Medieval Disputationes de obligationibus as Formal Dialogue Systems

Abstract

Formal dialogue systems model rule-based interaction between agents and as such have multiple applications in multi-agent systems and AI more generally. Their conceptual roots are in formal theories of natural argumentation, of which Hamblin's formal systems of argumentation in Hamblin (Fallacies. Methuen, London, 1970, Theoria 37:130-135, 1971) are some of the earliest examples. Hamblin cites the medieval theory of obligationes as inspiration for his development of formal argumentation. In an obligatio, two agents, the Opponent and the Respondent, engage in an alternating-move dialogue, where the Respondent's actions are governed by certain rules, and the goal of the dialogue is establishing the consistency of a proposition. We implement obligationes in the formal dialogue system framework of Prakken (Knowl Eng Rev 21(2):163-188, 2006) using Dynamic Epistemic Logic (van Ditmarsch et al. in Dynamic epistemic logic, Synthese Library Series. Springer, Berlin, 2007). The result is a new type of inter-agent dialogue, for consistency-checking, and analyzing obligationes in this way also sheds light on interpretational and historical questions concerning their use and purpose in medieval academia.

A dialectical approach to presupposition

“…A proposition was verified either absolutely, at a "metaphysical" level (through a comparison with an objective state of affairs), or dialectically, by assessing the consistency of a sentence with the set of sentences previously agreed upon by the participants to a dialogue, nowadays called "commitments." Such agreed upon sentences constitute the interlocutors' "obligations" (Martin 2001;Uckelman 2013;Novaes Dutilh 2007: chap. 3), limiting the interlocutors' freedom to contradict or deny them. On the dialectical (commitment-based) account of verification, a sentence needs to be assessed considering the commitment set of the participant that is evaluating it.…”

What Hamblin’s Formal Dialectic Tells About the Medieval Logical Disputation

“…It can be explained by the supposition that he assumes employing some basic formal system on the lower level of the game, and that the evaluation should proceed with the help of it. However, the same question arises with respect to the formalisation of C. Dutilh-Novaes, as S.Uckelman notices in [23]. In order to keep track of the propositions accepted by the respondent Ch.…”

Interactive logic in the middle ages

“…If this is correct, then actual obligational moves  perhaps even recognized as such  are the vehicle whereby real argument takes place" [20, p. 6], and thus obligationes provide a "meta-methodology" for reasoning [20, p. 7]. In recent work we have shown how this idea of a meta-methodology can be made formal and precise, by explaining how rules for different types of obligationes can be viewed as giving rise to protocols governing systems of formal dialogues [36].…”

“…The questioning exercise cannot be bounded/terminated (terminari). 36 However, he gives no explanation of this rule, or why it is introduced, and while he says that this rule is "just as in the preceding [types of] obligationes" 37 , no similar rule is mentioned in his discussions of other types of obligatio.…”