Towards a Proof Theory of G\"odel Modal Logics

George Metcalfe; Nicola Olivetti

doi:10.2168/LMCS-7(2:10)2011

George Metcalfe ; Nicola Olivetti - Towards a Proof Theory of Gödel Modal Logics

lmcs:972 - Logical Methods in Computer Science, May 17, 2011, Volume 7, Issue 2 - https://doi.org/10.2168/LMCS-7(2:10)2011

Towards a Proof Theory of Gödel Modal LogicsArticle

Authors: George Metcalfe ; Nicola Olivetti

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of Gödel logic. The calculi are used to establish completeness and complexity results for these fragments.

https://doi.org/10.2168/LMCS-7(2:10)2011

Source: arXiv.org:1105.1256

Volume: Volume 7, Issue 2

Published on: May 17, 2011

Imported on: July 25, 2010

Keywords: Mathematics - Logic,Computer Science - Logic in Computer Science,cs.LO

Licence: arXiv.org - Non-exclusive license to distribute

Funding:

Source : OpenAIRE Graph

Admissible Rules in Logic and Algebra; Funder: Swiss National Science Foundation; Code: 129507
Immunologie des Typ-1 Diabetes.; Funder: Swiss National Science Foundation; Code: 20002

Classifications

Mathematics Subject Classification 2020¹

Sources:

[1] zbMATH Open.

Bibliographic References

16 Documents citing this article

Marta Bílková;Sabine Frittella;Daniil Kozhemiachenko, Lecture notes in computer science, Non-standard Modalities in Paraconsistent Gödel Logic, pp. 420-436, 2023, 10.1007/978-3-031-43619-2_29.

Marta Bílková;Sabine Frittella;Daniil Kozhemiachenko, Lecture notes in computer science, Paraconsistent Gödel Modal Logic, pp. 429-448, 2022, 10.1007/978-3-031-10769-6_26, https://doi.org/10.1007/978-3-031-10769-6_26.

Martín Diéguez;David Fernández-Duque, Studies in computational intelligence, Decidability for $\mathsf S4$ Gödel Modal Logics, pp. 1-7, 2022, 10.1007/978-3-031-07707-4_1.

Xavier Caicedo;George Metcalfe;Ricardo Rodríguez;Olim Tuyt, 2021, One-variable fragments of intermediate logics over linear frames, Information and Computation, 287, pp. 104755, 10.1016/j.ic.2021.104755, https://doi.org/10.1016/j.ic.2021.104755.

Amanda Vidal, 2020, On transitive modal many-valued logics, arXiv (Cornell University), 407, pp. 97-114, 10.1016/j.fss.2020.01.011, https://arxiv.org/abs/1904.01407.

Ricardo Oscar Rodriguez;Amanda Vidal, 2020, Axiomatization of Crisp Gödel Modal Logic, arXiv (Cornell University), 109, 2, pp. 367-395, 10.1007/s11225-020-09910-5, https://arxiv.org/abs/2004.14706.

Petr Cintula;Paula Menchón;Carles Noguera, 2018, Toward a general frame semantics for modal many-valued logics, Soft Computing, 23, 7, pp. 2233-2241, 10.1007/s00500-018-3369-5.

Marco Cerami;Francesc Esteva;Àngel García-Cerdaña, 2017, On the relationship between fuzzy description logics and many-valued modal logics, International Journal of Approximate Reasoning, 93, pp. 372-394, 10.1016/j.ijar.2017.11.006.

Michel Marti;George Metcalfe, 2017, Expressivity in chain-based modal logics, BORIS (University Library Bern), 57, 3-4, pp. 361-380, 10.1007/s00153-017-0573-4, https://boris.unibe.ch/102069/.

Petr Cintula;Carles Noguera, 2017, Neighborhood semantics for modal many-valued logics, Use Siena air (University of Siena), 345, pp. 99-112, 10.1016/j.fss.2017.10.009, https://hdl.handle.net/11365/1200590.

Xavier Caicedo;George Metcalfe;Ricardo Rodríguez;Jonas Rogger, 2017, Decidability of order-based modal logics, BORIS (University Library Bern), 88, pp. 53-74, 10.1016/j.jcss.2017.03.012, https://boris.unibe.ch/102027/.

Tuan-Fang Fan, 2015, Fuzzy Bisimulation for Gödel Modal Logic, IEEE Transactions on Fuzzy Systems, 23, 6, pp. 2387-2396, 10.1109/tfuzz.2015.2426724.

Agata Ciabattoni;Revantha Ramanayake;Heinrich Wansing, 2014, Hypersequent and Display Calculi – a Unified Perspective, Studia Logica, 102, 6, pp. 1245-1294, 10.1007/s11225-014-9566-z.

Francesc Esteva;Lluís Godo;Siegfried Gottwald;Franco Montagna, DIGITAL.CSIC (Spanish National Research Council (CSIC)), Introduction, pp. 3-20, 2014, 10.1007/978-3-319-06233-4_1, http://hdl.handle.net/10261/247471.

Tuan-Fang Fan;Churn-Jung Liau, 2014, Logical characterizations of regular equivalence in weighted social networks, Artificial Intelligence, 214, pp. 66-88, 10.1016/j.artint.2014.05.007, https://doi.org/10.1016/j.artint.2014.05.007.

Xavier Caicedo;George Metcalfe;Ricardo Rodríguez;Jonas Rogger, BORIS (University Library Bern), A Finite Model Property for Gödel Modal Logics, pp. 226-237, 2013, 10.1007/978-3-642-39992-3_20, https://boris.unibe.ch/41260/.

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