Abstract. For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomatic-deductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimental, psychological and social aspects, yesterday only marginal, but now changing radically the very essence of proof. In this paper, we try to organize this evolution, to distinguish its different steps and aspects, and to evaluate its advantages and shortcomings. Axiomatic-deductive proofs are not a posteriori work, a luxury we can marginalize nor are computer-assisted proofs bad mathematics. There is hope for integration! 1

Abstract: In a standard (rhetoric) perspective ironic communication is considered a semantic inversion between the literal (primary) meaning and the nonliteral (implicated) one. Nevertheless, in common use irony is not necessarily bound to the rhetoric concept of semantic inversion. Rather, it can be defined as an alteration of a reference aiming at stressing the reality of a fact by means of the apparent dissimulation of its true nature. In a communicative perspective, irony aims to get an effective protection of interpersonal relationships, so as to leave wide ranges of freedom for managing both meanings and interaction. The point of view herein followed concerns irony as a paradigmatic expression of miscommunication, since it is a chance in widening the psychological space available to the communicators. Irony as miscommunication fits rather well the MaCHT framework proposed by Anolli. In fact, by means of an ironic remark, the speaker can lay the responsibility of the ironic value of the utterance on the intention ascription of the interlocutor.

polyphonique

We propose in this paper DIAL, a framework for inter-agents dialogue, which formalize a deliberative process. This framework bounds a dialectics system in which argumentative agents arbitrate and play to reach an agreement. For this purpose, we propose an argumentation-based reasoning to manage the conflicts between arguments having different strengths for different agents. Moreover, we propose a model of argumentative agents which justify the hypothesis to which they commit and take into account the commitments of their interlocutors. In the scope of our dialectics system, a third agent is responsible of the final decision outcome which is taken by resolving the conflict between two players according to their competence and the advanced arguments. 1

History in fast-forward Logic and argumentation are a natural combination. Though the precise origins of logic are hidden in the mists of antiquity, reflection on patterns in legal or philosophical debate may have been one of the driving forces in the genesis of the discipline. But afterwards, the main emphasis over time shifted to consequence relations in an abstract universe of propositions, and the formal systems to which these give rise. Though contacts were never lost entirely between logic and the realities of discussion and debate, the 20 th century saw a deep split. Perelman & Olbrechts-Tyteca 1958 pointed out how actual reasoning may be more like weaving a piece of cloth from many threads than forging a chain with links in linear mathematical proof style, and rhetoric and informal logic then took their own course. Likewise, Toulmin 1958 made a powerful case how legal procedure and functional schemas – ‘formalities’ rather than logical form – may be the best paradigm for understanding argumentation. Both critics have inspired follow-up frameworks that continue to flourish today (cf. Walton & Krabbe 1995, van Eemeren & Grootendorst 2004). But this split was not inevitable, and it was not forever. Already Lorenzen 1955 used innovative gametheoretical