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Logic and Logical Philosophy

Local Applications of Logics via Model-Theoretic Interpretations
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  3. Vol. 31 No. 4 (2022): December /
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Local Applications of Logics via Model-Theoretic Interpretations

Authors

  • Carlos Benito-Monsalvo University of Barcelona, Logos Research Group in Analytic Philosophy

DOI:

https://doi.org/10.12775/LLP.2022.023

Keywords

interpretations, model-theoretic semantics, proof-theoretic semantics, localism, ST-hierarchy

Abstract

This paper analyses the notion of ‘interpretation’, which is often tied to the semantic approach to logic, where it is used when referring to truth-value assignments, for instance. There are, however, other uses of the notion that raise interesting problems. These are the cases in which interpreting a logic is closely related to its justification for a given application. The paper aims to present an understanding of interpretations that supports the model-theoretic characterization of validity to the detriment of the proof-theoretic one. This is done by making use of the hierarchy of ST-related logics. Finally, a localist conception of logic is defended as the natural view stemming from the model-theoretic approach.

References

Abbott, B., 1997, “Models, truth and semantics”, Linguistics and Philosophy 20: 117–138.

Barrio, E., and B. Da Ré, 2018, “Paraconsistency and its philosophical interpretations”, The Australasian Journal of Logic 15 (2): 151–171. DOI: http://dx.doi.org/10.26686/ajl.v15i2.4860

Barrio, E. A., F. Pailos, and D. Szmuc, 2018, “Substructural logics, pluralism and collapse”, Synthese. DOI: http://dx.doi.org/10.1007/s11229-018-01963-3

Barrio, E. A., F. Pailos, and D. Szmuc, 2019, “(Meta)Inferential levels of entailment beyond the Tarskian paradigm”, Synthese. DOI: http://dx.doi.org/10.1007/s11229-019-02411-6

Barrio, E. A., F. Pailos, and D. Szmuc, 2020, “A hierarchy of classical and paraconsistent logics”, Journal of Philosophical Logic 49 (1): 93–120. DOI: http://dx.doi.org/10.1007/s10992-019-09513-z

Beall, J. C., and G. Restall, 2006, Logical Pluralism, Oxford University Press, Oxford. DOI: http://dx.doi.org/10.1093/acprof:oso/9780199288403.001.0001

Cobreros, P., P. Egré, D. Ripley, and R. van Rooij, 2012, “Tolerant, classical, strict”, Journal of Philosophical Logic 41(2): 347–385. DOI: http://dx.doi.org/10.1007/s10992-010-9165-z

Cobreros, P., E. La Rosa and L. Taranchini, 2021, “Higher-level inferences in the strong-Kleene setting: A proof-theoretic approach”, Journal of Philosophical Logic. DOI: http://dx.doi.org/10.1007/s10992-021-09639-z

Cozzo, C., 1994, Meaning and Argument, Almqvist & Wiksell, Stockholm. Dummett, M., 1977, Elements of Intuitionism, Clarendon Press, Oxford.

Field, H., 2009, “Pluralism in logic”, The Review of Symbolic Logic 2 (2): 342–359. DOI: http://dx.doi.org/10.1017/S1755020309090182

Haack, S., 1978, Philosophy of Logics, Cambridge University Press, Cambridge. DOI: http://dx.doi.org/10.1017/CBO9780511812866.002

Hjortland, O., and S. Standefer, 2018, “Inferentialism, structure, and conservativeness”, in O. Beran, V. Kolman and L. Koren (eds.), From Rules to Meanings, New York: Routledge. DOI: http://dx.doi.org/10.4324/9781315103587

Lynch, M. P., 2009, Truth as One and Many, Oxford University Press, Oxford. DOI: http://dx.doi.org/10.1093/acprof:oso/9780199218738.003.0005

MacFarlane, J. G., 2000, “What does it mean to say that logic is formal?”, PhD Thesis, University of Pittsburgh.

Popper, K. R., 1979, Truth, Rationality and the Growth of Scientific Knowledge, Frankfurt am Main: Klostermann.

Prawitz, D., 1965, Natural Deduction, Almqvist & Wiksell, Stockholm.

Prawitz, D., 2015, “Classical versus intuitionistic logic”, Why is this a Proof? Festschrift for Luiz Carlos Pereira 27: 15–32.

Priest, G., 2005, Doubt Truth to be a Liar, Oxford University Press, Oxford. DOI: http://dx.doi.org/10.1093/0199263280.001.0001

Prior, A. N., 1960, “The runabout inference-ticket”, Analysis 21 (2): 38–39. DOI: http://dx.doi.org/10.1093/analys/21.2.38

Quine, W. V., 1970, The Philosophy of Logic, Prentice-hall.

Shapiro, S., 2014, Varieties of Logic, Oxford University Press, Oxford. DOI: http://dx.doi.org/10.1093/acprof:oso/9780199696529.001.0001

Steinberger, F., 2011, “Why conclusions should remain single”, Journal of Philosophical Logic 40: 333–355. DOI: http://dx.doi.org/10.1007/s10992-010-9153-3

van Benthem, J., 2008, “Logical dynamics meets logical pluralism?”, The Australasian Journal of Logic 6: 182–209. DOI: http://dx.doi.org/10.26686/ajl.v6i0.1801

Wittgenstein, L., 1922, Tractatus Logico-Philosophicus, Routledge & Kegan Paul, London.

Wright, C., 1992, Truth and Objectivity, Harvard University Press, Cambridge.

Zardini, E., 2018, “Generalised Tarski’s thesis hits substructure”, in J. Wyatt, N. J. L. L. Pedersen and N. Kellen (eds.), Pluralisms in Truth and Logic, Palgrave Macmillan. DOI: http://dx.doi.org/10.1007/978-3-319-98346-2

Logic and Logical Philosophy

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Published

2022-07-09

How to Cite

1.
BENITO-MONSALVO, Carlos. Local Applications of Logics via Model-Theoretic Interpretations. Logic and Logical Philosophy. Online. 9 July 2022. Vol. 31, no. 4, pp. 535-556. [Accessed 2 July 2025]. DOI 10.12775/LLP.2022.023.
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Vol. 31 No. 4 (2022): December

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Copyright (c) 2022 Carlos Benito-Monsalvo

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This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

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