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49The basic constructive logic for absolute consistencyJournal of Logic, Language and Information 18 (2): 199-216. 2009.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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36The basic constructive logic for negation-consistencyJournal of Logic, Language and Information 17 (2): 161-181. 2008.In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction. The basic constructive logic BKc4, 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 BKc4 up to minimal intuitionistic logic. All logics defined in this paper are paraconsistent logics.
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44An Interpretation of Łukasiewicz’s 4-Valued Modal LogicJournal of Philosophical Logic 45 (1): 73-87. 2016.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 arisi…Read more
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11Intutionistic Propositional Logic with the Converse Ackerman PopertyTeorema: International Journal of Philosophy 22 (1-2): 46-54. 2003.
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132A Routley-Meyer semantics for relevant logics including TWR plus the disjunctive syllogismLogic Journal of the IGPL 19 (1): 18-32. 2011.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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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.
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30A paraconsistent 3-valued logic related to Godel logic G3Logic Journal of the IGPL 22 (4): 515-538. 2014.
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22A constructive negation defined with a negation connective for logics including Bp+Bulletin of the Section of Logic 34 (3): 177-190. 2005.The concept of constructive negation we refer to in this paper is (minimally) intuitionistic in character (see [1]). The idea is to understand the negation of a proposition A as equivalent to A implying a falsity constant of some sort. Then, negation is introduced either by means of this falsity constant or, as in this paper, by means of a propositional connective defined with the constant. But, unlike intuitionisitc logic, the type of negation we develop here is, of course, devoid of paradoxes …Read more
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42Relevance logics, paradoxes of consistency and the K rule II. A non-constructive negationLogic and Logical Philosophy 15 (3): 175-191. 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 non-constructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency
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Paraconsistency and consistency understood as the absence of the negation of any implicative theoremReports on Mathematical Logic 147-171. 2012.
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56Strong paraconsistency and the basic constructive logic for an even weaker sense of consistencyJournal of Logic, Language and Information 18 (3): 357-402. 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
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21Exhaustively Axiomatizing S3°→ and S4°→Teorema: 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 S4o that can be formulated with a modification of Anderson and Belnap's list of valid entailments.
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37A semantical proof of the admissibility of the rule assertion in some relevant and modal logicsBulletin of the Section of Logic 41 (1/2): 51-60. 2012.
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50A General Characterization of the Variable-Sharing Property by Means of Logical MatricesNotre Dame Journal of Formal Logic 53 (2): 223-244. 2012.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 this way, any logic verified…Read more
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1Two versions of minimal intuitionism with the CAP. A noteTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 20 (2): 183-190. 2005.
Gemma Robles
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 |