Argumentation is a form of reasoning consisting of the three following steps:
- The first goal is to construct an argumentation structure, i.e., a structure containing arguments, attack relations between them, and possibly several other elements: support relations, basic argument weights, redundancies or synergies between arguments, etc.
- The second step consists in evaluating the arguments. An argument evaluation is a function transforming any argument into a value that can take the form of a number, a position in a ranking, a compound object, or anything that can represent the overall strengh (or acceptability) of an argument. An acceptability semantics is a function transforming any argumentation structure (of a given type) into an argument evaluation (of a given type as well).
- Finally, the last task is to take advantage of an argument evaluation to draw conclusions, make decisions, participate in a discussion, etc.
The goal of the PhD consists of the four following steps:
- Type of semantics. First of all, the goal is to fix a certain type of input for acceptability semantics. The simplest form of argumentation structure is a graph whose nodes and arrows represent arguments and attacks, respectively. Concerning the output, a ranking of the arguments is a very a natural form of argument evaluation. Of course, as the work progresses richer inputs and outputs will be considered.
- Axioms. Next, the goal is to establish axioms for acceptability semantics (of a given type). By axiom, we mean any external property, i.e., any interesting property based only on the input and the output of a semantics, not the internal objects used in the definition of the latter. As a consequence, an axiom is an excellent criterion for judging and comparing semantics. Indeed, such a criterion can be applied to any of them and is based only on well-understood concepts, namely argumentation structures and argument evaluations.
- Construction and analysis of semantics. The main objective of the PhD is
to analyse existing acceptability semantics on the basis of a list of axioms and, if some crucial ones are falsified, construct new semantics satisfying them.
- Applications. Finally, the last task is to use semantics (validated by solid axioms) to construct important theoretical objects like paraconsistent logics, decision procedures, or dialogue strategies. In addition, acceptability semantics have direct practical outlets, for example, debate wikis.