The Logical Burdens of Proof. Assertion and Hypothesis

Daniele Chiffi; Fabien Schang

doi:10.12775/LLP.2017.006

Authors

Daniele Chiffi Tallinn University of Technology
Fabien Schang Universidade Estadual de Maringá

DOI:

https://doi.org/10.12775/LLP.2017.006

Keywords

logic for pragmatics, assertion, hypothesis, question-answer semantics, logical opposition

Abstract

The paper proposes two logical analyses of (the norms of) justification. In a first, realist-minded case, truth is logically independent from justification and leads to a pragmatic logic LP including two epistemic and pragmatic operators, namely, assertion and hypothesis. In a second, antirealist-minded case, truth is not logically independent from justification and results in two logical systems of information and justification: AR₄ and AR₄_¢, respectively, provided with a question-answer semantics. The latter proposes many more epistemic agents, each corresponding to a wide variety of epistemic norms. After comparing the different norms of justification involved in these logical systems, two hexagons expressing Aristotelian relations of opposition will be gathered in order to clarify how (a fragment of) pragmatic formulas can be interpreted in a fuzzy-based question-answer semantics.

Author Biography

Fabien Schang, Universidade Estadual de Maringá

Centro de Cięncias Humanas

References

Bellin, G., “Assertions, hypotheses, conjectures, expectations: Roughsets semantics and proof-theory”, pages 193–241 in Advances in Natural Deduction: A Celebration of Dag Prawitz’s Work, L.C. Pereira, E.H. Haeusler, V. de Paiva (eds.), “Trends in Logic”, vol. 39, Springer, Dordrecht, 2014. DOI: 0.1007/978-94-007-7548-0_10

Bellin, G., M. Carrara, D. Chiffi, D., and A. Menti, “Pragmatic and dialogic interpretations of bi-intuitionism. Part I”, Logic and Logical Philosophy 23, 4 (2014): 449–480. DOI: 10.12775/LLP.2014.011

Bellin, G., M. Carrara, and D. Chiffi, “On an intuitionistic logic for pragmatics”, Journal of Logic and Computation, exv036 (2015). DOI: 10.1093/logcom/exv036

Carrara, M., D. Chiffi, and C. De Florio, “Assertions and hypotheses: A logical framework for their opposition relations”, Logic Journal of the IGPL 25, 2 (2017): 131–144. DOI: 10.1093/jigpal/jzw036

Carrara, M., and D. Chiffi, “The knowability paradox in the light of a logic for pragmatics”, pages 47–58 in Recent Trends in Philosophical Logic, R. Ciuni, H. Wansing, and C. Willkommen (eds.), “Proceedings of Trends in Logic XI”, Studia Logica Library, “Trends in Logic”, vol. 41, Springer, Berlin, 2014. DOI: 10.1007/978-3-319-06080-4_3

Carrara, M., D. Chiffi, and D. Sergio, “Knowledge and proof: a multimodal pragmatic language”, pages 1–13 in Logica Yearbook 2013, V. Punčochář and M. Dančák (eds.), College Publication, London, 2014.

Dalla Pozza, C., and C. Garola, “A pragmatic interpretation of intuitionistic propositional logic”, Erkenntnis 43 (1995): 81–109. DOI: 10.1007/BF01131841

Dugundji, J., “Note on a property of matrices for Lewis and Langford’s calculi of propositions”, The Journal of Symbolic Logic 5, 4 (1940): 150–151. DOI: 10.2307/2268175

Schang, F., “Abstract logic of oppositions”, Logic and Logical Philosophy 21 (2012): 415–438. DOI: 10.12775/LLP.2012.019

Schang, F., “A four-valued strong implication”, 2017 (unpublished manuscript).

Schang, F., and A. Costa-Leite, “Une sémantique générale des croyances justifiées”, CLE 16, 3 (2016).

Shramko, Y. “Dual intuitionistic logic and a variety of negations: the logic of scientific research”, Studia Logica 80, 2–3 (2005): 347–367. DOI: 10.1007/s11225-005-8474-7

Shramko, Y., “A modal translation for dual-intuitionistic logic”, The Review of Symbolic Logic 9, 2 (2016): 251–265. DOI: 10.1017/S1755020316000022

Smessaert, H., “On the 3D visualization of the logical relations”, Logica Universalis 3 (2009): 212–231. DOI: 10.1007/s11787-009-0010-5