Logic 2 : Logic [ LFILO1250 ]

The final mark is awarded on the basis of the results from volume 1 (course) and volume 2 (exercises) in the following way :
Where one or both parts have been failed, the global mark is the weaker of the two.
Where both parts have been passed, the global mark is calculated according to an 80 (vol.1) / 20 (vol.2) weighting.

Logic is the part of  philosophy which studies the notions of concept, judgement and reasoning, as well as the properties   associated with them, such as   truth and  necessity.

 The course starts by trying to elucidate the concepts of truth of a judgement and of validity of a  reasoning  in a semantic way, by reducing them  to those of model, sentence  and  truth. 

An examination of the Liar's paradox, to which one adopts the so called "orthodox'' solution, will compel to distinguish language and metalanguage. With  this proviso, the definitions of the basic concepts will be explicitly given within the framework of  propositional and predicative languages. 

It also develops a proof-theoretic approach  of the reasoning by studying firstly Gentzen's sequent calculus, again for propositional and predicative languages and, secondly, the concept of axiomatic system. Some of the fundamental results belonging to the folklore of 20th century logic    will be stated and explained;  e.g. completeness,   compactness and    Löwenheim-Skolem  theorem.