Foreign students graduate courses

Logical form.

Propositional and predicate logic: basics.

Classical connectives and truth-tables; tautologies and correct inferences. Informal semantics of quantification.

Propositional and predicate logic: refutation trees.

Labelled trees; refutation trees; counterexample extraction. Elementarily valid formulas and inferences.

Classes, relations, functions, cardinality.

Classes, membership, inclusion; comprehension (abstraction); boolean operations; relations and functions; equinumerosity and cardinality; finite sets, denumerable sets; non-denumerable sets: Cantor’s theorems; set-theoretic paradoxes.

Traditional logic.

Categorical propositions; traditional square of oppositions; syllogisms.

Computability: basics.

Informal notions of algorithm, decidability, effective enumerability, computability; Post’s theorem; Turing machines; universal machines; Turing-Church thesis; undecidability of the halting problem and applications to logic. Generative grammars: Chomsky’s hierarchy.

Part B – 30 hrs (detail)

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.

Syntax of elementary logic.

Informal notions of deduction; “Frege-Russell-Hilbert” vs “Gentzen” paradigms; the axiomatic calculus CQ; the calculus NK of natural deduction; equivalence between CQ and NK; structural properties of elementary deducibility.

Gödel’s completeness theorem for elementary logic.

Soundness, completeness, adequacy, compactness. Proof of the soundness theorem for NK. Proof of the completeness theorem for NK (saturated sets, Lindenbaum-Henkin lemma, canonical model) and corollaries: compactness, Löwenheim-Skolem. Limits to the expressiveness of elementary logic.

Incompleteness, undefinability, undecidability.

Elementary theories; first order Peano arithmetic; Gödel’s, Rosser’s, Tarski’s and Church’s theorems (hypothetic form); second-order logic.

Propositional modal logics and Kripke’s semantics.

Modal and multimodal propositional languages; possibile-worlds semantics; main normal modal systems (K, D, T, S4, S5); their semantic and syntactic characterization; modal tableaux. Hints to: epistemic logic (distributed knowledge and common knowledge); dynamic logics.

Non classical logics (hints).

Intuitionistic logic: the “BHK” explanation of the meaning of intuitionistic logical constants; natural deduction and axiomatic calculi for intuitionistic logic; relations between classical and intuitionistic logic (Glivenko’s and Gödel-Gentzen’s theorems). Substructural logics (linear logic, Grišin’s logic, infinite valued Łukasiewicz’ logic).

Reading list:

Further information about the reading list will be given by the lecturer.

LINGUA FRANCESE PERFEZIONAMENTO

FRENCH (ADVANCE COURSE)
3 ECTS

LEVEL Graduate

YEAR

Second

SEMESTER FIRST

LECTURER Gabriela Cultrera

ASSISTANT

Annapaola Pioggiosi

E-MAIL

gabriela.cultrera@unipv.it

COURSE PROGRAM Management of enterprises Entrepreneurial logic Managerial logic Aims of enterprises Strategic management and operational management Grammar: Structure of the sentence Gallicisms
The indefinite Expressions of time and space Adverbs Passive form Subjunctive Subordinates (time- space- cause- consequence – aim – concession- condition – hypothesis)
EDUCATIONAL AIM
The purpose of the advanced course is to acquire a profound knowledge of spoken and written language in order to possess the grammatical and linguistic tools which makes possible the understanding and analysing of socio-economic topics in French.

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