- Thomas Piecha, Three Lectures on Dialogues. Institut d'Histoire et de Philosophie des Sciences et des Techniques, CNRS / Université Paris 1 Panthéon-Sorbonne / École normale supérieure, Paris 2013.
Slides from talks:
- Slides from the Proof and Dialogues (ProDi) Workshop, 25–27 February 2011 in Tübingen, can be found here.
Blog post about the workshop by Catarina Dutilh Novaes.
- Thomas Piecha and Peter Schroeder-Heister, Implications as rules. Cross-CRP workshop "Dialogues, Inference, and Proof – Logical and Empirical Perspectives (DIPLEAP)" at the Vienna University of Technology on 26–28 November, 2010.
- Sara L. Uckelman, A curious dialogical logic and its composition problem. Cross-CRP workshop "Dialogues, Inference, and Proof – Logical and Empirical Perspectives (DIPLEAP)" at the Vienna University of Technology on 26–28 November, 2010.
- Jesse Alama, Some further properties of the dialogical logic N. Cross-CRP workshop "Dialogues, Inference, and Proof – Logical and Empirical Perspectives (DIPLEAP)" at the Vienna University of Technology on 26–28 November, 2010.
- Thomas Piecha, Dialogues, End-Rules and Definitional Reasoning. Cross-CRP workshop "Modelling Interaction, Dialog, Social Choice, and Vagueness (MIDiSoVa)" at the Institute for Logic, Language and Computation of the University of Amsterdam on 26-28 March 2010.
Abstract: We present a dialogue calculus with an end-rule for complex formulas. In sequent calculi this end-rule corresponds to initial sequents with complex formulas. Equivalence can be proved for this dialogue calculus and the corresponding sequent calculus for propositional intuitionistic logic. This is of importance for reasoning about definitions of atomic formulas whose defining conditions are complex. In order to reason about such definitions we introduce definitional dialogues with an additional argumentation form. This approach also suggests an analysis of paradoxes.
- Sara L. Uckelman, Dialogical Properties of Obligationes. Cross-CRP workshop "Modelling Interaction, Dialog, Social Choice, and Vagueness (MIDiSoVa)" at the Institute for Logic, Language and Computation of the University of Amsterdam on 26-28 March 2010.
Abstract: The recent trend in logic has been to shift emphasis from static systems developed for purely theoretical reasons to dynamic systems designed for application to real world situations, such as modeling knowledge and belief, interaction, and reasoning in multi-agent systems. This emphasis on the situational and applied aspects of logic and reasoning is relatively new in contemporary logic, but it was the dominant approach to logic by logicians in the high Middle Ages, especially in mid-13th to mid-14th C. Medieval logic was not concerned so much with abstract logical systems valid for all subject matters and suited for dealing with, e.g., mathematical reasoning, but more so in techniques of reasoning that could be applied in real reasoning contexts, and thus which could vary from context to context. This pragmatic approach to logic was complimented with a strong interest in modeling dynamic, interactive systems, where reasoning is not an armchair process of a single agent but is instead a dispute or debate between two or more agents, each of which have different knowledge and different roles in the disputation.In this talk we will:
The clearest example of the interactive nature of logic in the Middle Ages is the development of disputations de obligationibus. In an obligatio, two agents, the Opponent and the Respondent, engage in a turn based dialogue where the Opponent puts forward a proposition (or set of propositions) at each round, and the Respondent can either accept, deny, or doubt the proposition(s), in accord with certain rules that are fixed in advance. Many different variants of obligationes exist. These dialogues/disputations differ from modern dialogical approaches to logic (à la Lorenzen) in that they are not intended to give semantic meaning to the logical connectives, or to demonstrate the validity of a proposition. Instead, the rules of inference for reasoning must be known in advance by both the Opponent and the Respondent, and an obligational disputation about a sentence φ can be understood as testing the Respondent's ability to reason about φ, either propositionally (i.e., about the truth or falsity of φ) or at the meta-level (e.g., about whether φ is known or in doubt to him). As a result, when looking to model different types of obligationes with modern formal tools, ordinary game-based logics such as dialogical logic or game-theoretic semantics are going to be less appropriate than one might suspect given the superficial similarity between the three. Instead, we argue that, at the meta-level, obligationes are best understood as Abstract Dialogue Systems (such as those introduced by Prakken), and, at the object-level, the reasoning involved is a type of multi-agent Dynamic Epistemic Logic.
- Introduce the medieval theory of obligationes, providing examples of different rules for variants, and giving some applications of these rules to the solving of sophismata.
- Introduce the framework of Abstract Dialogue Systems and show how the rules for an obligatio can be seen as specifying a protocol for an ADS, thus giving a clear foundation for a meta-level view of obligationes, that is, from outside the disputation.
- Provide a multi-agent Dynamic Epistemic Logic framework to explicate the reasoning that takes place at the object-level, that is, within the disputation, and show how ordinary fragments of DEL can be extended to non-standard applications required to model reasoning within obligationes.
- Sara L. Uckelman, Dialogue games before Lorenzen: A brief introduction to obligationes. LogICCC Launch Conference, Prague 5–7 October, 2008.