Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

A unifying theorem for algebraic semantics and dynamic logics

AbstractA unified single proof is given which implies theorems in such diverse fields as continuous algebras of algebraic semantics, dynamic algebras of logics of programs, and program verification methods for total correctness. The proof concerns ultraproducts and diagonalization

Una lógica para programación lógica

"Trabajo presentado por el autor en la Facultad de Ciencias Matemáticas de la Universidad Complutense de Madrid para acceder al grado de Licenciado" Universidad Complutense de Madrid. Facultad de Ciencias Matemáticas..Fac. de Ciencias MatemáticasTRUEProQuestpu

Una lógica no estandar admisible para programas funcionales

Tesis de la Universidad Complutense de Madrid,Facultad de Ciencias Matemáticas, Departamento de Informática y Automática, leída en Madrid el 3 de febrero de 1990; Dirigida por Teresa Hortalá González.Sección Deptal. de Sistemas Informáticos y ComputaciónFac. de Ciencias MatemáticasTRUEProQuestpu