Handbook of Automated Reasoning

4.5 D-WFS and D-STABLE

Before we can state the definition of D-WFS we have to extend our principles to disjunctive programs with default-negation.

4.21. Definition

Disjunctive Logic Program

A disjunctive logic program consists of a finite number of rules of the form

$A_1\vee \dots \vee A_k\leftarrow B_1,\dots ,B_m,not{C}_1,\dots ,not{C}_n$

where A ₁ ,…,A_k, B ₁ ,…,B_m,C ₁ ,…,C_n are positive atoms (containing possibly free variables). We call A ₁∨…A_k the head of the rule, B ₁,…,B_m its positive body and C1,…,C_n its negative body. The comma represents conjunction ∧.

We abbreviate these rules by

$\mathcal{A}\leftarrow {ℬ}^{+},not{ℬ}^{}$