Adaptive Logic

In this paper we provide a proof theoretical investigation of logical argumentation, where arguments are represented by sequents, conflicts between arguments are represented by sequent elimination rules, and deductions are made by dynamic proof systems extending standard sequent calculi. The idea is to imitate argumentative movements in which certain claims are introduced or withdrawn in the presence of counter-claims. This is done by a dynamic evaluation of sequences of sequents, in which the latter are considered ‘derived’ or ‘not derived’ according (...) to the content of the sequence. We show that decisive conclusions of such a process correspond to well-accepted consequences of the underlying argumentation framework. The outcome is therefore a general and modular proof-theoretical approach for paraconsistent and non-monotonic reasoning with argumentation systems. (shrink)

The aim of the paper is to introduce the concept of adaptive logics (AL) or rather adaptive logical approach. In the introduction, a motivation and an emergence of AL are briefly discussed. In the second part of the paper, specifics of AL are analysed – especially nonmonotonic character, internal and external dynamics, as well as the structure of AL, namely the distinction between upper limit logic and lower limit logic. In this part, the dynamic proof is also described. Applications of (...) AL are presented in the third part. Three illustrations from three different branches of philosophy are presented. First one is an illustration of description of science – a traditional application of AL. Second one is an illustration of solving a deontic conflict – this is a new direction within in AL which has recently been researched. Third one is an illustration of analyses of metaphors – an example of an unusual application of AL. In the conclusion of the paper, contemporary results of AL are critically evaluated with respect to some problems of the project of AL. (shrink)

Následující text si klade za cíl představit koncepci adaptivních logik (dále AL), či lépe adaptivně logický přístup. Úvodní oddíl textu stručně pojednává o vzniku AL a o motivacích pro tento přístup. Druhý oddíl následně rozebírá specifika AL, především jejich nemonotónní charakter, interní a externí dynamiku, dále pak jejich strukturu, tedy rozlišení mezi upper limit logic a lower limit logic, a představuje pojetí dynamického důkazu. Třetí oddíl ilustruje vybrané aplikace AL ve třech oblastech – v tradiční, totiž při popisu vědy, v (...) moderní, při řešení deontických konfliktů, a v nezvyklé, při analýze metafor. V závěru práce jsou zhodnoceny dosavadní výsledky v rámci celého projektu AL a je poukázáno na některé problémy, které jsou s tímto projektem spjaty. (shrink)