**LOGICA (LM)**

The course is entirely based on handouts provided by the lecturers.

**Module 1 (Prof. Hykel Hosni)**:

**From classical to non-monotonic logic **

http://www.filosofia.unimi.it/~hosni/teaching/logica/

**Module 2 (Prof. Marcello D’Agostino):**

**Alternatives to classical logic: intuitionistic logic, relevance logic, linear logic, paraconsistent logics.**

**2.1 Intuitionistic logic**

Handout n. 1 : Natural Deduction Systems

Handout n .2: Gentzen’s original paper where he introduced his natural deduction and sequent calculi.

Handout n. 3: A suggested reading on the intuitionistic explanation of the logical operators.

Handout n. 4: Excerpt from Michael Dummett, *Elements of Intuitionism, *Clarendon Press, Oxford 1977.

Handout n. 5: Excerpt from Michael Dummett, *Elements of Intuitionism, *Clarendon Press, Oxford 1977.

Handout n.6: Excerpt from M. D’Agostino, D.M: Gabbay and S. Modgil: Normality and non-contamination in classical natural deduction.

**2.2 Substructural logics**

Handout n. 5: excerpt from A.A. Anderson and N.D. Belpnap Jr., *Entailment: The Logic of Relevance and Necessity *Vol. I, Princeton University Press, 1975.

Handout n. 6: excerpt from M. Dunn and G. Restall. Relevance Logic, In. *Handbook of Philosophical Logic*, 2nd edition, vol. 6, Springer-Verlag, 2002.

Handout n. 7: excerpt from M. D’Agostino et al. *Tableaux Methods for Substructural Logics*. In: Handbook of Tableaux Methods, Kluwer Academic Publishers, 1999.

Handout n. 8: A. Avron. Semantics and proof theory of Linear Logic, *Theoretical Computer Computer Science*, 57 (1988) (in particular Sections 1 and 2).

**2.3 Relevance and paraconsistency**

Handout n. 10: excerpt from M. D’Agostino, Investigations into the Complexity of Some Propositional Calculi, PhD Thesis, Oxford University, Computing Laboratory 1990.

Handout n. 11: Neil Tennant. Natural deduction and sequent calculus for intuitionistic relevant logic. *Journal of Symbolic Logic*, 52 (1987)

**Module 3 (Prof. Marcello D’Agostino): **

**Logic and Information, Depth-Bounded Logics**

Handout 12: M. D’Agostino. An informational view of Classical Logic. *Theoretical Computer Science* 606 (2015)

Handout 13: M. D’Agostino. Analytic inference and the informational meaning of the logical operators. *Logique et Analyse* 227 (2014).

Handout 14: M. D’Agostino. The philosophy of mathematical information. In: *Routledge Handbook of the Philosophy of Information* (2017).

Handout 15: Excerpt from: M. D’Agostino. Semantic Information and the trivialization of logic. *Information*, 4 (2013) (Sections 1–3).

Handout 16: Presentation on Logic and Information Part I

Handout 17: Presentation on Logic and Information Part II

**The exam will consist in a discussion of an essay of about 3000 words written by the candidates on one of the topics of the course at their choice, followed by some general questions on the other topics.**

**For further references and assistance in writing the essays the candidates are requested to contact by e-mail the lecturer responsible for the relevant module. **