Both undergraduate and graduate students.
Prerequisites: An introductory logic course.
Through the course, the student will get an introduction to philosophical logic, its motivations, inferential systems, and main directions of development. The final project option will give the possibility to develop presentation skills.
The course will present the motivations of modal and other philosophical logics, review their semantics and present inferential systems. Whereas the former has been developed systematically since late fifties/early sixties, after the introduction of possible worlds semantics by Kripke, Hintikka, and others, the latter has not had such a strong development, and many fundamental questions have remained unresolved for decades.
The course will proceed to review the basics of proof theory, discuss the limitations of traditional proof systems for philosophical logic and present methods for building inferential systems for a wide variety of modal and non-classical logics, starting from basic systems of normal modal logics and gradually enriching them to include multi-modal and collective modalities.
The proof systems obtained will also be applied for the study of the meta-theory of such logics, covering completeness, decidability, definability, and embedding results.
The course provides background knowledge for possible postgraduate work on the topic.
Planned course coverage:
Review of Hilbert systems, sequent calculus, Kripke semantics.
The deduction theorem in modal logic.
Normal modal logics.
First-order modal logic.
Relevant and other substructural logics.
Intuitionistic modal logic; Knowability logic; Analysis of epistemic paradoxes.
Systems with collective modalities: distributed and common knowledge.
Based on three elements:
Homework assignments (25 %);
Project paper or written exam (65 %);
Participation in class and feedback to presentations (10 %).
(A minimum of 80% attendance is required, together with written justification to absences.)
Lectures (Sara Negri) Thursday 10-12: 10.9, 17.9, 1.10, 8.10, 29.10, 5.11, 12.11, 19.11, 26.11, 3.12
Exercises (Lassi Saario) Tuesday 10-12: 15.9, 22.9, 6.10, 27.10, 10.11, 24.11, 1.12
Written exam: 17.12
|Studiematerial och litteratur
Handouts and selected readings from research articles and textbooks, including the following:
-Fagin, R., Halpern, J.Y., Moses Y. and Vardi, M. Y. (1995) Reasoning about Knowledge. Cambridge: MIT Press;
-Jaquette, D. (2002) A Companion to Philosophical Logic, Blackwell.
-Meyer, J.-J.Ch and van der Hoek, W. (1995) Epistemic Logic for AI and Computer Science. Cambridge University Press.
-Negri, S. and J. von Plato (2011) Proof Analysis. Cambridge University Press.
-Priest, G. (2008) An Introduction to Non-Classical Logic, Cambridge University Press.