Relational Semantics for Kleene Logic and Action Logic

Bimbó, Katalin; Dunn, J.~Michael

Notre Dame J. Formal Logic, Tome 46 (2005) no. 3, p. 461-490 / Harvested from Project Euclid

Résumé

Kleene algebras and action logic were proposed to be solutions to the finite axiomatization problem of the algebra of regular sets (of strings). They are treated here as nonclassical logics—with Hilbert-style axiomatizations and semantics. We also provide intuitive accounts in terms of information states of the semantics which provide further insights into the formalisms. The three types of "Kripke-style'' semantics which we define develop insights from gaggle theory, and from our four-valued and generalized Kripke semantics for the minimal substructural logic. Soundness and completeness are proven each time.

Publié le : 2005-10-14
Classification: gaggle theory, Routley-Meyer semantics, Kripke semantics, nonclassical logics, modal logics, join semi-lattice, residuation, reflexive transitive closure, Kleene star, regular languages, 03B47, 03B45, 68Q70, 03D05

@article{1134397663,
     author = {Bimb\'o, Katalin and Dunn, J.\textasciitilde Michael},
     title = {Relational Semantics for Kleene Logic and Action Logic},
     journal = {Notre Dame J. Formal Logic},
     volume = {46},
     number = {3},
     year = {2005},
     pages = { 461-490},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1134397663}
}

Bimbó, Katalin; Dunn, J.~Michael. Relational Semantics for Kleene Logic and Action Logic. Notre Dame J. Formal Logic, Tome 46 (2005) no. 3, pp.  461-490. http://gdmltest.u-ga.fr/item/1134397663/