(i) Knowledge and competence. Aim of the course is to introduce students to the main notions of logical semantics, and two fundamental results in metalogic (Goedel’s completeness theorem, Turing’s undecidability of the Halting problem). Competence includes improving learning skills, extending the toolbox of rigorous analysis, and sharpening the communication means of the students. (ii) Applying knowledge. Students will learn (also through the exercises discussed in class) to apply knowledge to the analysis of specific problems in logic and philosophy of logic.
Course Prerequisites
Istituzioni di Logica-A
Teaching Methods
Lecture-based teaching, with the aid of a digital whiteboard.
Assessment Methods
Oral examination
Texts
a) A. Cantini, P. Minari, INTRODUZIONE ALLA LOGICA. Linguaggio, significato, argomentazione. Mondadori Education, Milano 2009. b) Lecture notes.
Contents
This course introduces fundamental concepts, ideas and results of contemporary logic from a metalogical point of view: axiomatic and natural deduction calculi; model-theoretic semantics; computability (Turing machines). PROGRAM (i) Computability: basics (informal notions of algorithm, decidability, effective enumerability, computability; Turing machines; Halting problem). (ii) Elementary languages and model-theoretic semantics (inductive definitions and proofs by induction; elementary languages; correspondence theory of truth; semantic paradoxes. Tarskian semantics: structures and interpretations; satisfiability; logical consequence). (iii) Syntax of elementary logic (informal notion of deduction; “Frege- Russell-Hilbert” vs “Gentzen” paradigms; axiomatic calculi; Gentzen’s natural deduction calculus NK). (iv) The completeness theorem for classical predicate logic (v) Non classical logics (intuitionistic logic; modal logics; many-valued logics): hints.
