Solving Disjunctive Fuzzy Answer Set Programs

Abstract

Fuzzy Answer Set Programming (FASP) is an extension of the popular Answer Set Programming (ASP) paradigm which is tailored for continuous domains. Despite the existence of several prototype implementations, none of the existing solvers can handle disjunctive rules in a sound and efficient manner. We first show that a large class of disjunctive FASP programs called the self-reinforcing cycle-free (SRCF) programs can be polynomially reduced to normal FASP programs. We then introduce a general method for solving disjunctive FASP programs, which combines the proposed reduction with the use of mixed integer programming for minimality checking. We also report the result of the experimental benchmark of this method.

Modeling multi-valued biological interaction networks using fuzzy answer set programming

“…Following [31], we consider the finite-valued answer sets of a FASP program P , by restricting the values of the interpretation function I to the set…”

“…For a non-positive program P , a k-model P is a k-answer set of P iff it is a kanswer set of P I . If we consider only rational-valued answer sets, then every answer set of a FASP program is necessarily a k-answer set of the program for some finite k. However, the converse is generally not true: a k-answer set of a program may not be an answer set of that program [31], [48].…”

Fuzzy answer set computation via satisfiability modulo theories

“…The structure of FASP programs can be simplified through rewritings that leave at most one connective in each rule body (Mushthofa et al 2014). Essentially, a rule of the form α ← β ⊙ γ, with ⊙ ∈ {⊗, ⊕, ⊻, ⊼}, is replaced by the rules α ← p ⊙ q, p ← β, and q ← γ, with p and q fresh atoms.…”

“…Essentially, a rule of the form α ← β ⊙ γ, with ⊙ ∈ {⊗, ⊕, ⊻, ⊼}, is replaced by the rules α ← p ⊙ q, p ← β, and q ← γ, with p and q fresh atoms. A further simplification, implicit in the translation into crisp ASP by (Mushthofa et al 2014), eliminates ⊼ in rule heads and ⊻ in rule bodies: a rule of the form p 1 ⊼ · · · ⊼ p n ← β, n ≥ 2, is equivalently replaced by n rules p i ← β, for i ∈ [1..n]; and a rule of the form α ← β ⊻ γ is replaced by α ← β, α ← γ. Moreover, a rule of the form α ← ∼β can be equivalently replaced by the rules α ← ∼p and p ← β, where p is a fresh atom.…”

“…The performance of fasp2smt did not change, while ffasp improves considerably, especially regarding memory consumption. We also tested 180 instances (not reported in Table 1) of two simple problems called Stratified and Odd Cycle (Alviano and Peñaloza 2013;Mushthofa et al 2014), which both fasp2smt and ffasp solve in less than 1 second. The main picture resulting from the experimental analysis is that fasp2smt is slower than ffasp in Graph Coloring, but it is faster in Hamiltonian Path.…”