Computational Argumentation Framework
In artificial intelligence, traditionaly, a knowledge base is a set of
rules representing the knowledge of an expert in a specific domain. In
this context, there are no contradictions in the knowledge base and
undefeasible conclusions can be derived from it by the modus ponens
inference rule. In the context of argumentation, however, a knowledge
base combines the knowledge of multiple experts, who can have
divergent opinions about a same topic (i.e., the knowledge base can
have imperfect informations). In this case, another reasoning schema,
called modus non excipiens, must be used to derive defeasible
conclusions.
Argumentation is a general technique to reason in the presence of
imperfect information, which involves the formulation of arguments
concerning a specific claim. Because arguments are normally
constructed from imperfect information, there are often
counterarguments for them. Arguments and counterarguments are usually
formulated from information, taken from a conflicting knowledge base,
which can be incomplete, inconsistent, uncertain or subjective.
A conflicting knowledge base is composed of strict rules (i.e., rules
which have no exceptions) and defeasible rules (i.e., rules which have
exceptions). A strict rule has the form conditions -> conclusion (if
the conditions hold, then we necessarily have the conclusion),
whereas a defeasible rule has the form conditions >- conclusion (if
the conditions hold, then we possibly have the conclusion). In this
rules, 'conditions' is a conjuntion of literals (or a single literal)
and 'conclusion' is a single literal. A literal is an atom (e.g., p)
or the strong negation of an atom (i.e., ~p). Unlike negation as
failure (or weak negation), strong negation is not based on the Closed
World Assumption (CWA). It worth noticing that (i) a strict rule with
condition 'true' is a 'fact', whereas a defeasible rule with condition
'true' is a 'presumption'; (ii) rules with variables are, in fact,
schemas for propositional rules). Rules are univocally numbered and,
if a defeasible rule i is an exception to another defeasible rule j,
then the declaration i>j must be included in the conflicting knowledge
base. For example, consider the following rules: