Modal Logic, Probability and Machine Learning Systems for Metadata Extraction

Simone Cuconato

Abstract


Artificial intelligence, since its inception, has had two major subfields, namely: logical reasoning and machine learning. Despite this, the interactions between these two fields have been relatively limited. In this paper, we highlight the need for closer integration of logical reasoning and machine learning. In our approach, logical reasoning tools such as probabilistic modal logic, are employed to provide qualitative feedback on the extracted descriptive metadata. The logical system we consider emerges from combining of S5 modal logic with the formulas of the infinite-valued Łukasiewicz logic and the unary modality P that describes the behaviour of probability functions. The result is a well-motivated system of probabilistic modal logic, that defines a probability distribution over possible worlds of the truth value of metadata extracted from precision medicine approach to Alzheimer’s disease articles through machine learning systems.


Keywords


Modal logic, Probability, Logical reasoning, Machine learning systems

Full Text:

PDF

References


Ganesh, V., Seshia, S.A., Jha, S.: Machine learning and logic: a new frontier in artificial intelligence. Formal Methods in System Design 60, 426–451 (2022). https://doi.org/10.1007/s10703-023-00430-1

Calegari, R., Ciatto, G., Denti, E., Omicini, A.: Logic-Based Technologies for Intelligent Systems: State of the Art and Perspectives. Information 11, (2020). https://doi.org/10.3390/info11030167

De Mol, L., Primiero, G.: When Logic Meets Engineering: Introduction to Logical Issues in the History and Philosophy of Computer Science. History and Philosophy of Logic 36(3), 195–204 (2015). https://doi.org/10.1080/01445340.2015.1084183

Batini, C., Rula, A., Scannapieco, M., Viscusi, G.: From data quality to big data quality. Journal of Database Management 26(1), 60–82 (2015). https://dx.doi.org/10.4018/JDM.2015010103

Berti-Equille, L., Borge-Holthoefer, J.: Veracity of Data: From Truth Discovery Computation Algorithms to Models of Misinformation Dynamics. Morgan & Claypool Publishers (2015).

Cuconato, S.: Fol-Based Applied Ontology for Metadata Extraction in Mathematical Knowledge Management. Romanian Journal of Mathematics and Computer Science 14(1), 1–11 (2024).

Cuconato, S.: A Four-Valued Epistemic Logic for Metadata Modelling from Medical Articles on Pain Therapies. In: Das, A.K., Nayak, J., Naik, B., Vimal, S., Pelusi, D. (eds.) Computational Intelligence in Pattern Recognition (CIPR 2023), Lecture Notes in Networks and Systems, vol. 725, Springer, Singapore (2023). https://doi.org/10.1007/978-981-99-3734-9_5

Cuconato, S.: Epistemic logic for metadata modelling from scientific papers on COVID-19. Science & Philosophy 9(2), 83–96 (2021). http://dx.doi.org/10.23756/sp.v9i2.652

Tkaczyk, D., Szostek, P., Dendek, P.J., Fedoryszak, M., Bolikowski, Ł.: CERMINE—automatic extraction of metadata and references from scientific literature. In: 11th IAPR International Workshop on Document Analysis Systems, pp. 217–221, Tours, France (2014). https://doi.org/10.1109/DAS.2014.63

Pomerantz, J.: Metadata. MIT Press Ltd (2015).

Mayernik, M.S.: Metadata accounts: Achieving data and evidence in scientific research. Social Studies of Science 49(5), 732–757 (2019). https://doi.org/10.1177/0306312719863494

Hood, L., Friend, S.H.: Predictive, personalized, preventive, participatory (P4) cancer medicine. Nature Reviews Clinical Oncology 8, 184–187 (2011). doi:10.1038/nrclinonc.2010.227

Behl, T., Kaur, I., Sehgal, A., Singh, S., Albarrati, A., Albratty, M., Najmi, A., Meraya, A.M., Bungau, S.: The road to precision medicine: Eliminating the “One Size Fits All” approach in Alzheimer’s disease. Biomedicine & Pharmacotherapy 153 (2022). https://doi.org/10.1016/j.biopha.2022.113337

Adornetto, C., Bruno, P., Calimeri, F., De Rose, E., Greco, G.: Artificial Intelligence in Medicine: From Imaging to Omics. Ital-IA 2023, 140–145 (2023).

Silva-Spínola, A., Baldeiras, I., Arrais, J.P., Santana, I.: The Road to Personalized Medicine in Alzheimer’s Disease: The Use of Artificial Intelligence. Biomedicines 10, 1–19 (2022). https://doi.org/10.3390/biomedicines10020315

Baldeiras, I., Santana, I., Leitão, M.J., Gens, H., Pascoal, R., Tábuas-Pereira, M., Beato-Coelho, J., Duro, D., Almeida, M.R., Oliveira, C.R.: Addition of the Aβ42/40 ratio to the cerebrospinal fluid biomarker profile increases the predictive value for underlying Alzheimer’s disease dementia in mild cognitive impairment. Alzheimer’s Research & Therapy 10 (2018). https://doi.org/10.1186/s13195-018-0362-2

van Benthem, J.: Modal Logic for Open Minds. Center for the Study of Language and Information, Stanford, CA, USA (2010).

Blackburn, P., van Benthem, J.F.A.K., Wolter, F.: Handbook of Modal Logic. Studies in Logic and Practical Reasoning 3, North-Holland (2007).

Hájek, P.: Metamathematics of Fuzzy Logic. Springer (1998). https://doi.org/10.1007/978-94-011-5300-3

Hájek, P.: On fuzzy modal logics. Fuzzy Sets and Systems 161(18), 2389–2396 (2010). https://doi.org/10.1016/j.fss.2009.11.011

Flaminio, T., Godo, L.: A logic for reasoning about the probability of fuzzy events. Fuzzy Sets and Systems 158(6), 625–638 (2007). https://doi.org/10.1016/j.fss.2006.11.008

Chatterjee, S., Das, A.K., Nayak, J., Pelusi, D.: Improving Facial Emotion Recognition Using Residual Autoencoder Coupled Affinity Based Overlapping Reduction. Mathematics 10, 1–18 (2022). https://doi.org/10.3390/math10030406

Corsi, E.A., Flaminio, T., Godo, L., Hosni, H.: A Modal Logic for Uncertainty: a Completeness Theorem. In: Miranda, E., Montes, I., Quaeghebeur, E., Vantaggi, B. (eds.) International Symposium on Imprecise Probability: Theories and Applications, Proceedings of Machine Learning Research, 119–129 (2023).

Chang, C.C.: A new proof of the completeness of the Łukasiewicz axioms. Transactions of the American Mathematical Society 93(1), 74–80 (1959).

Goldblatt, R.: Mathematical modal logic: A view of its evolution. Journal of Applied Logic 1(5–6), 309–392 (2003).

McKinsey, J.C.C., Tarski, A.: The Algebra of Topology. Annals of Mathematics 45(1), 141–191 (1944).

Kripke, S.A.: Semantical Analysis of Modal Logic I. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 9(5–6), 67–96 (1963).

Fine, K.: A theory of truth-maker content I: Conjunction, disjunction and negation. Journal of Philosophical Logic 46, 625–674 (2017).

Gawlikowski, J., Tassi, C.R.N., Ali, M. et al.: A survey of uncertainty in deep neural networks. Artificial Intelligence Review 56 (Suppl 1), 1513–1589 (2023). https://doi.org/10.1007/s10462-023-10562-9




DOI: http://dx.doi.org/10.23755/rm.v53i0.1592

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Simone Cuconato

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

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.