The Colloquium of Logic is organized by the Portuguese Logic Society and aims to promote the research and knowledge in this field, from mathematical logic to philosophical logic as well as logic for artificial intelligence and theoretical computer science. The talks of the Colloquium of Logic will be held in a hybrid way. The talks will take place at the Mathematics Department of Técnico ULisboa, room 3.10, and virtually on Zoom. The next speaker is:
- Manuel Martins (Department of Mathematics and Center for Research and Development in Mathematics and Applications, UAveiro), “Partiality in First-Order Hybrid Logic”, 29th May 2025, 16:30.
Abstract: In this talk, I will introduce a language of first-order hybrid logic in which function symbols are interpreted as partial functions. The language builds on the basic propositional hybrid framework, includes a primitive unary predicate symbol for testing whether a term denotes, and employs satisfaction operators to rigidify both predicate and function symbols. Semantically, the system is actualist and allows terms to be undefined. Furthermore, contrary to what is generally assumed, it admits a region inhabited by entities beyond the scope of any actualist quantifier. I will present a sound and complete axiomatization of the system. In addition, I will provide a brief overview of a hybrid partial type theory that combines William Farmer’s partial type theory with a strong form of hybrid logic, focusing on its main features.