User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

Nice Embedding in Classical Logic

Primary tabs

Verdée, Peter [UCL] Batens, Diderik

(eng) It is shown that a set of semi-recursive logics, including many fragments of CL (Classical Logic), can be embedded within CL in an interesting way. A logic belongs to the set iff it has a certain type of semantics, called nice semantics. The set includes many logics presented in the literature. The embedding reveals structural properties of the embedded logic. The embedding turns finite premise sets into finite premise sets. The partial decision methods for CL that are goal directed with respect to CL are turned into partial decision methods that are goal directed with respect to the embedded logics.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2015
Language Anglais
Journal information "Studia Logica : an international journal for symbolic logic" - Vol. 104, no.1, p. 47-78 (2015)
Peer reviewed yes
Publisher Springer Netherlands (Dordrecht)
issn 0039-3215
e-issn 1572-8730
Publication status Publié
Affiliation UCL - SSH/ISP - Institut supérieur de philosophie
Links
  1. Anderson A.R., Belnap N.D. Jr.: Entailment. The Logic of Relevance and Necessity, vol. 1. Princeton University Press, Princeton (1975)
  2. Arruda Ayda I., On the Imaginary Logic of N. A. Vasil'év, Non-Classical Logics, Model Theory, And Computability (1977) ISBN:9780720407525 p.3-24, 10.1016/s0049-237x(08)70642-6
  3. Batens Diderik, Spoiled for choice?, 10.1093/logcom/ext019
  4. Batens, D., Paraconsistent extensional propositional logics, Logique et Analyse 90–91:195–234, 1980.
  5. Batens, D., Inconsistency-adaptive logics, in E. Orłowska (ed.), Logic at Work. Essays Dedicated to the Memory of Helena Rasiowa, Physica Verlag (Springer), Heidelberg, New York, 1999, pp. 445–472.
  6. Batens D.: It might have been Classical Logic. Logique et Analyse 218, 241–279 (2012)
  7. Batens, D., and D. Provijn, Pushing the search paths in the proofs. A study in proof heuristics, Logique et Analyse 173–175:113–134, 2001 (Appeared 2003).
  8. Bates Larry, Cushman Richard, What is a completely integrable nonholonomic dynamical system?, 10.1016/s0034-4877(99)80142-6
  9. Boolos George S., Burgess John P., Jeffrey Richard C., Computability and Logic, ISBN:9781139164931, 10.1017/cbo9781139164931
  10. Carnielli Walter A., Coniglio Marcelo E., D’Ottaviano Itala M. L., New Dimensions on Translations Between Logics, 10.1007/s11787-009-0002-5
  11. da Costa N.C.A.: Calculs propositionnels pour les systèmes formels inconsistants. Comptes rendus de l’Académie des sciences de Paris 259, 3790–3792 (1963)
  12. da Costa Newton C. A., On the theory of inconsistent formal systems., 10.1305/ndjfl/1093891487
  13. Gabbay Dov M., Olivetti Nicola, Goal-Directed Proof Theory, ISBN:9789048155262, 10.1007/978-94-017-1713-7
  14. Hughes, G. E., and M. J. Cresswell, An Introduction to Modal Logic, Methuen, London, New York, 1972 (First published 1968).
  15. JEŘÁBEK EMIL, THE UBIQUITY OF CONSERVATIVE TRANSLATIONS, 10.1017/s1755020312000226
  16. Kleene S.C.: Introduction to Metamathematics. North-Holland, Amsterdam (1952)
  17. Meheus, J., An extremely rich paraconsistent logic and the adaptive logic based on it, in D. Batens, C. Mortensen, G. Priest, and J. P. Van Bendegem (eds.), Frontiers of Paraconsistent Logic, Research Studies Press, Baldock, 2000, pp. 189–201.
  18. Priest Graham, In Contradiction, ISBN:9789401081511, 10.1007/978-94-009-3687-4
  19. Rosser J. B., Turquette A. R., Axiom schemes for m-valued propositions calculi , 10.2307/2267026
  20. Schütte K.: Beweistheorie. Springer, Berlin (1960)
Bibliographic reference Verdée, Peter ; Batens, Diderik. Nice Embedding in Classical Logic. In: Studia Logica : an international journal for symbolic logic, Vol. 104, no.1, p. 47-78 (2015)
Permanent URL http://hdl.handle.net/2078.1/171530