Gemma Robles

Papers | Books | Book chapters | Conference proceedings

Note: PDFs of some of my publications can be found here and also at BULERIA (Universidad de León institutional repository).

G. Robles (Forthcoming). On three-valued logics with the variable sharing property. Australasian Journal of Logic. Special issue celebrating the work of Ross Brady (S. Logan, Guest Ed.)

G. Robles, J. M. Méndez (2024). The lattice of all 4-valued implicative expansions of Belnap-Dunn logic containing Routley and Meyer's basic logic B^{d}. Logic Journal of the IGPL, 32(3), 493-516, DOI: 10.1093/jigpal/jzad005 (Open access)

G. Robles, J. M. Méndez (2023). A variety of De Morgan negations in relevant logics. Australasian Journal of Logic, Special Issue on Valerie Plumwood’s Contributions to Logic (A. Tedder and G. Badía, Guest Eds.), 20(2), 348-374, DOI: https://doi.org/10.26686/ajl.v20i2.8311 (Open access)

G. Robles (2023). Two 4-valued implicative expansions of first-degree entailment logic, FDE: The relevant logic BN4^{VSP} and the (relevant) entailment logic BN4^{AP}. Journal of Logic and Computation, 33(2), 462-484, DOI: 10.1093/logcom/exac101 (Open access)

G. Robles, J. M. Méndez (2023). A class of implicative expansions of Belnap-Dunn logic in which Boolean negation is definable. Journal of Philosophical Logic, 52, 915-938, DOI: 10.1007/s10992-022-09692-2 (Open access)

G. Robles, J. M. Méndez (2023). A note on functional relations in a certain class of implicative expansions of FDE related to Brady's 4-valued logic BN4. Logic Journal of the IGPL, 31(3), 475-482, 1-8. DOI: 10.1093/jigpal/jzac045 (Open access)

— G. Robles, J. M. Méndez (2023). Correction to: A note on functional relations in a certain class of implicative expansions of FDE related to Brady’s 4-valued logic BN4. Logic Journal of the IGPL, 32(3), 572. DOI: 10.1093/jigpal/jzad004 (Open access)

G. Robles, S. M. López, J. M. Blanco (2022). Relational semantics for the paraconsistent and paracomplete 4-valued logic PŁ4. Logic and Logical Philosophy, Special Issue: Logics and Their Interpretations, Part II (H. Antunes and D. Szmuc, Guest Eds.), 31(4), 665-687. DOI: 10.12775/LLP.2022.016 (Open access)

G. Robles, J. M. Méndez (2022). A 2 set-up binary Routley semantics for Gödelian 3-valued logic G3 and its paraconsistent counterpart G3_{\ L}^{\leq}. Bulletin of the Section of Logic, 51(4), 487-505, DOI: 10.18778/0138-0680.2022.20 (Open access)

G. Robles, J. M. Méndez (2022). A remark on functional completeness of binary expansions of Kleene’s strong 3-valued logic. Logic Journal of the IGPL, 30(1), 21-33. DOI: 10.1093/jigpal/jzaa028. PDF

G. Robles (2021). The class of all 3-valued implicative expansions of Kleene's strong logic containing Anderson and Belnap's First degree entailment logic. Journal of Applied Logics — IfCoLog Journal of Logics and their Applications, 8(7), 2035-2071. www.collegepublications.co.uk/downloads/ifcolog00049.pdf (Open access)

G. Robles, J. M. Méndez (2021). A 2 set-up Roultey-Meyer semantics for the 4-valued logic PŁ4. Journal of Applied Logics — IfCoLog Journal of Logics and their Applications, 8(10), ‍2435-2446. www.collegepublications.co.uk/downloads/ifcolog00052.pdf (Open access)

G. Robles, J. M. Méndez (2021). Basic quasi-Boolean expansions of relevance logics. Journal of Philosophical Logic, 50, 727-754. DOI: 10.1007/s10992-020-09583-4. View-only. PDF

G. Robles, J. M. Méndez (2021). 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. Journal of Logic, Language and Information, 30, 533-556. DOI: 10.1007/s10849-021-09336-9. View-only. PDF

