
47Formal Ontology and Mathematics. A Case Study on the Identity of ProofsTopoi 42 (1): 307321. 2023.We propose a novel, ontological approach to studying mathematical propositions and proofs. By “ontological approach” we refer to the study of the categories of beings or concepts that, in their practice, mathematicians isolate as fruitful for the advancement of their scientific activity (like discovering and proving theorems, formulating conjectures, and providing explanations). We do so by developing what we call a “formal ontology” of proofs using semantic modeling tools (like RDF and OWL) dev…Read more

76Weaker variants of infinite time Turing machinesArchive for Mathematical Logic 59 (34): 335365. 2020.Infinite time Turing machines represent a model of computability that extends the operations of Turing machines to transfinite ordinal time by defining the content of each cell at limit steps to be the lim sup of the sequences of previous contents of that cell. In this paper, we study a computational model obtained by replacing the lim sup rule with an ‘eventually constant’ rule: at each limit step, the value of each cell is defined if and only if the content of that cell has stabilized before t…Read more
Notre Dame, Indiana, United States of America
Areas of Specialization
Epistemology of Mathematics 
Intuitionism and Constructivism 
Logic and Philosophy of Logic 
Areas of Interest
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