Abstract
Binary classifiers are traditionally studied by propositional logic (\(\textsf{PL}\)). \(\textsf{PL}\) can only represent them as white boxes, under the assumption that the underlying Boolean function is fully known. Binary classifiers used in practical applications and trained by machine learning are however opaque. They are usually described as black boxes. In this paper, we provide a product modal logic called PLC (Product modal Logic for binary input Classifier) in which the notion of “black box” is interpreted as the uncertainty over a set of classifiers. We give results about axiomatics and complexity of satisfiability checking for our logic. Moreover, we present a dynamic extension in which the process of acquiring new information about the actual classifier can be represented.
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Notes
- 1.
Notice that p denotes an input variable, while x is an output value rather than the output variable, which makes sense of the symbolic difference between p and \(\textsf{t}({x})\).
- 2.
In the real world, partial knowledge may come from the data set as well as from the training process. For example, through learning, we may acquire knowledge that certain input features behave monotonically [26].
- 3.
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Support from the ANR-3IA Artificial and Natural Intelligence Toulouse Institute (ANITI) is gratefully acknowledged.
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Liu, X., Lorini, E. (2022). A Logic of “Black Box” Classifier Systems. In: Ciabattoni, A., Pimentel, E., de Queiroz, R.J.G.B. (eds) Logic, Language, Information, and Computation. WoLLIC 2022. Lecture Notes in Computer Science, vol 13468. Springer, Cham. https://doi.org/10.1007/978-3-031-15298-6_10
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