G. Robles, J. M. Méndez (2021). A note on Gödel-Dummett logic LC. Bulletin of the Section of Logic, 50(3), 325-335. DOI: 10.18778/0138-0680.2021.15 (Open access)

G. Robles, J. M. Méndez (2021). Natural implicative expansions of variants of Kleene's strong 3-valued logic with Gödel-type and dual Gödel-type negation. Journal of Applied Non-Classical Logics, 31(2), 130-153. DOI: 10.1080/11663081.2021.1948285. PDF

G. Robles, J. M. Méndez (2021). A basic dual intuitionistic logic and some of its extensions included in G3_{DH}. Journal of Logic, Language and Information, 30, 117-138. DOI: 10.1007/s10849-020-09321-8. View-only. PDF

G. Robles (2020). A basic quasi-Boolean logic of intuitionistic character. Journal of Applied Non-classical Logics, 30(4), 291-311. DOI: 10.1080/11663081.2020.1826155. PDF

G. Robles, S. M. López (2020). Selecting the class of all 3- valued implicative expansions of Kleene's strong logic containing Routley and Meyer's logic B. Logique et Analyse, 252, 443-464. DOI: 10.2143/LEA.252.0.3289034. PDF

G. Robles, J. M. Méndez (2020). The class of all natural implicative expansions of Kleene's strong logic functionally equivalent to Łukasiewicz's 3-valued logic Ł3. Journal of Logic, Language and Information, 29(3), 349-374. DOI: 10.1007/s10849-019-09306-2. View-only. PDF

G. Robles (2019). Reduced Routley–Meyer semantics for the logics characterized by natural implicative expansions of Kleene's strong 3-valued matrix. Logic Journal of the IGPL, 27(1), 69-92. DOI: 10.1093/jigpal/jzy019. PDF

G. Robles, J. M. Méndez (2019). Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values. Journal of Applied Non-Classical Logics, 29(1), 37-63. DOI: 10.1080/11663081.2018.1534487. PDF

G. Robles, J. M. Méndez (2019). Partiality and its dual in natural implicative expansions of Kleene’s strong 3-valued matrix with only one designated value. Logic Journal of the IGPL, 27(6), 910-932. DOI: 10.1093/jigpal/jzz021. PDF

G. Robles, F. Salto, J. M. Méndez (2019). Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix II. Only one designated value. Journal of Applied Non-Classical Logics 29(3), 307-325. DOI: 10.1080/11663081.2019.1644079. PDF

J. M. Méndez, G. Robles (2016). The logic determined by Smiley's matrix for Anderson and Belnap's First Degree Entailment Logic. Journal of Applied Non-Classical Logics, 26(1), 47-68. DOI: 10.1080/11663081.2016.1153930. PDF

J. M. Méndez, G. Robles (2016). Strengthening Brady's paraconsistent 4-valued logic BN4 with truth-functional modal operators. Journal of Logic, Language and Infomation, 25(2), 163-189. DOI: 10.1007/s10849-016-9237-8. View-only. PDF

J. M. Méndez, G. Robles, F. Salto (2016). An interpretation of Łukasiewicz's 4-valued modal logic. Journal of Philosophical Logic, 45(1), 73-87. DOI: 10.1007/s10992-015-9362-x. View-only. PDF

G. Robles (2016). The quasi-relevant 3-valued logic RM3 and some of its sublogics lacking the variable-sharing property. Reports on Mathematical Logic, 51, 105-131. DOI: 10.4467/20842589RM.16.008.5285 (Open access).

G. Robles, J. M. Blanco, S. M. López, J. R. Paradela, M. M. Recio (2016). Relational semantics for the 4-valued relevant logics BN4 and E4. Logic and Logical Philosophy, 25, 173-201. DOI: 10.12775/LLP.2016.006 (Open access).

G. Robles, S. M. López, J. M. Blanco, M. M. Recio, J. R. Paradela (2016). A 2-set-up Routley-Meyer semantics for the 4-valued relevant logic E4. Bulletin of the Section of Logic, 45(2), 93-109. DOI: 10.18778/0138-0680.45.2.03 (Open access).

