The quasi-relevant 3-valued logic RM3 and some of its sublogics lacking the variable-sharing property

• Autorzy: Robles G.

Identyfikatory

DOI

10.4467/20842589RM.16.008.5285

• Języki publikacji: EN

Abstrakty

EN

The logic RM3 is the 3-valued extension of the logic R-Mingle (RM). RM (and so, RM3) does not have the variable- sharing property (vsp), but RM3 (and so, RM) lacks the more “offending" “paradoxes of relevance”, such as A → (B → A) or ⌐A → (A → B). Thus, RM and RM3 can be useful when “some relevance”, but not the full vsp, is needed. Sublogics of RM3 with the vsp are well known, but this is not the case with those lacking this property. The first aim of this paper is to define an ample family of sublogics of RM3 without the vsp. The second one is to provide these sublogics and RM3 itself with a general Routley- Meyer semantics, that is, the semantics devised for relevant logics in the early seventies of the past century.

Słowa kluczowe

EN

RM3; R-Mingle; relevant logics; quasi-relevant logics; Routley-Meyer semantics; relational semantics; substructural logics

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2016
• Tom: Vol. 51
• Strony: 105--131
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Robles G.

• Dpto. de Psicología, Sociología y Filosofía Universidad de León Campus de Vegazana, s/n 24071, León Spain , http://grobv.unileon.es

Bibliografia

• [1] A. R. Anderson and N. D. Belnap Jr., Entailment. The Logic of Relevance and Necessity, vol I. Princeton University Press, 1975.
• [2] R. T. Brady, Completeness Proofs for the Systems RM3 and BN4, Logique et Analyse 25 (1982), 9-32.
• [3] R. T. Brady, Depth relevance of some paraconsistent logics, Studia Logica 43 (1984), 63-73.
• [4] R. T. Brady, Hierarchical semantics for relevant logics, Journal of Philosophical Logic 25 (1992), 357-374.
• [5] R. T. Brady (ed.), Relevant Logics and Their Rivals, Vol. II, Ashgate, Aldershot, 2003
• [6] R. T. Brady, Universal Logic, CSLI, Stanford, CA, 2006.
• [7] J. M. Dunn, Algebraic completeness results for R-Mingle and its extensions , Journal of Symbolic Logic 35 (1970), 1-13.
• [8] J. M. Dunn, Partiality and its Dual , Studia Logica bf 65 (2000), 5-40.
• [9] G. Robles, A Routley-Meyer semantics for Gödel 3-valued logic and its paraconsistent counterpart, Logica Universalis 7 (2013), 507-532.
• [10] G. Robles and J. M. Mendez, The basic constructive logic for a weak sense of consistency, Journal of Logic Language and Information 17 (2008), 89-107.
• [11] G. Robles and J. M. Mendez, A Routley-Meyer semantics for truth-preserving and well-determined Lukasiewicz 3-valued logics, Logic Journal of the IGPL 22 (2014), 1-23.
• [12] G. Robles, F. Salto, and J. M. Mendez, A weak logic with the axiom mingle lacking the variable-sharing property, Bulletin of the Section of Logic 40:3-4 (2011), 195-202.
• [13] R. Routley, R. K. Meyer, “The semantics of Entailment III”, Journal of Philosophical Logic 1 (1972), 192-208.
• [14] R. Routley, R. K. Meyer, V. Plumwood, and R. T. Brady,Relevant Logics and their Rivals, vol. 1, Ridgeview Publishing Co., Atascadero, CA 1982.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.