Goal-directed calculi for Gödel-Dummett logics

George Metcalfe; Nicola Olivetti; Dov Gabbay

doi:10.1007/978-3-540-45220-1_33

Goal-directed calculi for Gödel-Dummett logics

George Metcalfe, Nicola Olivetti, Dov Gabbay

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

12 Scopus citations

Abstract

In this work we present goal-directed calculi for the Gödel-Dummett logic LC and its finite-valued counterparts, LC_n (n ≥ 2). We introduce a terminating hypersequent calculus for the implicational fragment of LC with local rules and a single identity axiom. We also give a labelled goal-directed calculus with invertible rules and show that it is co-NP. Finally we derive labelled goal-directed calculi for LC_n.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Matthias Baaz, Johann A. Makowsky
Publisher	Springer Verlag
Pages	413-426
Number of pages	14
ISBN (Print)	3540408010, 9783540408017
DOIs	https://doi.org/10.1007/978-3-540-45220-1_33
State	Published - 2003
Externally published	Yes

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2803
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Keywords

Fuzzy Logics
Goal-Directed Calculi
Gödel Logics
Hypersequents
Intermediate Logics

Access to Document

10.1007/978-3-540-45220-1_33

Cite this

Metcalfe, G., Olivetti, N., & Gabbay, D. (2003). Goal-directed calculi for Gödel-Dummett logics. In M. Baaz, & J. A. Makowsky (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 413-426). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2803). Springer Verlag. https://doi.org/10.1007/978-3-540-45220-1_33

Metcalfe, George ; Olivetti, Nicola ; Gabbay, Dov. / Goal-directed calculi for Gödel-Dummett logics. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Matthias Baaz ; Johann A. Makowsky. Springer Verlag, 2003. pp. 413-426 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Metcalfe, G, Olivetti, N & Gabbay, D 2003, Goal-directed calculi for Gödel-Dummett logics. in M Baaz & JA Makowsky (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2803, Springer Verlag, pp. 413-426. https://doi.org/10.1007/978-3-540-45220-1_33

Goal-directed calculi for Gödel-Dummett logics. / Metcalfe, George; Olivetti, Nicola; Gabbay, Dov.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Matthias Baaz; Johann A. Makowsky. Springer Verlag, 2003. p. 413-426 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2803).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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Metcalfe G, Olivetti N, Gabbay D. Goal-directed calculi for Gödel-Dummett logics. In Baaz M, Makowsky JA, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2003. p. 413-426. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-45220-1_33

Goal-directed calculi for Gödel-Dummett logics

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