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In the past few decades, European and American logicians have attempted to provide mathematical foundations for logic and dialectic by formalising dialectical logic (cf. dialectical logic for the special treatment of dialectic in Hegelian and Marxist thought) or dialectical argument. There had been pre-formal treatises on argument and dialectic, from authors such as Stephen Toulmin (The Uses of Argument), Nicholas Rescher (Dialectics), and van Eemeren and Grootendorst (Pragma-dialectics). One can include the communities of informal logic and paraconsistent logic. However, building on theories of defeasible reasoning (see John L. Pollock), systems have been built that define well-formedness of arguments, rules governing the process of introducing arguments based on fixed assumptions, and rules for shifting burden. Many of these logics appear in the special area of artificial intelligence and law, though the computer scientists' interest in formalizing dialectic originates in a desire to build decision support and computer-supported collaborative work systems.

References

1. Rescher, Nicholas (1978). "Dialectics: A Controversy-Oriented Approach to the Theory of Knowledge". Informal Logic. 1 (#3).
2. Hetherington, Stephen (2006). "Nicholas Rescher: Philosophical Dialectics". Notre Dame Philosophical Reviews (2006.07.16).
3. Rescher, Nicholas (2009). Jacquette,Dale (ed.). Reason, Method, and Value: A Reader on the Philosophy of Nicholas Rescher. Ontos Verlag.
4. See Logical models of argument, CI Chesñevar, AG Maguitman, R Loui - ACM Computing Surveys, 2000 and Logics for defeasible argumentation, H Prakken, Handbook of philosophical logic, 2002 for surveys of work in this area.

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