G. Robles, J. M. Méndez (2016). A companion to Brady’s 4-valued relevant logic BN4: The 4-valued logic of entailment E4. Logic Journal of the IGPL, 24(5), 838-858. DOI: 10.1093/jigpal/jzw011.

J. M. Méndez, G. Robles (2015). A strong and rich 4-valued modal logic without Łukasiewicz-type paradoxes. Logica Universalis, 9(4), 501-522. DOI: 10.1007/s11787-015-0130-z. View-only. PDF

J. M. Méndez, G. Robles, F. Salto (2015). Brady’s deep relevant logic DR plus the qualified factorization principles has the depth relevance condition. Logique et Analyse, 232, 547-565. DOI: 10.2143/LEA.232.0.3144298 (Open access).

G. Robles, J. M. Méndez (2015). A binary Routley semantics for intuitionistic De Morgan minimal logic H_{M} and its extensions. Logic Journal of the IGPL, 23(2), 174-193. DOI:  10.1093/jigpal/jzu029.

G. Robles (2014). A simple Henkin-style completeness proof for Gödel 3-valued logic G3. Logic and Logical Philosophy, 23(4), 371-390. DOI: 10.12775/LLP.2014.001  (Open access).

G. Robles, J. M. Méndez (2014). The non-relevant De Morgan minimal logic in Routley-Meyer semantics with no designated points. Journal of Applied Non-Classical Logics, 24(4), 321-332. DOI: 10.1080/11663081.2014.972306. PDF

G. Robles, J. M. Méndez (2014). Blocking the routes to triviality with depth relevance. Journal of Logic, Language and Information, 23(4), 493-526. DOI: 10.1007/s10849-014-9199-7. View-only. PDF

G. Robles, J. M. Méndez (2014). Generalizing the depth relevance condition. Deep relevant logics not included in R-Mingle. Notre Dame Journal of Formal Logic, 55(1), 107-127. DOI: 10.1215/00294527-1960461. PDF

G. Robles, J. M. Méndez (2014). Curry’s Paradox, Generalized Modus Ponens Axiom and Depth Relevance. Studia Logica, 102(1), 185-217. DOI: 10.1007/s11225-013-9471-x. View-only. PDF

G. Robles, J. M. Méndez (2014). A Routley-Meyer semantics for truth-preserving and well-determined Łukasiewicz 3-valued logics. Logic Journal of the IGPL, 22(1), 1-23. DOI: 10.1093/jigpal/jzt017.

G. Robles, J. M. Méndez (2014). A paraconsistent 3-valued logic related to Gödel logic G3. Logic Journal of the IGPL, 22(4), 515-538. DOI: 10.1093/jigpal/jzt046.

G. Robles, F. Salto, J. M. Méndez (2014). Dual equivalent two-valued under-determined and over-determined interpretations for Łukasiewicz’s 3-valued logic Ł3. Journal of Philosophical Logic, 43(2/3), 303-332. DOI: 10.1007/s10992-012-9264-0. View-only. PDF

G. Robles (2013). A Routley-Meyer semantics for Gödel 3-valued logic and its paraconsistent counterpart. Logica Universalis, 7(4), 507-532. DOI: 10.1007/s11787-013-0088-7. View-only. PDF

G. Robles (2013). Admissibility of Ackermanns rule /delta in relevant logics. Logic and Logical Philosophy, 22(4), 411–427. DOI: 10.12775/LLP.2013.018 (Open access).

J. M. Méndez, G. Robles, F. Salto (2012). Ticket Entailment plus the mingle axiom has the variable-sharing property. Logic Journal of the IGPL, 20(1), 355-364. DOI: 10.1093/jigpal/jzr046.

G. Robles (2012). Paraconsistency and consistency understood as the absence of the negation of any implicative theorem- Reports on Mathematical logic, 47, 147-171. DOI: 10.4467/20842589RM.12.007.0688 (Open access).

G. Robles (2012). A semantical proof of the admissibility of the rule assertion in some relevant and modal logics. Bulletin of the Section of Logic, 41(1-2), 51-60. PDF.

