Solver for ADFs grounded semantics by utilising OBDDs - ordered binary decision diagrams

Abstract Dialectical Frameworks

An abstract dialectical framework (ADF) consists of abstract statements. Each statement has an unique label and might be related to other statements (s) in the ADF. This relation is defined by a so-called acceptance condition (ac), which intuitively is a propositional formula, where the variable symbols are the labels of the statements. An interpretation is a three valued function which maps to each statement a truth value (true, false, undecided). We call such an interpretation a model, if each acceptance condition agrees to the interpration.

Ordered Binary Decision Diagram

An ordered binary decision diagram is a normalised representation of binary functions, where satisfiability- and validity checks can be done relatively cheap.

Input-file format:

Each statement is defined by an ASP-style unary predicate s, where the enclosed term represents the label of the statement. The binary predicate ac relates each statement to one propositional formula in prefix notation, with the logical operations and constants as follows:

• and(x,y): conjunction
• or(x,y): disjunctin
• iff(x,Y): if and only if
• xor(x,y): exclusive or
• neg(x): classical negation
• c(v): constant symbol "verum" - tautology/top
• c(f): constant symbol "falsum" - inconsistency/bot