Rules and derivations in an elementary logic course

When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them, and are related to nothing they already know, unlike, for instance, the notion of model, that can be seen as a generalization of the notion of algebraic structure. In this note, we defend the idea that one strategy to introduce these notions is to start with the notion of inductive definition [1]. Then, the notion of derivation comes naturally. We also defend the idea that derivations are pervasive in logic and that defining precisely this notion at an early stage is a good investment to later define other notions in proof theory, computability theory, automata theory, ... Finally, we defend the idea that to define the notion of derivation precisely, we need to distinguish two notions of derivation: labeled with elements and labeled with rule names. This approach has been taken in [2]

Clausal Presentation of Theories in Deduction Modulo

International audienceResolution modulo is an extension of first-order resolution where axioms are replaced by rewrite rules, used to rewrite, or more generally narrow, clauses during the search. In the first version of this method, clauses were rewritten to arbitrary propositions, that needed to be dynamically transformed into clauses. This unpleasant feature can be eliminated when the rewrite system is clausal, i.e. when it transforms clauses to clauses. We show in this paper that how to transform any rewrite system into a clausal one, preserving the existence of cut free proof of any sequent

Proofs as Cryptography: a new interpretation of the Curry-Howard isomorphism for software certificates

19 pagesThe objective of the study is to provide a way to delegate a proof of a property to a possibly untrusted agent and have a small certificate guaranteeing that the proof has been done by this (untrusted) agent. The key principle is to see a property as an encryption key and its proof as the related decryption key. The protocol then only consists of sending a nonce ciphered by the property. If the untrusted agent can prove the property then he has the corresponding proof term (λ-term) and is thus able to decrypt the nonce in clear. By sending it back, he proves that the property has been proven without showing the proof. Expected benefits include small certificates to be exchanged and the zero-knowledge proof schema which allows the proof term to remain secret. External agents can only check whether a proof exists without having any information about it. It can be of interest if the proof contains some critical information about the code structure for instance

MOUVEMENTS SOCIAUX ET SENS DE LA VILLE : LA CIRCULATION DU DISCOURS URBAIN PAR LE NUMÉRIQUE

Differently from the conditions of production presented in the early 1980s, the digital space occupies a prominent place for contemporary subjects. It is in this space that social mobilizations, debates, discussions and, especially, circulation take place. When we talk about circulation, we can think of both the discourses and the subjects that circulate through the network. In other words, if in Mitterrand's victory the circulation of discourses took place through television, printed newspapers, radios and soccer stadiums, with the digital, we have a new element to add. And this element, as we will show in our analyses, overdetermines all these other media. In this way, we can put that the big question that moves this work is: how does the digital cross the processes of signification of urban subjects and cities? And, in order to answer this question, we will compose our corpus of analysis with the publications of four social movements, two French and two Brazilian, and the images of their demonstrations that circulated on the Internet. The two French movements are the Gilets jaunes and the Collectif Lyonnais pour la gratuité des transports en commun, and the Brazilian ones are the Movimento Passe Livre and the Movimento Brasil Livre.Contrairement aux conditions de production présentées au début des années 1980, l'espace numérique occupe une place de choix pour les sujets contemporains. C'est dans cet espace que se déroulent les mobilisations sociales, les débats, les discussions et, surtout, la circulation. Lorsque nous parlons de circulation, nous pouvons penser à la fois aux discours et aux sujets qui circulent dans le réseau. C'est-à-dire, si dans la victoire de Miterrand la circulation des discours était donnée par la télévision, les journaux imprimés, les radios et les stades de football, avec le numérique, nous avons un nouvel élément à ajouter. Et cet élément, comme nous le montrerons dans nos analyses, surdétermine tous ces autres médias. De cette façon, nous pouvons dire que la grande question qui anime ce travail est : comment le numérique traverse-t-il les processus de signification des sujets urbains et des villes ? Et, afin de répondre à cette question, nous composerons notre corpus d'analyse avec les publications de quatre mouvements sociaux, deux français et deux brésiliens, et les images de leurs manifestations circulant sur internet. Les deux mouvements français sont les Gilets jaunes et le Collectif Lyonnais pour la gratuité des transports en commun, et les mouvements brésiliens sont le Movimento Passe Livre et le Movimento Brasil Livre