G. Robles, J. M. Méndez (2012). A general characterization of the variable-sharing property by means of logical matrices. Notre Dame Journal of Formal Logic, 53(2), 223-244. DOI: 10.1215/00294527-1715707.

J. M. Méndez, G, Robles, F. Salto (2011). Adding the disjunctive syllogism to relevant logics including TW plus the contraction and reductio rules. Logique et Analyse, 215, 343-358. https://www.jstor.org/stable/44085013.

G. Robles, J. M. Méndez (2011). A class of simpler logical matrices for the variable-sharing property. Logic and Logical Philosophy, 20(3), 241–249. DOI: 10.12775/LLP.2011.014 (Open access).

G. Robles, J. M. Méndez (2011). A Routley-Meyer semantics for relevant logics including TWR plus the disjunctive syllogism. Logic Journal of the IGPL, 19(1), 18-32. DOI: 10.1093/jigpal/jzp083.

G. Robles, F. Salto, J. M. Méndez (2011). A weak logic with the axiom mingle lacking the variable-sharing property. Bulletin of the Section of Logic, 40(3-4), 195-202. PDF.

G. Robles (2010). The non-involutive Routley star: relevant logics without weak double negation. Teorema, XXIX(3), 103-116.

G. Robles (2010). Minimal non-relevant logics without the K axiom II. Negation introduced with the unary connective. Reports on Mathematical Logic, 45, 97-118. http://rml.tcs.uj.edu.pl/rml-45/04-Robles.pdf (Open access).

G. Robles, J. M. Méndez (2010). Paraconsistent logics included in Lewis’ S4. Review of Symbolic Logic, 3(3), 442-466, 2010. DOI: 10.1017/S1755020310000109

G. Robles, J. M. Méndez (2010). Axiomatizing S4+ and J+ without the suffixing, Prefixing and self-distribution of the conditional axioms. Bulletin of the Section of Logic, 39(1-2), 79-91. PDF.

G. Robles, J. M. Méndez (2010). A Routley-Meyer type semantics for relevant logics including Br plus the Disjunctive Syllogism. Journal of Philosophical Logic, 39, 139-158. DOI: 10.1007/s10992-009-9117-7.

G. Robles, J. M. Méndez, F. Salto (2010). A modal restriction of R-Mingle with the variable-sharing property. Logic and Logical Philosophy, 19, 341-351. DOI:  10.12775/LLP.2010.013 (Open access).

J. M. Méndez, G. Robles (2009). The basic constructive logic for absolute consistency. Journal of Logic, Language and Information, 18(2), 199-216. DOI: 10.1007/s10849-008-9077-2

G. Robles (2009). Relevance logics and intuitionistic negation II. Negation introduced with the unary connective. Journal of Applied Non-Classical Logics, 19(3), 371-388. DOI:  10.3166/jancl.19.371-388

G. Robles (2009). Weak consistency and strong paraconsistency. Triple C (Open Access Journal for a Global Sustainable Information Society), 7(2), 185-193. DOI: 10.31269/triplec.v7i2.99 (Open access).

G. Robles, J. M. Méndez (2009). Strong paraconsistency and the basic constructive logic for an even weaker sense of consistency. Journal of Logic, Language and Information, 18(3), 357-402. DOI: 10.1007/s10849-009-9085-x.

G. Robles, J. M. Méndez (2009). The basic constructive logic for weak consistency and the reductio axioms. Bulletin of the Section of Logic, 38(1-2), 61-76, 2009. PDF.

J. M. Méndez, G. Robles (2008). Relevance logics and intuitionistic negation. Journal of Applied Non-Classical Logics, 18(1), 49-65. DOI: 10.3166/jancl.18.49-65.

G. Robles (2008). A note on the non-involutive Routley Star. Bulletin of the Section of Logic, 37(1), 19-27. PDF.

G. Robles (2008). The basic constructive logic for absolute consistency defined with a falsity constant. Logic Journal of the IGPL, 16(3), 275-291. DOI: 10.1093/jigpal/jzn007.

