The logic of hypothetical thinking
The preliminary title of my doctoral dissertation is Hypothetical Reasoning. From Formal Learning Theory to Machine Learning. My research is embedded in a broader project conducted by Peter Verdée entitled Relevance criteria in entailment, epistemic grounding and counterfactuals: semantic and linguistic aspects. The project is funded by Fonds Spécial de Recherche (FSR) and started on March 1, 2017.
The goal of my doctoral thesis is to obtain an interpretation of certain conditional sentences of the natural language in terms of formal learning theory; and more specifically, conditional sentences which correspond to various forms of hypothetical reasoning. This problem relates to an analogous program of interpreting conditional sentences in machine learning, in particular to the issue of opinion mining and feature- or topic-based sentiment analysis (see Narayanan, Liu and Choudhary (2009) for an example of how to use conditional analysis to assign positive, neutral or negative sentiments to topics or product features). An additional objective of my work is to ensure that the obtained interpretation satisfies certain relevance and explainability criteria, which in machine learning correspond to the problem of black box interpretability.
Algebra and algebraic logic
I am also interested in a variety of topics related to universal algebra and algebraic logic, including:
- the problem of the existence of a finite basis for certain algebraic matrices;
- the relation between the existence of a finite basis to the term-equivalence of matrices;
- relational algebras treated as semantics for relevant logics and the properties of those algebras;
- using relational algebras as semantics for various natural language structures and the application of relational algebraic semantics to databases.
Political and legal theory
Outside my main research area, I am involved in the following topics:
- the right to privacy and its roots in protecting popular sovereignty,
- the civil society and the methodology of evaluating its condition,
- free journalism, free speech and their relation to national security.