Propositional Argumentation Systems and Symbolic Evidence Theory

106 7 APPLICATIONS
(-> (xray) (or (and lung-cancer a7)
(and tuberculosis a8) a9))
(-> (tuberculosis a10) dyspnoea)
(-> (lung-cancer a11) dyspnoea)
(-> (bronchitis a12) dyspnoea)
(-> a13 dyspnoea)
(-> (dyspnoea) (or (and tuberculosis a10)
(and lung-cancer a11)
(and bronchitis a12) a13))
(observations (dyspnoea smoker asia))
(assumptions ((a1 0.1) (a2 0.01) (a3 0.2) (a4 0.01) (a5 0.3)
(a6 0.1) (a7 0.9) (a8 0.8) (a9 0.1) (a10 0.9)
(a11 0.8) (a12 0.7) (a13 0.1)))
Generally, ABL commands are defined as prefix expressions. According to Common
Lisp, this requires the use of corresponding parentheses. Implications of the
form p 1 ∧ · · · ∧ p n → q, for example, are written as (-> (p1 ... pn) q). Furthermore,
there are two important special commands: (observations (o1 o2...)) is
used to enter facts or observations; and (assumptions ((a1 pr1) ...) declares
assumptions with corresponding probabilities. For example, a 1 is an assumption
with probability 0.1. Probabilities can also be omitted.
After compiling the above ABL–code, one can use Evidenzia to produce symbolic or
numerical arguments for hypotheses like “Does the patient suffer from tuberculosis?”,
“Does the patient suffer from bronchitis?”, etc. The command (sp h), for
example, returns the (symbolic) support of a hypothesis h. In contrast, (dsp h)
computes the (numerical) degree of support for h. For the hypotheses t (tuberculosis)
and b (bronchitis) the system reports the following results:
? (sp tuberculosis) ? (sp bronchitis)
(a1 and a10) or (a5 and a12) or
(a1 and a13) or (a6 and a12) or
(a2 and a10) or (a5 and a13) or
(a2 and a13) or (a6 and a13) or
(a1 and a3 and a11) or (a1 and a5 and a10) or
(a1 and a4 and a11) or (a1 and a6 and a10) or
(a1 and a5 and a12) or (a2 and a5 and a10) or
(a1 and a6 and a12) or (a2 and a6 and a10) or
(a2 and a3 and a11) or (a3 and a5 and a11) or
(a2 and a4 and a11) or (a3 and a6 and a11) or
(a2 and a5 and a12) or (a4 and a5 and a11) or