G. Robles (2008). Extensions of the basic constructive logic for weak consistency B_{Kc1} defined with a falsity constant. Logic and Logical Philosophy, 16(4), 311-332. DOI: 10.12775/LLP.2007.010 (Open access).

G. Robles (2008). Extensions of the basic constructive logic for negation-consistency B_{Kc4} defined with a falsity constant. Logique et Analyse, 201, 57-80.

G. Robles (2008). The basic constructive logic for negation-consistency. Journal of Logic Language and Information, 17(2), 161-181. DOI: 10.1007/s10849-007-9056-z.

G. Robles, J. M. Méndez (2008). The basic constructive logic for a weak sense of consistency. Journal of Logic Language and Information, 17(1), 89-107. DOI: 10.1007/s10849-007-9042-5.

G. Robles, J. M. Méndez (2008). The basic constructive logic for a weak sense of consistency defined with a propositional falsity constant. Logic Journal of the IGPL, 16(1), 33-41. DOI: 10.1093/jigpal/jzm015

G. Robles, F. Salto, J. M. Méndez (2008). Exhaustively axiomatizing S3o-> and S4o->. Teorema, XXVII(2), 79-89.

J. M. Méndez, G. Robles, F. Salto (2007). The basic constructive logic for negation-consistency defined with a propositional falsity constant. Bulletin of the Section of Logic, 36(1-2), 45-57. PDF.

J. M. Méndez, F. Salto, G. Robles (2007). El sistema Bp+: una lógica positiva mínima para la negación mínima. Theoria, 22(1), 81-91. DOI: 10.1387/theoria.483 (Open access).

G. Robles, J. M. Méndez (2007). Minimal non-relevant logics without the K axiom. Reports on Mathematical Logic, 42, 117-144. http://rml.tcs.uj.edu.pl/rml-42/07-robles.pdf (Open access).

G. Robles, J. M. Méndez, F. Salto (2007). Relevance logics, paradoxes of consistency and the K rule. Logique et Analyse, 198, 129-145.

J. M. Méndez, G. Robles (2006). Relevance logics, paradoxes of consistency and the K rule II. A non-constructive negation. Logic and Logical Philosophy, 15, 175-191. DOI: 10.12775/LLP.2006.011 (Open access).

G. Robles, J. M. Méndez (2006). Converse Ackermann Property and constructive negation defined with a negation connective. Logic and Logical Philosophy, 15, 113-130. DOI: 10.12775/LLP.2006.007 (Open access).

G. Robles, J. M. Méndez (2005). A constructive negation for logics including TW+. Journal of Applied Non-Classical Logics, 15(4), 389-404. DOI: 10.3166/jancl.15.389-404.

G. Robles, J. M. Méndez (2005). Constructive negation defined with a falsity constant for positive logics with the CAP defined with a truth constant. Logique et Analyse, 189-192, 87-100.

G. Robles, J. M. Méndez (2005). Two versions of minimal intuitionism with the CAP. Theoria, 20(2), 183-190. DOI: 10.1387/theoria.571 (Open access).

G. Robles, J. M. Méndez (2005). Relational ternary semantics for a logic equivalent to Involutive Monoidal t-norm based logic IMTL. Bulletin of the Section of Logic, 34(2), 101-116. PDF

G. Robles, J. M. Méndez (2005). Converse Ackermann Property and minimal negation. Teorema, 24(1), 5-12.

G. Robles, J. M. Méndez, F. Salto (2005). Minimal negation in the ternary relational semantics. Reports on Mathematical Logic, 39, 47-65. http://rml.tcs.uj.edu.pl/rml-39/mendez.pdf (Open access).

G. Robles, F. Salto, J. M. Méndez (2005). A constructive negation defined with a negation connective for logics including Bp+. Bulletin of the Section of Logic, 34(3), 177-189. PDF

G. Robles, J. M. Méndez (2004). The logic B and the reductio axioms. Bulletin of the Section of Logic, 33(2), 87-94. PDF

G. Robles, J. M. Méndez, F. Salto, P. Méndez R. (2003). Intuitionistic propositional logic with the Converse Ackermann Property. Teorema, 2(1-2), 43-54.

