Abstract:
Introduction and elimination (briefly intelim) rules are in a natural sense the simplest of all Horn rules for propositional connectives. They have also played a prominent role in some philosophical discussions of the meaning of the connectives. For this reason, their behaviour has more than a purely formal interest.
We consider two questions about such rules for classical connectives: the existence, for a given truth-functional connective, of at least one such rule that it satisfies, and the uniqueness of a connective with respect to the set of all of them. The answers are easy and well known in the context of rules using set/set sequents of formulae, but more complex and interesting for the restricted (and more often used) context of set/formula sequents on which we focus, as well as for the set/formula-or-empty context, which we also describe briefly if time available.
Bio:
Professor David Clement Makinson is currently Visiting Professor in the Department of Philosophy, Logic and Scientific Method, London School of Economics (LSE). He has been a Senior Research Fellow in the Department of Computer Science, King’s College London,Chairman of the Department in the American University of Beirut, Lebanon, and Programme Specialist with Unesco.
His field of research is Logic and its relations with other disciplines, particularly philosophy and computer science. His most recent research has been on:
- Uncertain reasoning: qualitative and quantitative and their interconnections
- Parallel interpolation and its application
- Relevance criteria for belief change operations
- Input/output logics, logics of directives and norms
- The concept of logical friendliness