Abstract
Characterizations of admissible quasi-identities, which may be understood as quasi-identities holding in free algebras on countably infinitely many generators, are provided for classes of De Morgan algebras and lattices.
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References
Bergman C (1991) Structural completeness in algebra and logic. In: Andréka H, Monk J, Nemeti I (eds) Algebraic logic (proc. conf., Budapest, 8–14 August 1988), Colloquia Mathematica Societatis János Bolyai, vol 54. North-Holland, Amsterdam, pp 59–73
Burris S, Sankappanavar HP (1981) A course in universal algebra. Graduate texts in mathematics, vol 78. Springer, New York
Cintula P, Metcalfe G (2009) Structural completeness in fuzzy logics. Notre Dame J Formal Log 50(2):153–183
Cintula P, Metcalfe G (2010) Admissible rules in the implication-negation fragment of intuitionistic logic. Ann Pure Appl Log 162(10):162–171
Font JM (1997) Belnap’s four-valued logic and De Morgan lattices. Log J IGPL 5(3):1–29
Gaitán H, Perea MH (2004) A non-finitely based quasi-variety of De Morgan algebras. Stud Log 78(1–2):237–248
Galatos N, Jipsen P, Kowalski T, Ono H (2007) Residuated lattices: an algebraic glimpse at substructural logics. Elsevier, Amsterdam
Gehrke M, Walker CL, Walker EA (2003) Normal forms and truth tables for fuzzy logics. Fuzzy Sets Syst 138:25–51
Ghilardi S (1999) Unification in intuitionistic logic. J Symb Log 64(2):859–880
Ghilardi S (2000) Best solving modal equations. Ann Pure Appl Log 102(3):184–198
Iemhoff R (2001) On the admissible rules of intuitionistic propositional logic. J Symb Log 66(1):281–294
Jeřábek E (2005) Admissible rules of modal logics. J Log Comput 15:411–431
Jeřábek E (2010a) Admissible rules of Łukasiewicz logic. J Log Comput 20(2):425–447
Jeřábek E (2010b) Bases of admissible rules of Łukasiewicz logic. J Log Comput 20(6):1149–1163
Kalman JA (1958) Lattices with involution. Trans Am Math Soc 87:485–491
Moisil G (1935) Recherches sur l’algébre de la logique. Ann Sci Univ Jassy 22(3):1–117
Olson JS, Raftery JG (2007) Positive Sugihara monoids. Algebra Univers 57:75–99
Olson JS, Raftery JG, Alten CJV (2008) Structural completeness in substructural logics. Log J IGPL 16(5):453–495
Pynko AP (1999) Implicational classes of De Morgan lattices. Discrete Math 205(1–3):171–181
Rybakov VV (1997) Admissibility of logical inference rules. Studies in logic and the foundations of mathematics, vol 136. Elsevier, Amsterdam
Acknowledgments
We are grateful for the helpful comments of both the anonymous referees and Leonardo Cabrer. The authors acknowledge support from Swiss National Science Foundation Grant 20002_129507.
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Metcalfe, G., Röthlisberger, C. Admissibility in De Morgan algebras. Soft Comput 16, 1875–1882 (2012). https://doi.org/10.1007/s00500-012-0839-z
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DOI: https://doi.org/10.1007/s00500-012-0839-z