J. M. Méndez, F. Salto, G. Robles (2002). Anderson and Belnap's minimal implicative logic with minimal negation. Reports on Mathematical Logic, 36, 117-130. http://rml.tcs.uj.edu.pl/rml-36/36-mendez.pdf (Open access).

G. Robles, J. M. Méndez (2002). Exhaustively axiomatizing Eo-> and Ro->. Logical Studies, 9, 1-10.

F. Salto, G. Robles, J. M. Méndez (2001). Exhaustively axiomatizing EMO->. Logical Studies, 7, 1-6.

F. Salto, J. M. Méndez, G. Robles (2001). Restricting the contraction axiom in Dummett’s LC: LC with the Converse Ackermann Property. Bulletin of the Section of Logic, 30(3), 139-146. PDF.

G. Robles, J. M. Méndez (2018). Routley-Meyer ternary relational semantics for intuitionistic-type negations, Elsevier, ISBN: 9780081007518.

G. Robles Vázquez (2006). Negaciones subintuicionistas para lógicas con la Conversa de la Propiedad Ackermann. [PhD thesis] Ediciones Universidad de Salamanca, ISBN: 84-7800-468-8.

G. Robles, J. M. Méndez (Forthcoming). The only 3‐valued logic which is a natural implication expansion with the variable-sharing property of Kleene’s strong logic. New Directions in Relevant Logics (A. Tedder, I. Sedlar, S. Standefer, Eds.). Trends in Logic Book Series. Springer.

G. Robles, J. M. Méndez (2022). A class of 4-valued implicative expansions of first-degree entailment logic (FDE) with the variable-sharing property. In Relevance Logics and Other Tools for Reasoning. Essays in Honor of J. Michael Dunn (ed. by Katalin Bimbó). Tributes, vol. 46, 338-364. College Publications, London, UK. https://www.collegepublications.co.uk/tributes/?00046 (Open access)

G. Robles, J. M. Méndez (2009). On defining constructive negation in logics of entailment. In Dimensions of Logical Concepts (ed. J-Y. Béziau, A. Costa-Leite). Coleção CLE, vol. 54, UNICAMP, Campinas, Brazil. ISBN: 978-85-86497-05-6, 2009, 265-277.

J. M. Méndez, G. Robles (2007). Lógica de la relevancia. In Filosofía de la Lógica (ed. M. J. Frápolli). Tecnos, Madrid, 2007, 255-286.

G. Robles (2021). A variant with the variable-sharing property of Brady’s 4-valued implicative expansion BN4 of Anderson and Belnap’s logic FDE. In Logic and Argumentation. Fourth International Conference, CLAR 2021, Hangzhou, China, October 20–22, 2021, Proceedings (eds P. Baroni, C. Benzmüller, Y. N. Wáng), LNAI, vol. 13040, 362-376. DOI: 10.1007/978-3-030-89391-0_20

G. Robles (2010). La regla ECQ, el silogismo disyuntivo y las lógicas modales de Lewis. Actas del Sexto Congreso de la Sociedad Española de Filosofía Analítica, SEFA 2010 (Eds. A. Jaume, M. Liz, D. Pérez, M. Ponte, M. Vázquez), pp. 147-148, Puerto de la Cruz, octubre, 2010, Universidad de La Laguna, ISBN: 978-84-614-4383-3.

 J. M. Méndez, G. Robles (2010). La regla \delta, \pi^{prime} y E. Actas del Sexto Congreso de la Sociedad Española de Filosofía Analítica, SEFA 2010 (Ed. A. Jaume, M. Liz, D. Pérez, M. Ponte, M. Vázquez), pp. 125-126, Puerto de la Cruz, October, 2010, Universidad de La Laguna, ISBN: 978-84-614-4383-3.

G. Robles (2008). Weak consistency and srong paraconsistency. Actas del I Encuentro Internacional de Expertos en Teorías de la Información, Un Enfoque Interdisciplinar (Eds. J. M. Nafría, F. Salto), León, November, 2008, Universidad de León, ISBN: 978-84-9773-451-6.