Logic (master)

Pre-requisites: first-year course in Logic and second-year course in Mathematics

Course objectives: Student should learn to prove and falsify formulae in intuitionistic propositional logic and in the modal propositional logics S4 and S5. Natural deduction is favoured for proving, and Kripke's models for falsifying.

Course description: Elements of intuitionistic logic and modal logic and some concepts of relevant logic and other substructural logics.

Learning Outcomes: The study of modal logic should lead via modal translations to an understanding of intuitionistic logic from the point of view of classical logic. The philosophical motivation for the introduction of intuitionistic logic is extensively discussed. Substructural logics are treated in a more summary fashion.

Literature/Reading:

• D. van Dalen, Logic and structure (peto poglavlje, o intuicionističkoj logici)
• M.A.E. Dummett, Elements of Intuitionism
• G.E. Hughes and M.J. Cresswell, A New Introduction to Modal Logic
• A.G. Dragalin, Matematičeskiй intuicionizm
• Ž. Mijajlović i drugi, Hilbertovi problemi i logika (drugo poglavlje)
• Z. Šikić (prir.), Novija filozofija matematike (radovi Hejtinga, Gedela i Pravica)