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A FORMALISATION OF CONSTRUCTIVE EVIDENCE-BASED REASONING: CONSTRUCTING JUSTIFICATIONS

Part of: General logic Artificial intelligence (68Txx)

Published online by Cambridge University Press:  03 March 2025

JUAN C. AGUDELO-AGUDELO Open the ORCID record for JUAN C. AGUDELO-AGUDELO [Opens in a new window]  and
WALTER CARNIELLI Open the ORCID record for WALTER CARNIELLI [Opens in a new window]
JUAN C. AGUDELO-AGUDELO*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF ANTIOQUIA MEDELLIN, 050010, COLOMBIA
WALTER CARNIELLI
Affiliation:
CENTRE FOR LOGIC EPISTEMOLOGY AND THE HISTORY OF SCIENCES STATE UNIVERSITY OF CAMPINAS CAMPINAS, 13083-852, BRAZIL E-mail: walterac@unicamp.br
*
E-mail: juan.agudelo9@udea.edu.co
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Abstract

A Constructive Logic of Evidence and Truth ($\mathsf {LET_C}$) is introduced. This logic is both paraconsistent and paracomplete, providing connectives for consistency and determinedness that enable the independent recovery of explosiveness and the law of excluded middle for specific propositions. Dual connectives for inconsistency and undeterminedness are also defined in $\mathsf {LET_C}$. Evidence is explicitly formalised by integrating lambda calculus terms into $\mathsf {LET_C}$, resulting in the type system $\mathsf {LET_C^{\lambda }}$. In this system, lambda calculus terms represent procedures for constructing evidence for compound formulas based on the evidence of their constituent parts. A realisability interpretation is provided for $\mathsf {LET_C}$, establishing a strong connection between deductions in this system and recursive functions.

Keywords

paraconsistent logicparacomplete logicconstructive logicevidence-based logic

MSC classification

Primary: 03B53: Paraconsistent logics 68T27: Logic in artificial intelligence

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Type
Article
Information
Bulletin of Symbolic Logic , First View , pp. 1 - 25
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

Almukdad, A. and Nelson, D., Constructible falsity and inexact predicates . The Journal of Symbolic Logic , vol. 49 (1984), no. 1, pp. 231–233.Google Scholar
Antunes, H., Carnielli, W. A., Kapsner, A., and Rodrigues, A., Kripke-style models for logics of evidence and truth . Axioms , vol. 9 (2020), no. 3, p. 100.Google Scholar
Artemov, S., Logic of proofs . Annals of Pure and Applied Logic , vol. 67 (1994), pp. 29–59.Google Scholar
Artemov, S., Explicit provability and constructive semantics . The Bulletin of Symbolic Logic , vol. 7 (2001), no. 1, pp. 1–36.Google Scholar
Artemov, S., The logic of justification . The Review of Symbolic Logic , vol. 1 (2008), no. 4, pp. 477–513.Google Scholar
Artemov, S. and Fitting, M., Justification Logic: Reasoning with Reasons , Cambridge Tracts in Mathematics, 216, Cambridge University Press, New York, 2019.Google Scholar
van Benthem, J. and Pacuit, E., Dynamic logics of evidence-based beliefs . Studia Logica , vol. 99 (2011), pp. 61–92.Google Scholar
Carnielli, W. A. and Bueno-Soler, J., Where the truth lies: A paraconsistent approach to Bayesian epistemology . Studia Logica , vol. In print (2024).Google Scholar
Carnielli, W. A., Frade, L., Rodrigues, A., and Bueno-Soler, J., On factive and non-factive evidence: Combining the modal logics S4 and KX4, unpublished manuscript, 2024.Google Scholar
Carnielli, W. A. and Rodrigues, A., An epistemic approach to paraconsistency: A logic of evidence and truth . Synthese , vol. 196 (2019), pp. 3789–3813.Google Scholar
Epstein, R. L. and . Carnielli, W. A, Computability: Computable Functions, Logic, and the Foundations of Mathematics , third ed., Advanced Reasoning Forum, Socorro, 2008.Google Scholar
Fitting, M., Paraconsistent logic, evidence and justification . Studia Logica , vol. 105 (2017), pp. 1149–1166.Google Scholar
Kamide, N., Natural deduction systems for nelson’s paraconsistent logic and its neighbors . Journal of Applied Non-Classical Logics , vol. 15 (2005), pp. 405–435.Google Scholar
Kleene, S. C., On the interpretation of intuitionistic number theory . The Journal of Symbolic Logic , vol. 10 (1945), no. 4, pp. 109–124.Google Scholar
Martin-Löf, P., Intuitionistic type theory, Technical report, Bibliopolis, Napoli, 1984, Notes by Giovanni Sambin of a series of lectures given in Padua 1980.Google Scholar
Negri, S. and von Plato, J., Structural Proof Theory , Cambridge University Press, New York, 2001.Google Scholar
Nelson, D., Constructible falsity . The Journal of Symbolic Logic , vol. 14 (1949), no. 1, pp. 16–26.Google Scholar
Odintsov, S. P., Constructive Negations and Paraconsistency , Trends in Logic, 26, Springer, Dordrecht, 2008.Google Scholar
Priest, G., In Contradiction: A Study of the Transconsistent , Martinus Nijhoff, Dordrecht, 1987.Google Scholar
Rodrigues, A., Bueno-Soler, J., and Carnielli, W. A., Measuring evidence: A probabilistic approach to an extension of Belnap-Dunn logic . Synthese , vol. 198 (2021), no. 22, pp. 5451–5480.Google Scholar
Rodrigues, A., Coniglio, M. E., Antunes, H., Bueno-Soler, J., and Carnielli, W. A., Paraconsistency, evidence, and abduction , Handbook of Abductive Cognition (L. Magnani, editor), Springer, Cham, 2023, pp. 313–350.Google Scholar
Rose, G. F., Propositional calculus and realizability . Transactions of the American Mathematical Society , vol. 75 (1953), no. 1, pp. 1–19.Google Scholar
Shramko, Y., What is a genuine intuitionistic notion of falsity? Logic and Logical Philosophy , vol. 21 (2012), pp. 3–23.Google Scholar
Sørensen, M. H. and Urzyczyn, P., Lectures on the Curry-Howard isomorphism , Studies in Logic and the Foundations of Mathematics, 149, Elsevier, Amsterdam, 2006.Google Scholar
Wansing, H., Constructive negation, implication and co-implication . Journal of Applied Non-Classical Logics , vol. 18 (2008), nos. 2–3, pp. 341–364.Google Scholar