Research

Academic Background

I am generally interested in different aspects of logical reasoning, from mathematical modeling and abstraction to the mining of logical reasoning and the application of logic in computer science and AI.

• Normative Systems:

  As a mathematician, I am interested in modeling both natural and social phenomena. While mathematics typically focuses on modeling natural and descriptive systems, I am primarily interested in modeling normative systems and reasoning.

  A key feature of normative reasoning is non-reflexivity. For instance, just because a statement is true does not necessarily mean it imposes an obligation. Nelson Goodman illustrates this concept through his analysis of perspective in art as a symbolic system, which does not inherently possess reflexivity but instead interprets reality through cultural and conventional rules (Goodman, 1976). In my Bachelor's thesis, I used Goodman’s arguments and psychological experiments to support anti-Platonism in relation to mathematical objects.

  This concept of non-reflexivity extends beyond perception into cognition, as evidenced by phenomena such as Moore’s Paradox, where individuals hold contradictory beliefs, and belief update mechanisms, which illustrate how new information is integrated into existing knowledge without necessarily maintaining consistency. My Master's thesis explored dynamic epistemic logic to model Moore’s Paradox, aiming to abstract this phenomenon through category theory.

  During my Ph.D., I focused on input/output logic, introduced by David Makinson and Leon van der Torre, as a framework for modeling normative conditionals. This logic is characterized by a non-reflexive consequence relation, distinct from Tarskian consequence relations. I developed a discursive version of input/output logic that can manage multiple perspectives simultaneously.

  Currently, I am working on algebraic and topological models of input/output logic. In collaboration with Alessandra Palmigiano and her Ph.D. students, we have connected input/output logic with subordination algebras—two areas previously pursued independently. These structures unify constructive and point-free mathematics, non-classical logics, and their applications to the semantics of programming languages.

  I am interested in exploring questions that span from the mathematical foundations to the modeling of more complex normative systems, such as multi-agent systems, game-theoretic models, and AI.

• Neuro-Symbolic System:

  I am also interested in finding logical arguments in daily use, such as Walton’s argument schemes. After completing my PhD, I undertook a postdoctoral position at the Computer Engineering Department of the Iran University of Science and Technology. Our core aim was to engineer scalable, explainable AI tools geared towards reasoning with legal knowledge graphs. Specifically, we worked on a hybrid reasoning module that amalgamated a neural model with a logical forward-chaining mechanism.

  With the rapid growth and evolution of Machine Learning (ML) models and their subsequent AI applications, it is evident that hybrid models can enhance both the scalability of logical reasoning tools and the explainability of neural network outputs. I am particularly interested in mining arguments with neural networks and combining them with abstract rule-based logical systems.

• Computational Logics:

  One of my broad interests is "How to compute logics?" focusing primarily on rule-based logics abstractly represented as input/output logics. To address this question, I have explored both theoretical computer science and automated reasoning, as well as mathematical representational theories like Stone dualities.

  From (Set-theoretic) Models to Computing: I studied the shallow semantical embedding shallow semantical embedding of deontic logics in HOL in collaboration with Christoph Benzmüller and Xavier Parent. This work developed into LogiKEy, a methodology designed to support the development and experimentation with ethical reasoners, normative theories, and deontic logics.

  From Logic to (Set-theoretic) Models: The LogiKEy methodology is based on aligning models of the target logic with Henkin models. This is challenging for input/output (I/O) logics, which lack standard models. Thanks to duality techniques and algebraic models for I/O logics (developed together with Alessandra Palmigiano), we could implement I/O logics faithfully in HOL. This research indicates how combining duality techniques with shallow semantical embedding is effective for computing rule-based logical systems.

  We are currently working on the translation of I/O logics into first-order logic, which will be mainly beneficial for the scalable automation of I/O logics.