MaGIC

MaGIC: Matrix Generator for Implication Connectives. The program MaGIC (Matrix Generator for Implication Connectives) is intended as a tool for logical research. It computes small algebras (normally with up to 14 elements) suitable for modelling certain non-classical logics. Along the way, it eliminates from the output any algebra isomorphic to one already generated, thus returning only one from each isomorphism class. Optionally, the user may specify a formula which is to be imvalid in each structure found. This enables MaGIC to be used for such purposes as showing invalidity of unwanted formulae, proving one system stonger than another and proving the independence of axioms. It can also be used to generate all the small algebras modelling some chosen logic. These can then be used as input for other programs: for instance, they can be used as a database for many purposes including those of refuting non-theorems. They can also be presented in a human-readable format so that they may be perused, for example to suggest metatheorems to an imaginative logician or just to gain a “feel” for this or that system. MaGIC has already been used in the course of researches reported elsewhere (for example, in the paper “Finite Models for some Substructural Logics” TR-ARP-04-94 [DVI | PS])


References in zbMATH (referenced in 17 articles )

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  1. Blanco, José Miguel: EF4, EF4-M and EF4-Ł: a companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes (2022)
  2. Robles, Gemma; Méndez, José M.: Basic quasi-Boolean expansions of relevance logics (2021)
  3. Robles, Gemma; Méndez, José M.: Natural implicative expansions of variants of Kleene’s strong 3-valued logic with Gödel-type and dual Gödel-type negation (2021)
  4. Øgaard, Tore Fjetland: Farewell to suppression-freedom (2020)
  5. Øgaard, Tore Fjetland: Substitution in relevant logics (2020)
  6. Robles, Gemma: A simple Henkin-style completeness proof for Gödel 3-valued logic G3 (2014)
  7. Robles, Gemma; Salto, Francisco; Méndez, José M.: Dual equivalent two-valued under-determined and over-determined interpretations for Łukasiewicz’s 3-valued logic Ł3 (2014)
  8. Robles, Gemma; Méndez, José M.: Paraconsistent logics included in Lewis’ S4 (2010)
  9. Robles, Gemma; Méndez, José M.: A Routley-Meyer type semantics for relevant logics including (\textB_\textr) plus the disjunctive syllogism (2010)
  10. Méndez, José M.; Robles, Gemma: The basic constructive logic for absolute consistency (2009)
  11. Robles, Gemma: Relevance logics and intuitionistic negation. II. Negation introduced with the unary connective (2009)
  12. Robles, Gemma; Méndez, José M.: Strong paraconsistency and the basic constructive logic for an even weaker sense of consistency (2009)
  13. Robles, Gemma: A note on the non-involutive Routley star (2008)
  14. Robles, Gemma: The basic constructive logic for negation-consistency (2008)
  15. Robles, Gemma; Méndez, José M.: The basic constructive logic for a weak sense of consistency (2008)
  16. Ernst, Zachary; Fitelson, Branden; Harris, Kenneth; Wos, Larry: Shortest axiomatizations of implicational S4 and S5 (2002)
  17. Harris, Kenneth; Fitelson, Branden: Comments on some completeness theorems of Urquhart and Méndez & Salto (2001)