Logic

Aims

The characterization of the modal structure of the world is one of the main issue in contemporary metaphysics. The present course aims at introducing the basic systems of modal and temporal logic and at discussing the crucial connections between ontic modalities, modal semantics and metaphysics of necessity, on the one hand, and temporal modalities, temporal semantics and metaphysics of time, on the other.

Contents

The course is divided into two parts. The first one is dedicated to a general presentation of normal systems of modal logic, both from an axiomatic and a semantic point of view. In the second part, we will focus on temporal logic and consider the main metaphysical models of the structure of time and the way in which they are connected to our intuitions about the truth conditions of tensed proposition. In particular, we will study the basic Priorean systems, their possible extensions including Kamp’s operators, the Peircean and Ockhamist interpretations of branching time logic.

Coursework

The course consists of a series of lectures. The students will be required to do exercises.

References

Blackburn, P., de Rijke, M., and Venema, Y. (2001). Modal logic. Cambridge: CUP.

Hodkinson, I. and Reynolds, M. (2006). Temporal Logic, in Blackburn et al., pp. 655--720.

Hughes G.E. & Cresswell M.J. (1996) A New Introduction to Modal Logic: London: Routledge.

Øhrstrøm, P. and Hasle, P. (1995). Temporal Logic: From Ancient Ideas to Artificial Intelligence. Dordrecht: Kluwer Academic Publishers.

Venema, Y. Temporal Logic (2001). In Lou Goble, ed., Blackwell Guide to Philosophical Logic, Oxford: Blackwell Publishers.